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The equation of the line passing through (3,4) whose slope is -1 will be y = - x + 7.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is -1. Then the equation is written as,

y = - 1x + c

The equation passes through (3, 4), then we have

4 = - 1(3) + c

4 = - 3 + c

c = 4 + 3

c = 7

The equation of the line passing through (3,4) whose slope is -1 will be y = - x + 7.

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Answer:

See below.

Step-by-step explanation:

For this problem, we are asked for the value of x.

Let's use a Proportion to identify x.

A Proportion is a comparison of two equivalent fractions, or ratios.

An example of a proportion can be; [tex]\frac{x}{16} =\frac{16}{32}[/tex], where the value of x is 8.

For this example, we can find x by dividing the Numerator and Denominator by 2.

Let's use the example as a guide for our problem.

We can set up our problem as a ratio, or a fraction. Both represent the same data.

[tex]\frac{x}{8} = \frac{21}{24}[/tex]

We should know that 24 is 3 times bigger than 8, hence we should divide both the Numerator and Denominator by 8.

[tex]\frac{21 \div 8}{24 \div 8} = \frac{7 \ (x)}{8}[/tex]

The value of x is 7.

Answer: x = 7

Step-by-step explanation:

   Given:

x:8 = 21:24

   Rewrite as fractions:

[tex]\displaystyle \frac{x}{8} =\frac{21}{24}[/tex]

   Cross-multiply:

x * 24 = 8 * 21

24x = 168

   Divide both sides of the equation by 24:

x = 7

The single transformation that maps shape A onto shape C is a translation of 4 units to the right.

A single transformation is a mathematical operation that changes the position, orientation, or size of a geometric figure. It can be a translation, reflection, rotation, or dilation. It is a way to describe how a figure is transformed to obtain a new figure.

To map shape A onto shape C, we need to perform a sequence of transformations.

First, shape A is reflected in the line x = 2 to give shape B. This is a reflection in the vertical line passing through x = 2.

Next, shape B is reflected in the line x = 6 to give shape C. This is a reflection in the vertical line passing through x = 6.

To find the single transformation that maps shape A onto shape C, we can combine these two reflections into a single transformation.

The composition of two reflections in vertical lines is a translation.

In this case, the distance between the vertical lines x = 2 and x = 6 is 4 units. Since shape A is reflected in the first vertical line and shape C is reflected in the second vertical line, the movement is from the first line to the second line, which is to the right.

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Answer:

Terri paid $71.14

Step-by-step explanation:

$34.35+$15.50+$45.00=$94.85

$94.85-25%=$71.14

$94.85 is over $50, so Terri can get a 25% discount. After the 25% discount, Terri paid $71.14

Answer:

The APY would be D, 3.92%

Step-by-step explanation:

Attached Image

Using expressions, we get that$836 will be paid in total throughout the first 12 months.

The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs is known as a mathematical expression.

Given is that the starting balance is 62. As a result, the sum rises by 4%.

The time period is 12, but he will pay for 11 extra months, not including the first month's 62 dollars.

The formula is: y=62(1+0.11

y=62(1.04) ^11

The amount to be paid in the previous month is: y=95.45$

This geometric sequence has r equal to 1.04 in this case. The total will be determined as follows:

Sum = 62(1.04¹¹-1)/1.04-1

Sum = $836

Hence, $836 will be paid in total throughout the first 12 months.

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The solution is, the expression is -3+0i, so, a = -3 & b = 0.

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation {\displaystyle i^{2}=-1}; every complex number can be expressed in the form a + bi, where a and b are real numbers.

here, we have,

So we have:

given that,

(2+6i) - (5+6i)

First, distribute:

2+6i - 5 -6i

Combine like terms:

2 - 5 + 6i - 6i

Add:

-3 + 0

So, in the a+bi format, we will have:

-3 + 0i

Hence, The solution is, the expression is -3+0i, so, a = -3 & b = 0.

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Answer:

17,714.7

Step-by-step explanation:

a_n = 3^(2 n - 1) 10^(5 - n) (for all terms given)

{30000, 27000, 24300, 21870, 19683, 177147/10, 1594323/100, 14348907/1000, 129140163/10000, 1162261467/100000, 10460353203/1000000, 94143178827/10000000, 847288609443/100000000, 7625597484987/1000000000, 68630377364883/10000000000, 617673396283947/100000000000}

The tax owed by a person in 2021 who had a single filling status with a taxable income of $ 62, 000 is $ 9, 388. 50.

In 2021, the Internal Revenue Service issued rates such that a person with a single filling status and earning $ 62, 000 per year would be subject to tax of ;

= 4, 664 + 22 % of the amount over $ 40, 525

This means that the tax owed by this taxpayer with a $ 62, 000 gross income is :

= 4, 664 + ( 22 % x ( 62, 000 - 40, 525 ) )

= 4, 664 + ( 22 % x 21, 475 )

= 4, 664 + 4, 724. 50

= $ 9, 388. 50

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Answer:

A reciprocal function can be written in the form of f(x) = a / (x-h) + k, where a is a constant, h is the x-value of the vertical asymptote, and k is the y-value of the horizontal asymptote.

Given that the vertical asymptote is located at x = -2 and the horizontal asymptote is located at y = 5, we can write:

f(x) = a / (x - (-2)) + 5

Simplifying this expression, we get:

f(x) = a / (x + 2) + 5

Therefore, an equation that could represent this reciprocal function is:

f(x) = a / (x + 2) + 5

Step-by-step explanation:

A) R = -19t + 1890 B) 11 years from now, the total oil reserves will be 1681 billions of barrels. C)  The world's oil reserves will be completely depleted (all used up) approximately 99.47 years from now.

The slope of a line represents the rate of change between the x and y variables, or the rise over the run. A positive slope means that the line is increasing from left to right, while a negative slope means that the line is decreasing from left to right. A slope of zero means that the line is horizontal, while an undefined slope means that the line is vertical.

A) The rate of decrease in oil reserves is 19 billion barrels per year, which can be represented as a slope of -19. The initial oil reserves are 1890 billion barrels, which is the y-intercept. Therefore, the linear equation for the total remaining oil reserves R, in terms of t (the number of years since now) is:

R = -19t + 1890

B) To find the total oil reserves 11 years from now, we can substitute t = 11 into the equation:

R = -19(11) + 1890

R = -209 + 1890

R = 1681 billion barrels

Therefore, 11 years from now, the total oil reserves will be 1681 billions of barrels.

C) If no other oil is deposited into the reserves, the reserves will be completely depleted when R = 0. We can use the linear equation to find how long it will take for the reserves to reach 0:

0 = -19t + 1890

19t = 1890

t = 99.47 years

Therefore, the world's oil reserves will be completely depleted (all used up) approximately 99.47 years from now, assuming no new reserves are discovered or added.

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The correct inequality that represents how many video games he could buy is C. 15.99x + 9.99 ≤ 100.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let x be the number of video games Manny wants to buy.

The total cost will be the sum of the cost of the video games and the shipping charges:

Total cost = (number of video games) × (cost per game) + (shipping charges)

Total cost = 15.99x + 9.99

Since Manny can spend at most $100, we can write the inequality:

Total cost ≤ 100

15.99x + 9.99 ≤ 100

Therefore, the correct inequality that represents how many video games he could buy is C. 15.99x + 9.99 ≤ 100.

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Answer: H: (7, 1)

Step-by-step explanation: If the endpoints of A and B are (3, 5) and (11, -3), you just have to find the middle of the x and y coordinate for each endpoint. The middle of 3 and 11 is 7, and the middle of -3 and 5 is 1, therefore the middle point would be (7, 1).

Answer:

2x(1700%x4)+2=138

Step-by-step explanation:

2x2.00=4 2x17=34 34 per month plus the 2 that they already had. 34x4=136 there will be 136 plus 2 after the 4 months

Answer:

3 Burrito Bowls

Step-by-step explanation:

32.46 - 12.96 = 19.5

6.5 x 3 = 19.5, so 3 bowls

Answer:

the customer ordered 3 burrito bowls

Step-by-step explanation:

32.46=6.5x+12.96

-12.96 -12.96

19.5=6.5x

3=x

x=# of burrito bowls ordered

Answer: question 1 is 62° and radius is 1.0821  

question 2 is 454.91794m

question 3 is 855.57622m

Step-by-step explanation:

Given c=969 and ∠α=28°,

a = 454.91794

b = 855.57622

∠β = 62° = 1.0821 rad

h = 401.6687

area = 194,608.48704

perimeter = 2,279.49416

inradius = 170.74708

circumradius = 484.5

im only in 8th grade so don't trust me on this but i think im right

The vertex of function is (2, 0).

In mathematics, a graph is defined as a graphical representation or diagram that organises facts or values. The graph's points frequently reflect the relationship between two or more things.

A graph is a non-linear data structure composed of nodes (vertices) and edges. The edges in the graph connect any two nodes, which are also known as vertices.

Given:

y = |x - 2|

When we plot the graph as y = |x - 2|.

we get the vertex of the function y = |x - 2| at (2, 0).

Also, the function y = |x - 2| cuts the y axis at (0, 2).

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Answer:

60%

Step-by-step explanation:

The area of the rhombus is, A = (x² + 2x - 8) m².

A quadrilateral with all equal sides is a rhombus.

Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.

A rhombus has 360° of interior angles total.

A rhombus's adjacent angles add up to 180°.

A rhombus's diagonals are perpendicular to one another and cut each other in half.

We also know That the area of a rhombus is, Half times the product of the two diagonals.

Given, A rhombus, with d₁ = (2x + 8) m and d₂ = (x - 2) m.

Therefore, The area of the rhombus is,

= (1/2)×(2x + 8)(x - 2) m².

= (1/2)(2x² - 4x + 8x - 16) m².

= (1/2)(2x² + 4x - 15) m².

= (x² + 2x - 8) m².

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Answer:

Step-by-step explanation:

200,000 square kilometers is a good estimate for the area of South Dakota because the actual area of South Dakota is approximately 199,729 square kilometers according to the United States Geological Survey (USGS).

This means that the estimate is only off by about 0.1% of the actual area. This level of accuracy is generally considered to be very good for an estimate, especially when dealing with large areas like states or countries.

Additionally, 200,000 square kilometers is a round number and easy to remember, making it a useful estimate in contexts where a precise value is not necessary. It also allows for quick comparisons with other areas or states that may be roughly similar in size.

Overall, 200,000 square kilometers is a good estimate for the area of South Dakota because it is reasonably close to the actual value, easy to remember, and useful for rough comparisons with other areas.

ALSO:

South Dakota is approximately 383 miles long (east to west) and 237 miles wide (north to south).

It has the approximate shape of a rectangle, its Area = (Base x Height)= (383 x 237)= 90,771.00 miles ^2 which are 235,095.81 Km^2. So by this geometric reasoning we can have a correct approximation of the area of ​​South Dakota.

By using the properties of the diagonal of the parallelogram, we found the values of x and y as 2 and 7 respectively.

A parallelogram is a straightforward quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A parallelogram has adjacent angles that add up to 180 degrees.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.

Here the diagonal of the parallelogram intersects each other.

According to the properties of the paralleogram, the diagonal bisects each other.

So,

2x = x + 2

x = 2

and

5y -5 = y + 23

4y = 28

y = 7

Therefore by using the properties of the diagonal of the parallelogram, we found the values of x and y as 2 and 7 respectively.

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Answer:

[tex]625m^{2}[/tex]

Step-by-step explanation:

The line that the equation represents has a y-intercept of.

What is an example of a y-intercept?

Here are several y intercept instances. So we obtain y = 5(0)2 + 2 = 2 when we replace x = 0, so y-intercept of y Equal 5x2 + 2 is (0, 2). Because we obtain y = -5e0 = -5 when we try substituting x = 0, this same y-intercept of y Equal -5ex is (0, -5).

Y-intercept: Is it 0 or 1?

The point where a straight line intersects the X-axis is known as the Y interception. In the picture above, the line intersects the Value of y at 1. The point is shown by and the value of the Variable y is 1. (0,1). Remember that for the y-intercept, the point's such and such is always zero.

On this note, we must recall that the y-intercept of an equation is the value of when.

Therefore, we have;

-60(0) + 2y -120 = 0

2y = 120

y = 60

Hence, the y-intercept of the line represented by the equation is; 60.

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The complete question is:

Ernesto brings his dog to training classes. The equation -60x + 2y - 120 =0 relates y, the total cost of a pet's training, and x, the number of classes taken Ernesto states that the y-intercept of the line represented by the equation is 30. is he correct?

We can write the terms of the sequence as -

a(1) = 5

a(2) = 18

a(3) = 26

a(10) = 500

The nth term of a arithmetic progression is given by -

a{n} = a + (n - 1)d

Given is to find 1st, 2nd, 3rd and 10th term of the sequence function -

a{n} = 4n² + n

a{n} = n(4n + 1)

a(1) = 1 x (4 + 1) = 5

a(2) = 2 x (8 + 1) = 18

a(3) = 3 x (12 + 1) = 26

a(10) = 10 x (40 + 10) = 500

Therefore, we can write the terms of the sequence as -

a(1) = 5

a(2) = 18

a(3) = 26

a(10) = 500

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Answer:

The solution to the equation 7x [6+10(1+1)] = 4 x 5 is x = 10/91.

Step-by-step explanation:

o solve the equation 7x [6+10(1+1)] = 4 x 5, we can use the order of operations, which tells us to first perform the operations inside the parentheses, then the multiplication and finally the multiplication by 7x.

So, we have:

7x [6+10(1+1)] = 4 x 5

7x [6+10(2)] = 20

7x [6+20] = 20

7x [26] = 20

182x = 20

To solve for x, we can divide both sides by 182:

182x/182 = 20/182

x = 20/182

Simplifying the fraction by dividing both the numerator and denominator by their greatest common factor, we get:

x = 10/91

Therefore, the solution to the equation 7x [6+10(1+1)] = 4 x 5 is x = 10/91.

The Tape diagram for 7/8 is shown below.

A tape diagram is a visual model that students can use to show a mathematical connection or to help them grasp a math idea. Tape diagrams can be used to solve a variety of arithmetic problems, although they are most typically employed to solve word problems.

Tape diagrams are graphic representations that use rectangles to depict the portions of a ratio. Drawing them requires attention to detail because they are a visual model. They simplify complex mathematical word problems by breaking them down.

Given:

Here we can divide the fraction 7/8 as

7/8

= 2/8 + 5/8

= 2/8 + 2/8 + 3/8

So, the tape diagram will have 8 out tapes out of which 7 are shaded.

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The trade discount rate for the wholesaler at the net price is 0.45 or 45%.

A trade discount is a cut in the list price of products or services provided by a seller to a customer who makes frequent or significant purchases of such items. A trade discount is intended to encourage the customer to make further purchases from the supplier. The discount might change depending on the volume or regularity of purchases and is often given as a percentage of the list price. Retailers or wholesalers that purchase products from producers or suppliers to resell to consumers frequently receive trade discounts.

The discount rate is given by the following formula:

Trade Discount Rate = (List Price - Net Price) / List Price

Substituting the given values, we get:

Discount Rate = (13600 - 7480) / 13600

Discount Rate = 0.45 or 45%

Hence, the trade discount rate for the wholesaler is 0.45 or 45%.

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Answer:

Will is 122% of Wandas height.

Step-by-step explanation:

By answering the above question, we may infer that Thus, 12 is the result equation of 1/4 times 48.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

You can multiply 1/4 by 48 using the following formula:

1/4 x 48 = (1/4) * 48

The numerator (1) is first multiplied by the integer being multiplied (48):

1 * 48 = 48

Divide the result by the denominator (4) after that:

48 / 4 = 12

Thus, 12 is the result of 1/4 times 48.

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With the discount, each dresser would cost $450.

What is the discount?

A discount is a reduction in the price of a product or service that is offered by a seller to a buyer. It is a form of incentive that is used to encourage customers to purchase goods or services, often by making them more affordable or attractive.

To calculate the amount of discount off each item, we need to know the original price of each dresser and the percentage discount that is being offered. Let's assume that the original price of each dresser is $500, and the discount being offered is 10%.

To calculate the discount off each item, we can use the following formula:

Discount amount = Original price x Discount rate

where the discount rate is the percentage discount expressed as a decimal (e.g., 10% = 0.1).

So, for each dresser, the discount amount would be:

Discount amount = $500 x 0.1 = $50

Therefore, each dresser would be discounted by $50. This means that the new price for each dresser would be:

New price = Original price - Discount amount

New price = $500 - $50 = $450

Hence, with the discount, each dresser would cost $450.

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