use the relationships in the diagram to solve for t. Justify your solution with a definition or theorem ​

Answer:

-2x + 10

Step-by-step explanation:

-2(x - 5)

-2(x) -2(-5)

-2x + 10

Helping in the name of Jesus.

Answer: Its Slope

Step-by-step explanation: in the given graph both lines a parallel .meaning they both should have the same slope

The distance from points A(-2, 2) to B (4, -2)​ is equal to √52 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical expression:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given points into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - (-2))² + (-2 - 2)²]

Distance = √[(6)² + (-4)²]

Distance = √(36 + 16)

Distance = √52 units.

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Interval notation is a way to represent an interval of real numbers on the number line. Set notation is a way to represent a set of elements.

Interval notation is a way to represent an interval of real numbers on the number line.

The notation uses parentheses, brackets, and infinity symbols to indicate whether the endpoints of the interval are included or excluded from the set of numbers.

For example, [3, 8) represents the interval of real numbers from 3 (included) to 8 (excluded), while (-∞, 4) represents the interval of real numbers less than 4 (excluding 4), and extending to negative infinity.

Set notation is a way to represent a set of elements. It uses curly braces to enclose the elements of the set and can include various symbols to indicate properties of the set.

For example, {2, 3, 5, 7, 11} represents the set of prime numbers less than 12, while {x | x is an even number} represents the set of even numbers.

The vertical bar | is used to separate the variable (x in this case) from the condition that must be met for elements to be included in the set (x is an even number).

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Answer: The person paid $396.

Step-by-step explanation:

1. Since we need to find 60% of 360, we can do 360 x 60/100.

2. We are now left with 216.

3. Now we have to add the total together.

4. 216 + (15x12) = 396.

5. The person paid $396.

Answer: y = -192

Step-by-step explanation:

The equation given is:

-24 = y/8

To solve for y, we need to isolate the variable y on one side of the equation. We can do this by multiplying both sides by 8:

-24 x 8 = y

Simplifying the left side:

-192 = y

Therefore, the solution is y = -192.

1)  5/8 × 2 1/2 is slightly more than 1/4. Therefore, the correct option is:

C.

2) The area of the fortune cookie is: B. 1 25/16 square inches.

In mathematics, area is the measure of the size or extent of a two-dimensional shape or surface, such as a rectangle, triangle, circle, or any other closed figure. It is the amount of space inside the boundary of a shape, usually measured in square units.

For example, the area of a rectangle can be found by multiplying its length and width. The formula is:

Area = length × width

The area of a circle can be found by multiplying the square of its radius by pi (π). The formula is:

Area = πr²

where r is the radius of the circle.

Part A:

To estimate whether 5/8 × 2 1/2 is more or less than 1/4, we can round 5/8 to 1/2 and round 2 1/2 to 2. Then we have:

1/2 × 2 = 1

So, 5/8 × 2 1/2 is slightly more than 1/4. Therefore, the correct option is:

C. 5/8 × 2 1/2 is more than 1/4.

Part B:

The area of the fortune cookie can be found by multiplying its length by its height. The length is given as 2 1/2, which can be written as an improper fraction:

2 1/2 = 5/2

The height is given as 5/8. So, the area can be devised as:

Area = length × height

Area = (5/2) × (5/8)

Area = 25/16

Therefore, the area of the fortune cookie is:

B. 1 25/16 square inches.

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Answer is X=2.

1. Collect like terms

(x) + 4 + 9 = 17 - x

2. Add the numbers

x + (13) = 17 - x

3. Move the variable to the left-hand side and change its sign

x + 13 (+x) = 17

Move the constant to the right-hand side and change its sign

x + x = 17 - 13

4. Collect like terms

2x = 17 - 13

Subtract the numbers

2x = 4

5. Divide both sides of the equation by 2

Therefore, you get your solution: X=2.

Using the properties of equality, the steps for solving the equation is explained below.

To solve an equation, we would apply the properties of equalities where necessary to isolate the variable in the equation to one side.

Step 1: [tex]3x + 4 - 2x + 9 = 17 - x[/tex] [given]

Step 2: [tex]x + 13 = 17 - x[/tex] [Combine like terms]

Step 3: Add x to both sides of the equation

[tex]x + 13 + x = 17 - x + x[/tex] [addition property of equality]

Step 4: [tex]2x + 13 = 17[/tex] [simplify]

Step 5: Subtract 13 from both sides

[tex]2x + 13 - 13 = 17 - 13[/tex] [subtraction property of equality]

Step 6: [tex]2x = 4[/tex] [simplify]

Step 7: [tex]x = 2[/tex] [division property of equality]

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We can estimate that after 5 years, there will be approximately 215 stores remaining.

Assuming a 5% decline in the number of stores each year, the function to approximate the total number of stores remaining after x years is exponential, and can be written in the form:

g(x) = a *[tex](0.95)^x[/tex]

where g(x) is the total number of stores remaining after x years, and a is the initial number of stores (278 in this case).

Therefore, the equation for the function is:

g(x) = 278 * [tex](0.95)^x[/tex]

This function takes into account the compounding effect of the 5% decline each year on the initial number of stores and can be used to estimate the number of stores that will remain after any number of years. For example, after 5 years, the number of stores would be approximate:

g(5) = 278 *[tex](0.95)^5[/tex]

g(5) ≈ 214.5

Therefore, we can estimate that after 5 years, there will be approximately 215 stores remaining.

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Complete Question:

An electronics company currently has 278 stores throughout the U.S. Because of the popularity of online shopping, many of the company's stores are closing. The total number of stores is expected to decline by about 5% this year. Assuming the same decline continues, you can use a function to approximate the total number of stores remaining after x years. Write an equation for the function. If it is linear, write it in the form gx=mx+b . If it is exponential, write it in the form gx=abx. gx=___?

There are 4060 different groups of 3 pictures that can be displayed on the frame.

A combination is a method of choosing a subset of items from a bigger set when the order of the items is irrelevant. For instance, the two-letter possibilities for a set of three letters A, B, and C are AB, AC, and BC. Combinations are employed in many different mathematical and practical situations, including combinatorial optimization, statistics, and probability theory. Choosing a password with a specific amount of characters, picking a combination of things from a menu, and assembling a team from a group of players are all examples of how they are utilised in daily life.

Given that, from 30 pictures we need to form groups of 3.

The combination of selecting groups is given as:

nCk = n! / (k! * (n - k)!)

Substituting the values we have:

30C3 = 30! / (3! * (30 - 3)!)

= 30! / (3! * 27!)

= (30 * 29 * 28) / (3 * 2 * 1)

= 4060

Hence, there are 4060 different groups of 3 pictures that can be displayed on the frame.

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Answer:

44%

Step-by-step explanation:

the answer is 44% because 55/125 can be simplifed by dividing both sides by 5 to get 11/25

Answer: 45min

Step-by-step explanation:

3x60=180

2x60=120

120+15=135min

180-135=45min

Answer:

To sketch the given region on the Argand diagram, we need to find the intersection of the three conditions:

-3i < Im(z) < 3i (the imaginary part of z lies between -3 and 3 on the vertical axis)

1 < Re(z) ≤ 6 (the real part of z lies between 1 and 6 on the horizontal axis)

|z - 4| ≥ 1 (the distance between z and 4 is greater than or equal to 1, which means z is outside or on the boundary of the circle centered at 4 with radius 1)

The first two conditions define a rectangle in the complex plane with vertices at (1,-3i), (1,3i), (6,3i), and (6,-3i). The third condition excludes the inside of a circle centered at 4 with radius 1, which means the region we want is the rectangle with a circular hole in the middle.

To find the area of this region, we can subtract the area of the circle from the area of the rectangle. The area of the rectangle is:

A_rect = length x width = (6 - 1) x (3i - (-3i)) = 30i

The area of the circle is:

A_circle = πr^2 = π(1)^2 = π

Therefore, the area of the region is:

A_region = A_rect - A_circle = 30i - π

So the area of the region is 30i - π, written in terms of π.

The system of equation are

The profit function is = 20x + 6y

Let's define the following variables:

x: the number of boards of mahogany sold

y: the number of boards of black walnut sold

Based on the problem statement, we can write the following system of inequalities to represent the constraints:.

x ≤ 260 (there are only 260 boards of mahogany available)

y ≤ 320 (there are only 320 boards of black walnut available)

x + y ≤ 380 (the total number of boards sold can't exceed 380)

The profit function is:

P(x, y) = 20x + 6y

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The annual rate of population growth in the US was about 1.2% in 2015, then the growth factor will be 1.012. The growth factor depends upon annual growth rate.

Growth factor typically refers to a constant multiplier that is used to calculate the growth or decay of a quantity over time. It is given as:

Growth factor = (1 + annual growth rate)

Therefore, the growth factor for the US in 2015 can be calculated as follows:

Growth factor (1+0.012) = 1.012

Therefore, the growth factor for the population of the US in the year 2015 was about 1.012.

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Answer:

-½ and -⁵/₂

Step-by-step explanation:

solve for both 2x +3 = 2 and 2x +3 = -2

The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).

A way for resolving proportionality issues is the unitary method. Finding the value of one unit and then using that value to determine the value of another unit in relation to the first is what this process entails. If we already know that three pens cost $6, for instance, we can use the unitary technique to get the price of five pens as follows: 1 pen costs $6, 3 pens cost $2. Five pens cost $10, or $5 multiplied by $2.

given

The arrow on the right in the diagram above, which is equal to $29.12, represents the total cost of the cookies and lemons.

The first segment on the left, which is $2.66, represents the price of the cookies.

The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).

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The given conditional statements are false, true, false, True.

They are determined by following:

(a) False - The statement "If 10<7,10<7, then 3=43=4" is false, since 10 is not less than 7.
(b) True - The statement "If 7<10,7<10, then 3=43=4" is true, since 7 is less than 10.
(c) False - The statement "If 10<7,10<7, then 3+5=83+5=8" is false, since 10 is not less than 7.
(d) True - The statement "If 7<10,7<10, then 3+5=83+5=8" is true, since 7 is less than 10.

Conditional statements are used in mathematics and logic to express relationships between events and conditions. These statements consist of an "if-then" structure, where the "if" clause is the antecedent or condition, and the "then" clause is the consequent or outcome.

The truth value of the conditional statement depends on whether the condition is true or false. If the condition is true, then the outcome is also true, and the statement is considered true.

If the condition is false, then the outcome may be true or false, and the statement is considered false. Conditional statements are widely used in mathematical proofs, programming, and reasoning to establish logical connections between different events and conditions.

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A particular solution to the differential equation is [tex]y = Ae^(iwt) =(1/4)e^({i\sqrt{3t} )}.[/tex]

A particular solution to the differential equation,

[tex]\frac{d^4y}{dt^4} +5\frac{d^2y}{dy^2} +3y=2[/tex],

we assume that y has the form [tex]y = Ae^(iwt)[/tex], where A is a complex constant and w is a real constant to be determined. Substituting this form of y into the differential equation, we get:

[tex](-w^4 + 5w^2 + 3)Ae^(iwt) = 2.[/tex]

we solve the quadratic equation [tex]-w^4 + 5w^2 + 3 = 0[/tex], which can be factored as:

[tex](w^2 - 3)(-w^2 + 1) = 0.[/tex]

The roots are w = ±√3 and w = ±i. Since w must be real, we choose w = √3. Substituting this value of w and solving for A, we get:

[tex]A= \frac{2}{\sqrt{(-\sqrt{3} )^4 + 5(\sqrt{3})^2 +3 } }[/tex] [tex]=\frac{2}{5+3} = \frac{1}{4}[/tex]

Therefore, the particular solution is:

[tex]y = Ae^(iwt) =(1/4)e^({i\sqrt{3t} )}.[/tex]

A differential equation is a mathematical equation that relates a function to its derivatives. It is a powerful tool used in many fields of science and engineering to describe how physical systems change over time. The equation typically includes the independent variable (such as time) and one or more derivatives of the dependent variable (such as position, velocity, or temperature).

Differential equations can be classified based on their order, which refers to the highest derivative present in the equation, and their linearity, which determines whether the equation is a linear combination of the dependent variable and its derivatives. Solving a differential equation involves finding a function that satisfies the equation. This can be done analytically or numerically, depending on the complexity of the equation and the available tools.

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By using addition calculation, we determine that Angela will end up making 42 cards in total.

Angela made 23 cards for her friends, but she wants to make even more to share with others. To determine how many cards she will make in total, we need to add the number of cards she has already made with the number of cards she plans to make.

So, we add 23 (the number of cards she has made) and 19 (the number of cards she plans to make) so in total, she will make:

23 + 19 = 42

Therefore, Angela will make 42 cards in all.

By using simple arithmetic calculation of basic addition, we find that  Angela will make 42 cards in all.

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Answer:$2.60

Step-by-step explanation:40*0.065

Answer:42.06

Step-by-step explanation:

Answer:

To use an area model to determine the quotient of 556 and 16, we can divide a rectangle of area 556 into 16 equal parts. Each part will have an area of 556/16.

We can start by dividing 556 into 16 groups of 10 (160), and then into 16 groups of 3 (48). That leaves us with a remainder of 4.

So we have:

556 = 16 x 34 + 48 + 4

This shows that 556 can be written as 16 times some whole number (34) plus a remainder of 48 + 4/16.

Simplifying the remainder, we have:

48 + 4/16 = 48 + 1/4 = 48.25

Therefore, the quotient of 556 and 16 is:

556/16 = 34 1/4

The quotient of 556 and 16 using an area model can be determined by producing a rectangle with the total area of 556 and one side of 16. The length of the other side will be the quotient. In this case, the quotient is 34 3/4.

When asked to determine the quotient of 556 and 16 using the area model, one way to think of this is making a rectangle. The total area is 556 and one side is 16. The length of the other side will be the quotient.

Start by first estimating how many times 16 could fit into 556. Let's take 30 as an estimate, because 30*16 = 480, which is relatively close to 556. Draw a rectangle with the width of 16 and the length of 30.

Find the difference between the rectangle's area and 556. So, 556 - 480 = 76. Now, 76 is our remaining area to fill. 16 goes into 76 four more times, adding up to 64.

There is still a leftover area, which is 76-64 = 12. This is smaller than our width of 16. So, your final answer is 34 12/16 or 34 3/4 in simplest form.

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The distance Mrs. Smith covers is 3520 yards during the duration of the week by Friday morning.

One week has seven days in total.

Mrs. Smith walks half a mile each day after work, she walks a total of

0.5 miles/ day × 7 days/ week = 3.5 miles/ week

Now, if we calculate the distance on Friday morning, she must have walked four times till Friday morning since she has to walk after her work.

Therefore,

0.5 miles/ day × 4 days = 2 miles

To convert miles to yards, we can use the fact that there are 1760 yards in one mile:

2 miles/week × 1760 yards/mile = 3520 yards/week

Therefore, by Friday morning, Mrs. Smith will have walked 3520 yards.

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Answer:

Angle CAB= 28°

Angle ABC= 45°

Angle DCA= 73°

Angle DCE=107°

Step-by-step explanation:

Answer: 9, 10, and 11

Step-by-step explanation:

If the sum of three consecutive natural numbers is 30, then we can represent the smallest of the three numbers as x. The next two consecutive natural numbers would be x+1 and x+2. Therefore, we can form the equation:

x + (x+1) + (x+2) = 30

Simplifying the left-hand side, we get:

3x + 3 = 30

Subtracting 3 from both sides, we get:

3x = 27

Dividing by 3, we get:

x = 9

Therefore, the three consecutive natural numbers are 9, 10, and 11.

Answer:

120 km/h.

Step-by-step explanation:

480 km / 4h

Divide top and bottom by 4 to get the desired km/h.

We have 120 km/h.

Hope this helps!

The equations that arise when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers are:

1 = 10 - 3.3, 1 = 37.10 - 3.123, and 1 = 37.2347-706 - 123.

The Euclidean algorithm is a recursive method for finding the greatest common divisor (GCD) of two positive integers. When we divide the larger number by the smaller number, we obtain the remainder. The smaller number and the remainder are then passed on as input to the next round. The process continues until the remainder is zero, at which point the GCD is obtained.

The solution to the given problem is as follows:

We will use the Euclidean algorithm to compute gcd(123, 2347).

123 ÷ 2347 = 0 remainder 123.2347 ÷ 123 = 19 remainder 106.123 ÷ 106 = 1 remainder 17.106 ÷ 17 = 6 remainder 4.17 ÷ 4 = 4 remainder 1.4 ÷ 1 = 4 remainder 0.The last nonzero remainder we get is 1.

Therefore, the greatest common divisor (GCD)(123, 2347) = 1.

The greatest common divisor of 123 and 2347 can be expressed as a linear combination of the two numbers in the following ways:1 = 10 - 3.3, 1 = 37.10 - 3.123, and 1 = 37.2347-706 - 123.

Thus, the equations arising when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers are:

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