Find the measure of each angle in the angle pair described.
The measure of one angle is twice the measure of its supplement. What are the measures of the two angles?

Answer:

Step-by-step explanation:

a) The quadratic function g(x) = 2f(x-4) + 5 is defined as a transformed version of the original quadratic function f(x). The transformation applied to f(x) is a horizontal shift of 4 units to the left and a vertical shift of 5 units upward. This can be observed from the fact that x is replaced with (x-4) in the function g(x). The function is also scaled by a factor of 2.

How does a quadratic function work?

f(x) = ax2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.

b) The turning point of the quadratic function f(x) is (-3, 2). To find the turning point of g(x), we must first apply the horizontal shift of 4 units to the left to the x-coordinate, and then apply the vertical shift of 5 units upward to the y-coordinate.

The turning point of g(x) is (-3+4, 2+5) = (1,7)

So, the turning point of the transformed function g(x) is (1,7)

We can see that the transformation of g(x) moves the turning point of f(x) to the right and up, as expected from the transformation.

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Third quadrant the complex plane is where the number -14 - 5i is situated.

Based on the common knowledge, the complex number's real and imaginary components are considered as the x- and y- coordinates of an ordered pair in a 2-D plane.

first quadrant a+bi =(a,b)

second quadrant -a+bi= (-a,b)

third quadrant -a-bi=(-a,-b)

fourth quadrant a,-b=(a,-b)

According to the question,-14-5i is located in third quadrant(-14,-5)

As a result, the complex plane's third quadrant is where the number -14 - 5i is situated.

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2 with an exponent of 7 is 128. It means 2 multiplied by itself 7 times.

When a number is raised to a certain power, it means that the number is multiplied by itself that many times. For example, 2 with an exponent of 7 means 2 multiplied by itself 7 times.

So, 2 with an exponent of 7 is 128.

It's important to note that the exponent is also known as the power, so 2^7 is also read as 2 to the power of 7.

Exponents are a way of shorthand for repeated multiplication. Understanding this concept is important for solving mathematical problems, especially in algebra and calculus.

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Answer:The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Add 10 10 to both sides of the equation. Using the slope-intercept form, the y-intercept is 10 .

Step-by-step explanation:

Problem 4

I recommend to draw a number line. Place the baseball park at 0 on the number line.

Then place Luke's house at -3. The distance from -3 to 0 is 3 units, to represent the 3 miles.

Place Logan's house at 2 on the number line.

To go from -3 to 2, move 5 units to the right. This is the longest distance possible because each person's house is on opposite sides of the baseball park.

To get the shortest distance possible, we'll place each person's house to the right of 0. This time each person's house is on the same side.

We'll move Luke from -3 to +3. Keep Logan at 2. The distance from 2 to 3 is 1 unit. This is the shortest distance possible.

Answers:

Shortest distance = 1 mile

Longest distance = 5 miles

===============================================

Problem 5

d = distance between Luke's house and Logan's house

Refer to the result of problem 4, where we found d = 1 the smallest possible value of d. And also d = 5 the largest possible value.

In other words: d is between 1 and 5, including each endpoint.

The compound inequality to set up is [tex]1 \le d \le 5[/tex]

The graph involves closed filled in circles at 1 and 5 on the number line. Shade the region between these endpoints. Closed endpoints visually tell the reader "include this endpoint".

Answers:

Inequality:  [tex]\boldsymbol{1 \le d \le 5}[/tex]

Graph: Closed filled in circles at 1 and 5; shading in between

===============================================

Problem 6

The largest distance we previously found was 5 miles.

Luke traveled 0.5 miles so far, meaning he has at most 5-0.5 = 4.5 miles left to go.

Answer:  

4.5 miles

Answer:

Q4  
Shortest distance = 1 mile
Longest distance = 5 miles

Q5
1 ≤ d ≤ 5

Q6
4.5 miles

Step-by-step explanation:

A diagram does help for these questions

Q4

If both Luke and Logan's houses are on the same straight line in the same direction then the difference between their individual distances from the field will be the shortest distance.

See the first diagram

Shortest distance = 3 - 2 = 1 mile

However, if they lived in exactly opposite directions on a straight line then the distance would be the longest and would be 2 + 3 = 5 miles

--------------------------------------------------------------------------------

Q5

The compound inequality would be 1 ≤ d ≤ 5 where d represents all possible distances from the two homes.

(We can also write this as [1, 5] which is called interval notation)

See second figure for how this would be represented on a number line

------------------------------------------------------------------------------

Q6

Since we have determined the greatest distance between the two houses as 5 miles, and Luke has already biked 0.5 mile he has 5 - 0.5 = 4.5 miles left to bike

We multiply by -3/2 to get rid of y and figure out the system of equations.

A mathematical assertion that has an "equal to" symbol between two expressions with equivalent values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including straight, quadratic, cubic, and others.

So, we have:

9x+3/4y=6 and 2x+1/2y=9

By removing y, we must solve a system of equations.

Therefore, we will first make the y-coefficient equal but with the opposite sign.

In the first equation, the y-coefficient is 3/4

The coefficient of y in equation two is half.

LCM: 3/4 and 1/2 = 3/2
To maintain the same coefficient of y, multiply the second equation by -3/2.

-3/2*2x-3/2*1/2y = -3/2*9

-3x-3/4y = -27/2

9x+3/4y = 6

Combine the two equations and get rid of the y variable.

-3x+9x = -27/2+6

6x = -15/2

x = -5/4

Therefore, we multiply by -3/2 to get rid of y and figure out the system of equations.

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Complete question:

Given the equations 9x+3/4y=6 and 2x+1/2y=9, by what factor the equation to eliminate y and solve the system through linea would you multiply the second equation to eliminate y and solve the system through linear combinations?

Options;

A.) -4/3

B.) -3/4

C.) -3/2

D.) -7/2

Answer: 1 3/5

Step-by-step explanation:15 x 1 3/5 = 24

Answer:

first one is 1.-.5

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

This IS basically an experiment with  15 hits out of 45 at-bats

   15/45 = .333    or  33.3 %  experimental probability

Answer:

--------------------------------------

Given:

Find the experimental probability.

Probability of getting a hit is:

Answer:

I believe… ( it might be wrong… )

Reflect across the line y = x.

translate 1 unit right.

Step-by-step explanation:

i took the same test before but i believe i had a question just like this and got it right soooo….. ye

So on solving the provided question we can say that -  the function is  f(x) = x= +2, -2

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

the function is -

f(x) = x^2 - 2

f(x) = x= +2, -2

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Answer: no

Step-by-step explanation:

35 -9 = 26

you add 1+1 =2

then you look at the equal and that is your answer

The correct option: 3. Apply the distributive property or FOIL; to determine the value of zw.

Let z = 19 + i and w = 4 + 10i.

Making a decision is the first step.

The steps to find the product of complex numbers z and w are as follows.

z. w = ( 19 + i )( 4 + 10i ).

z. w = 19 * (4 10i) i * (4 10i).

z. w = 19 * 4 + 19*10i + i * 4 + i * 10i.

z. w = 76 +  190i  + 4i + 10i².

because i² = -1.

z. w = 76 + 194i - 10.

z. w = 66 + 194i.

Thus, in order to find zw in the first step, use the distributive property or FOIL.

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The correct question is-

Let z = 19 + i and w = 4 + 10i.

What is the first step in determining zw?

According to number line, x > 5 is correct,

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when plotting a point.

Here,

Given :

∵ The inequality is -3(2x - 5) < 5(2 - x)

At first simplify each side

∵ -3(2x - 5) = -3(2x) + -3(-5)

Remember (-)(-) = (+)

∴ -3(2x - 5) = - 6x + 15

∵ 5(2 - x) = 5(2) + 5(-x)

Remember (+)(-) = (-)

∴ 5(2 - x) = 10 - 5x

∴ - 6x + 15 < 10 - 5x

Subtract 15 from both sides

∴ - 6x < -5 - 5x

Add 5x to both sides

∴ - x < - 5

∵ The coefficient of x is -1

∴ Divide both sides by -1

∴ x > 5

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Answer: 3^2

Step-by-step explanation: i would say that is my answer because , there are 2 threes and in exponential form i think it would be unless its a decimal in between the two threes and not a times

Answer: they each carried 5 water bottles.

Step-by-step explanation: 8x5 equals 40

Answer: 5

Step-by-step explanation:

40 divided by 8

When MN = 5x + 10, the lengths of MN, RS, and NP are 410, 400, and 320, respectively in this triangle .

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

given

as AMNP-ARST

the x = 80

so MN = 5 * 80 + 10

= 410

RS = 6* 80 - 8

= 400

When MN = 5x + 10, the lengths of MN, RS, and NP are 410, 400, and 320, respectively in this triangle .

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Answer:

-4 x^3 y^2 thus: # 4

Step-by-step explanation:

Simplify the following:

(24 x^6 y^3)/(-6 x^3 y)

The gcd of 24 and -6 is 6, so (24 x^6 y^3)/(-6 x^3 y) = ((6×4) x^6 y^3)/((6 (-1)) x^3 y) = 6/6×(4 x^6 y^3)/(-x^3 y) = (4 x^6 y^3)/(-x^3 y):

(4 x^6 y^3)/(-1 x^3 y)

Combine powers. (4 x^6 y^3)/(-x^3 y) = (4 x^(6 - 3) y^(3 - 1))/(1 (-1)):

(4 x^(6 - 3) y^(3 - 1))/(-1)

6 - 3 = 3:

(4 x^3 y^(3 - 1))/(-1)

3 - 1 = 2:

(4 x^3 y^2)/(-1)

Multiply numerator and denominator of (4 x^3 y^2)/(-1) by -1:

Answer: -4 x^3 y^2

Answer: #4

Step-by-step explanation:

You would divide 24 by -6, leaving u with -4 then u would subtract the powers x to the power of 6 from x to the power of 3 leaving you with x to the power of 3 and then you would subtract y to the power of 3 by y leaving you with y squared.

-4x to the power of 3 y to the power of 2.

Answer:

9)  17 miles/hr

10)  7.14 miles

Step-by-step explanation:

See the attached worksheet.  Note the use of conversion factors.  In question 9 we want to convert minutes to hours.  We know there are 60 minutes/hr.  So we can set up a conversion factor in one of 2 ways:  (60 minutes/1 hr) or (1 hr/60 minutes).  Both are valid, and both are = 1, since the numerator and denominator are both equivalent.  This means we can invert a conversion factor and it is still = 1.  Since conversion facots are equal to 1, we can multiply them times anything, and the result is numerically the same (anything times 1 = anything) and only the units have changed.  For question 9, we want to convert miles/min to miles/hr.  I'll choose the conversion factor (60 min/1 hr), mostly because I like multiplication over division.  Note how the units cancel in the attachment, resulting in 17 miles/hr.  One may also use the factor (1hr/60min), but then a division is required.  Perfectly fine, but not my preferred route.

The same approach is used to answer question 10.  Again, note how he units cancel, leaving a number wth just the units desired,

N! also called N factorial is the product of all positive non-integers equal to or less than N or simply is the product of the Nth integer and all integers below it.

N! is represented as 1x2x3x4.......x n which is also equivalent to n x (n-1_x(n-2w)x(n-3)......x1.  Therefore the formula for N factorial is N! = n × (n - 1)!. For whole numbers, the factorial is a product of natural numbers till 1 of the values is equal to or less than whole numbers.

N is also used to represent the set of natural numbers up to infinity. Natural numbers include the values from till infinity, they can be represented like N=[1,2,3,4,5,6........].

Examples of N! are:-

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As per the unitary method, the cost of bag is $93.3 and the cost of pen is $64.45

The term unitary method in math is known as the process of solving the  the value of a single unit, and based on this value we can find the value of the required number of units.

Here we have given that the cost of pen and bag is $153.75.

Here we also know that the bag cost $28.85 more than the pen.

Let us consider that x be the cost of pen and here we know that the cost of bag is $28.85 more than the pen then it can be written as,

=> x + 28.85

Therefore, the equation is written as,

=> x + (x + 28.85) = 153.75

Now, we simplify the equation, then we get,

=> 2x + 28.85 = 153.75

Here we need to find the value of x, so, we have to move the other terms on the other side, then we get

=> 2x = 153.75 - 28.85

=> 2x = 124.9

Therefore, the value of x is 64.45.

Therefore, the cost of bag is calculated as,

=> x + 28.85

=> 64.45 + 28.85

=> 93.3

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The domain of the function f/x = 4x is all real numbers.

The domain of a function is the  et of all values that can be plugged into the equation and produce a valid output. Since any real number, positive, negative, or zero, can be plugged into the equation and produce a valid output, the domain of the function f/x = 4x is all real numbers.

The domain of a function is the set of values that can be plugged into the equation and produce a valid output. In the case of the function f/x = 4x, the domain is all real numbers; that is, any value, positive or negative, can be plugged into the equation and produce a valid output. This means that the domain of the function f/x = 4x includes all real numbers, from the smallest negative number to the largest positive number, as well as zero.

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It is not possible to construct a triangle whose sides are 10.2 cm 6.8 cm and 4.6 cm because the sum of two sides are greater than the third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 10.2 cm 6.8 cm and 4.6 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.

To check this we firstly add the 10.2 and 6.8

10.2 + 6.8 > 4.6

17 > 4.6

Now we add 10.2 and 4.6

10.2 + 4.6 > 6.8

14.8 > 6.8

Now we add 6.8 and 4.6

6.8 + 4.6 > 10.2

11.4 > 10.2

It is possible to construct a triangle whose sides are 10.2 cm 6.8 cm and 4.6 cm because the sum of two sides are greater than the third sides.

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3*(28) + 7 can be rewritten as 316 + 7, which can be further simplified by using the associative property of multiplication and the commutative property of addition as (3*16) + 7 = 48 + 7 = 55

The commutative property of addition states that the order of the numbers being added does not matter, for example, a+b = b+a.

The associative property of multiplication states that the grouping of the numbers being multiplied does not matter, for example, (ab)c = a(bc).

Therefore, the expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3*(2*8)+7 is (3*16) + 7 = 48 + 7 = 55.

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The ordering of the fraction from least to greatest will be 1/4, 3/8, 1/2, and 3/4.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

The value of 3/4 will be:

= 3/4 × 100

= 75%

The value of 3/8 will be:

= 3/8 × 100

= 37.5%

The value of 1/2 will be:

= 1/2 × 100

= 50%

The value of 1/4 will be:

= 1/4 × 100

= 25%

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A map uses scaled drawings. The distance between the two considered cities on that specified map is 6.25 inches

How are scale drawings formed?

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

1ft : s/k in.

All feet measurements will then we multiplied by s/k to get the drawing's corresponding lengths.

For this case, it is specified that the map uses scaling such that:

3/4 of an inch on map = 3 miles in reality.

Dividing both the quantities by 3, we get:

1 mile in reality = 3/4  / 3  inches on map = 1/4 inches on map

Multiplying both the quantities by 25, we get:

25 miles in reality = 25/4 = 6.25  in map

Since 25 miles is the distance between those two considered cities.

Therefore, the distance between those two cities on map would be of 6.25 inches.

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The given expression is equivalent to 486√3

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, √4 of 3√3 of 3⁵

√4 of 3√3 of 3⁵ = 2×3√3×243

= 486√3

Hence, the given expression is equivalent to 486√3

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Brooklyn could calculate how many arithmetic problems she completed and how many pages she read using the equations x = 2y and 2x + 3y = 70.

let

number of math problems Brooklyn solved = x

number of pages she read = y

Time to solve each math = 2 minutes

Time to read each page = 3 minutes

Brooklyn read twice as many pages as there were arithmetic problems to be done.

x = 2y

2x + 3y = 70

Substitute x = 2y into

2x + 3y = 70

2(2y) + 3y = 70

4y + 3y = 70

7y = 70

divide both sides by 7

y = 70/7

y = 10

Recall,

x = 2y

x = 2(10)

x = 20

Therefore, Brooklyn completed 20 math problems and read 10 pages, which equals 20 math problems and 10 pages, respectively.

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