The nurse is assessing a client’s lymphatic system. For which enlarged node should the nurse suspect that the client has a blockage within the right lymphatic duct?.

The equation of the linear function is: 3x + y = 1.

How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)
What is the y-intercept for a given line?
When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0.
What is the general equation of a line?
The equation for a standard line is y - y₁ = m(x - x₁), where m is the slope and c is the y-intercept.

Given, the line passes through the points (-2, 7) and (2, -5).
Now, using the formula established in the literature, we get:
Slope = m = (y₂ - y₁)/(x₂ - x₁) = (-5 - 7)/(2 - (-2)) = -12/4 = -3
Equation of the linear function: y - 7 = (-3)(x - (-2)) ⇒ y - 7 = (-3)(x + 2)
⇒ y - 7 = -3x - 6 ⇒ 3x + y = 1
Thus, the equation of the linear function is: 3x + y = 1.

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In the given triangle,

sides vx and vw are equal,

and ∠v = 40°

∠w = ∠x (Adjacent angles of the equal sides of a triangle are equal)

Also, ∠v + ∠w + ∠x = 180° (Angle sum property of a triangle)

⇒ 40° + ∠x + ∠x = 180°

⇒ 2∠x = 140°

⇒∠x = 70°

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The correct answer is options A and E.

f(x) = 6x + 4

f(1) = 6(1) + 4 = 10

f(2) = 6(2) + 4 = 16

f(3) = 6(3) + 4 = 22

Clearly, options A and E are the same sequences.

The area of the circle of radius r centered at the origin is π[tex]a^{2}[/tex]

Since the circle is symmetrical in relation to the x and y axes, we can calculate the area of a quarter of a circle and multiply it by 4 to get the entire circle's area.

The equation y y = + mn [a 2 - x 2] must be solved.

Y = [a 2 - x 2] = a [1 - x 2 / a 2] is the equation for the upper semicircle (y positive).

Using integrals, we can calculate the area of the circle's top right quarter as shown below.

(1 / 4) Circle's area is equal to 0a a [1 - x 2 / a 2]. dx

Let's replace x/a with sin t to make sin t equal to x/a, dx equal to a cos t dt, and the area is given by

The formula for area of a circle is (1 / 4) Area of circle = 0/2 a 2 (1 - sin2 t) cos t dt

Now that t can range from 0 to /2, we utilize the trigonometric identity [1 - sin2 t] = cos t, which equals (1 / 4) Circle area equals 0/2 a 2 cos2 t dt.

To linearize the integrand, use the trigonometric equation cos2 t = (cos 2t + 1) / 2;

(1 / 4) Circle's area is equal to 0/2 a (cos 2t + 1) / 2 dt.

the integral (1 / 4) be evaluated. Circle's area is equal to (1/2) a2 [(1/2) sin 2t + t]. 0π/2\s= (1/4) π a 2

The circle's entire area is calculated by multiplying by 4.

Area of a circle is equal to 4 * (1/4) a 2 a 2. additional references on integrals and calculus applications.

Area of circle = 4 * (1/4) π a 2 = π a 2 More references on integrals and their applications in calculus.

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Answer:

Step-by-step explanation

Third, second, first.

The third has 5% chance that it will get the investor its money back, second having a 34% of the investor getting its money back, and the first having a 54% chance. Hope this was quick enough for you!

The car will catch up the cyclist 3 hours after it starts moving.

The cyclist travels at 9 miles per hour, and travels for 4 hours before the car starts moving, so the equation for the position of the cyclist as a function of time, t, is:

C(t) = 9*4 + 9*t = 36 + 9*t

And the car moves at 21 miles per hour, then the position is:

P(t) = 21*t

The car will catch the cyclist when:

C(t) = P(t), this gives:

36 + 9*t = 21*t

36 = 21*t - 9*t = 12*t

36/12 = t

3 = t

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Answer:

y = 3x + 3

Step-by-step explanation:

The slope is 3

change in y over the change in x.  As the y increases by 3, the x increases by 1.  [tex]\frac{3}{1}[/tex] = 3

Use any of the points from the table to write the equation in the slope intercept form

Let's use the first point (0,3)  Any point would give us the same answer.

We will use the x from the point which is 0 and use the y from the point which is 3.  We will also use the slope of 3.  We will plug all of these into the equation and solve for b or the y-intercept.

y = mx + b

3 = 3(0) + b

3 = 0 + b

3 = b

y = 3x + 3

Accurate Whole numbers .

What is accurate whole number?

Accuracy is defined by the number of significant digits while precision is identified by the location of the last significant digit. For instance the number 1234 is more accurate than 0.123 because 1234 had more significant digits.

What does function mean?

Each element of x is given exactly one element of y via a function from a set x to a set y. The sets x and y are collectively referred to as the function's domain and codomain, respectively.

The following details must to be taken into account:

The term "whole number" refers to a number that is free of fractions and decimals.

It calculated the number of household online devices in relation to the number of occupants.

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Answer:

x = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

using the rule of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex]8^{x}[/tex] = 2

[tex]2^3)^{x}[/tex] = 2 , that is

[tex]2^{3x}[/tex] = [tex]2^{1}[/tex]

since the bases on both sides are equal, both 2, then equate the exponents

3x = 1 ( divide both sides by 3 )

x = [tex]\frac{1}{3}[/tex]

The inequality  x > 0 ,  x all real numbers .

What do you mean by inequality?

= 3(x-2) + 12x + 2(x+2)

= 3x - 6 + 12x + 2x + 4

= 12x + 2x + 3x -6 + 4

=  17x - 2

17x - 2 = 0

x = 2/17

x > 0 ,  x all real numbers ..

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The missing value in the solution to the equation y = -2x+4y is y.

According to the question,

We have the following information:

y = -2x+4y

y equals minus 2 x plus 4.

Now, look at the equation, we know that the solution of y is -2x+4y.

Now, the statement that is given is incomplete because we have 4 is multiplied by y.

(More to know: this equation can be further solved. We have y = -2x+4y. Now, we can move the same variables to one side. So, we have -3y = -2x. Now, the two negative signs when divided gives the positive result.)

Hence, the statement can be completed by y.

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Step-by-step explanation:

you can ask questions for clarification

Equation that can be used to represent the number of visits Violet must make to earn a free movie ticket is:

2.5v+45=75

A formula that expresses the equality of two expressions, by connecting them with the equals sign '= 'is called an equation

Unknowns are the variables for which the equation is solved and  unknown values that satisfy the equation are called solutions.

Firstly, multiply 2.5 by the number of visits (v) to calculate how many points Violet earned in total.

Now add 75 to the product of 2.5(v) because Violet started with 75 points.

To find out how many times Violet would require to visit the movie theater to get a free movie ticket:

Subtract 45 from 75,  that leaves you with 30, and after dividing that by 2.5, the number of points per visit comes out to be 12

Violet would need to visit the theater 12 times to earn a free movie ticket.

To check if that's right, substitute the value of 'v' in the equation,

12*2.5 + 45 = 75

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Answer:

8/25

Step-by-step explanation:

change the 5/4 into a 4/5 and change the divide into a mulltiple while you do this

then multiply 2 x 5 = 8

                      5 x 5 = 25

The equation the function after the transformation is  g(x) = -4x² - 8

The equation of the function is given as

f(x) = x²

The sequence of transformations is given as follows:

When the above transformations are combined, we have:

So, we have

g(x) = -4(x² + 2)

Expand

g(x) = -4x² - 8

Hence, the function g(x) is g(x) = -4x² - 8

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The inverse and domain of the function are y = x²-9 and all real numbers.

A function's inverse is a function that reverses the action of a function, such as g(x). If and only if g(x) is bijective, then the inverse of g(x) exists, and if it exist.

If the function f(x)=√x + 9, find the inverse;

y = √x+9

x = √y+9

x² = y+9
y = x²-9

The domain of the inverse function will exist on all real numbers.
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Answer:

A.    Bank B

Step-by-step explanation:

First the formulae necessary to calculate compound and simple interest

P = principal = amount deposited

r = interest rate as a decimal (i%  interest => r = i/100)

t = number of years

n = number of times compounded

[tex]\text{Compound Interest }= P\left(1 + \dfrac{r}{n}\right)^{nt} - P[/tex]

In this case, we have P = 800
r = 8/100 = 0.08
n = 12 since the interest is compounded monthly
t = 2 years

So compound interest

[tex]CI = 800\left(1 + \dfrac{0.08}{12}\right)^{12 \times 2} - 800\\\\CI = 800(1.00667)^{24} - 800\\\\\\CI = 938.31 - 800\\\\CI = $138.31[/tex]

For Bank B, the interest is calculated at 9% annually and the interest is given by the formula
SI = P x r x t
SI = 800 x 0.09 x 2    (r = 9%/100 = 0.09)

SI =  $144.00

So depositing in bank B is preferred

Answer:

Step-by-step explanation:

Problem 2:

Count the blocks.

You can find 1 1000 block

You can find 2 100 block

You can find 3 10 block

You can find 6 1 block.

Together it is 1236.

Problem 3:

Expanded notation is the number listed in groups of base 10. To solve, just put the number of blocks and the block number.

(1 x 1000)+(2 x 100)+(3 x 10) + (6 x 1)

Problem 4:

Find the number between the clues.

Since A is close to 100 and less than 100, you could put 75, which is close to 100 but not quite enough.

Since B is pretty close to a 100 but greater than 100, you could put 110.

Since C is in the middle of both 100 and 200, you could put 150 because it's in the middle of both numbers.

Since D is in between C which is 150 and 200, you could put 175 as that is half of both numbers.

Since E is close to 200 but bigger than D which is 175, you could put 180.

Answer:

Acute angle

OLN angle

Step-by-step explanation:

The actual distance between Dallas and Austin in miles is 180 miles.

Conversion of units means to convert between different units of measurement for the same quantity. Example of units are - m, cm, litre.

Given is the distance between Dallas and Austin on a map is about 9 centimeters. The map uses a scale in which 1 centimeter represents 20 miles.

The maps use scale in order to depict large distances with very small length measurements. As mentioned in the question - 1 cm represents 20 miles. This scale shrinks 20 miles of distance into 1 cm

Distance between Dallas and Austin on a map - 9 cm

On map - 1 cm = 20 miles

Therefore, 9 cm will be equivalent to (9 x 20) or 180 miles.

Hence, the actual distance between Dallas and Austin in miles is 180 miles.

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Answer:

it's a chemical change.

Step-by-step explanation:

a raw egg is converted into a hard boiled one by chemical changes happening inside it. Its also an irreversible change

Answer: 9

Step-by-step explanation:

1. To divide by 2 you need an even number, and the closest even number below 19.5 is 18.

2. 18 feet divided by 2 feet per piece of rope equals nine pieces of rope.

Answer:C = 1.75f

Step-by-step explanation:

C = Cost
F = Fabric in yards
Depending on the amount of fabric in yards she will buy that is the amount she spends.

A) The type of function that can be used to describe the value of the investment after a fixed number of years using option 1 and option 2 are respectively; Linear Function and Exponential function.

B) One function for each option to describe the value of the investment f(n), in dollars, after n years.;

Option 1; f(n) = n + 100

Option 2; f(n) = n + 100x

C) The amount from option 1 after 20 years would be 3000 and the amount from option 2 after 20 years would be 4900

A) For option 1, the linear function can be used to describe the value of the investment after a fixed number of years. This reason is that, in option one, the amount increases by a fixed amount every year.

For option 2, the exponential function can be used to describe the value of the investment after a fixed number of years. The reason is that, in option 2, the amount increase is higher than the previous year.

B) For option 1, the function is;

f(n) = n + 100

For option 2, the function is;

f(n) = n + 100x

C) After 20 years, the amount from option 1 would be 3000 and the amount from option 2 would be 4900. Thus, there is a difference of 1900.

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A graph represents the inequality 2.5 is less than the product of −0.5 and a number is: D. number line with open circle on point negative 5 and arrow shaded to the right.

A number line can be defined as a type of graph with a graduated straight line which is composed of both positive and negative numbers that are placed at equal intervals along its length.

In order to solve this word problem, we would assign a variable to the number and then translate the word problem into an algebraic equation as follows: Let x represent the number.

Translating the word problem into an algebraic equation, we have;

2.5 < -0.5x

Next, we would solve the given inequality as follows:

2.5/0.5 < -0.5x/0.5

5 < -x

x > -5

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17/28 of all the letters are X's.

Answer:

a) ∠13

b) ∠13

c) ∠2

Step-by-step explanation:

a) ∠ 8  + ∠13 = 180°  

Co - interior angles are supplementary, when m // l

b) ∠5 ≅ ∠13

If m // l, the corresponding angles are congruent.

c) ∠5 + ∠2 = 180°

∠5 and ∠2 are co interior angles and they are supplementary if a // b.

Answer:

The stadium’s seating options will include premium seats (boxes closest to the action), medium-priced seats, and budget-friendly bleachers. Your design calls for 4,500 upper-deck premium seats and 7,500 lower-deck premium seats. The team’s policy is to have a 3:2 ratio of premium seats to bleacher seats. How many bleacher seats will the stadium include?

Answer: 8,000 bleacher seats. 4,500 + 7,500 premium seats = 12,000. 12,000/x = 3/2. x = 8,000.

Answer:

A = 135 cm²

Step-by-step explanation:

the area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

here h = 9 , b₁ = 19 , b₂ = 11 , then

A = [tex]\frac{1}{2}[/tex] × 9 × (19 + 11) = 4.5 × 30 = 135 cm²

Answer:

C. t = 3/5

Step-by-step explanation:

[tex]10t + 4 - 2t = 2 - 2(t - 4)[/tex]

[tex]4 + 8t = 2 - 2t + 8[/tex]

[tex]4 + 8t = 10 - 2t[/tex]

[tex]4 + 10t = 10[/tex]

[tex]10t = 6[/tex]

[tex]t = .6 = \frac{3}{5} [/tex]