pls help me :<

which of the following is equivalent to
(8x + 7)(5z - 4)

a) (8x)(5x) +(7) (-4)
b) (8x)(5x)+7(5x - 4)
c) (8x + 7)(5x) + (8x + 7)(-4)
d) (8x + 7)(5x) + (8x + 7)(4)​

Answer:

C

Step-by-step explanation:

In order to find the slope, you can use rise over run.

(y₂ - y₁) over (x₂ - x₁)

You can use the points (1, 1) and (2, -1). y₂ can be -1 and y₁ can be 1, but you could do either as long as you make x₁ and x₂ from the corresponding points (so y₁ and x₁ are one coordinate pair and y₂ and x₂ are the other). This way, you get -2 as your slope. Then, the table shows that y = 3 when x is 0, so that's your y-intercept, which is how you get +3. Hope this helps!

y = -2x + 3 will be the equation represents the data in the table shown.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, A data Set of the value of x and y that represents a linear equation.

From the slope intercept form of a linear equation,

y = mx + b,

where m is the slope

b is the y-intercept

y- intercept is point in line where the value of x will be 0.

From our data set,

y - intercept = b = 3 (since, at x = 0, y is 3)

And Slope, (m) = (y₂ - y₁)/(x₂ - x₁)

in our case,

m = (1-3)/(1-0)(from first two values of data set)

m = -2

Thus,

Equation of line:

y = -2x + 3

Therefore, The equation of line for the given data set will be y = -2x + 3.

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Answer:

55-11=44 and 44-11=33 so 33 it is

Step-by-step explanation:

Well, 5 to 11 is just saying 5:11 just in a different way. This (:) means (to)  also. So how you get the roof to a 33 foot run is to change the 5 into a 3 and the you leave the 11 alone and then you 33 -foot run. Well I really don't really know if that is ther correct anser but if it isn't then read someone's other answer because I don't really know what kind of math this is and I really need to know what grade it is and then I will look it up on the internet. Because some times I get thinmgs wrong if I  don't remember them so I need someone to explain how to do it

Answer: 15 feet

Step-by-step explanation: took the test on edge

The horizontal asymptote of function f(x) is y=6.5, which is a straight line, which means that even if time is infinite, the pH of the mouth will not rise above 6.5, which is the normal pH of the mouth.

A function's horizontal asymptote is a horizontal line with which the function's graph appears to coincide but does not actually coincide. The horizontal asymptote is used to determine the behavior of the function.

When either lim x f(x) = k or lim x - f(x) = k, the horizontal asymptote of a function y = f(x) is a line y = k. . It is commonly abbreviated as HA. In this case, k is a real number that the function approaches when x is extremely large or extremely small.However, the maximum number of asymptotes that a function can have is 2.

Given,

\(f(x)=\frac{6.5x^2-89.4x+3734}{x^2+576}\)

The horizontal asymptote of the function f(x) can be determined by

\(y=\lim_{x \to \infty} f(x)\\\\=\lim_{x \to \infty}\frac{6.5x^2-89.4x+3734}{x^2+576}\\\\=\lim_{x \to \infty}\frac{x^2(6.5-\frac{89.4}{x}+\frac{3734}{x^2})}{x^2(1+\frac{576}{x^2})}\\\\=\lim_{x \to \infty}\frac{(6.5-\frac{89.4}{x}+\frac{3734}{x^2})}{(1+\frac{576}{x^2})}\\\\=\frac{(6.5-\frac{89.4}{ \infty}+\frac{3734}{ \infty})}{(1+\frac{576}{ \infty})}\\\\=\frac{6.5-0+0}{1+0}\\\\=\frac{6.5}{1}=6.5\)

Thus, the horizontal asymptote of function f(x) is y=6.5 which is straight line which means even the time reaches infinity the pH of mouth will not increase more than 6.5, which is the normal pH of mouth.

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Your question is incomplete, here is the complete question.

The function \(f(x)=\frac{6.5x^2-89.4x+3734}{x^2+576}\) models the pH level f(x) of a mouth x minutes after eating food containing sugar. The graph of this function is shown.

What is the equation is the horizontal asymptote associated with is function? Describe what this means in terms of mouth's pH level over time.

Step-by-step explanation:

To solve the given equations, let's assign variables to each equation and solve them step by step.

Let's assume:

a = x

b = y

c = z

d = w

e = v

From the given equations:

a * b = 1 -> x * y = 1 (Equation 1)

b * c = 4 -> y * z = 4 (Equation 2)

c * d = 9 -> z * w = 9 (Equation 3)

d * e = 16 -> w * v = 16 (Equation 4)

e * a = 25 -> v * x = 25 (Equation 5)

Now, let's solve the equations using substitution:

From Equation 1 (x * y = 1), we can rewrite it as y = 1/x.

Substituting y in Equation 2, we get (1/x) * z = 4, which gives us z = 4x.

Substituting z in Equation 3, we have (4x) * w = 9, which gives us w = 9/(4x).

Substituting w in Equation 4, we get (9/(4x)) * v = 16, which simplifies to v = (16 * 4x)/9.

Finally, substituting v in Equation 5, we have [(16 * 4x)/9] * x = 25.

Simplifying the equation, we get:

(64x^2)/9 = 25.

To solve for x, we can cross multiply and solve the quadratic equation:

64x^2 = 225.

Dividing both sides by 64, we get:

x^2 = 225/64.

Taking the square root of both sides, we have:

x = ±(√(225/64)).

So, x = ±(15/8).

Now, substituting the values of x in the respective equations, we can find the values of y, z, w, and v.

For x = 15/8:

y = 1/(15/8) = 8/15

z = 4 * (15/8) = 30/4 = 15/2

w = 9/(4 * (15/8)) = 9/(30/8) = 9 * (8/30) = 12/5

v = (16 * 4 * (15/8))/9 = (60/2)/9 = 60/18 = 10/3

For x = -15/8:

y = 1/(-15/8) = -8/15

z = 4 * (-15/8) = -30/4 = -15/2

w = 9/(4 * (-15/8)) = 9/(-30/8) = -9 * (8/30) = -12/5

v = (16 * 4 * (-15/8))/9 = (-60/2)/9 = -60/18 = -10/3

Therefore, the possible solutions for the variables are:

x = 15/8, y = 8/15, z = 15/2, w = 12/5, v = 10/3

or

x = -15/8, y = -8/15, z = -15/2, w = -12/5, v = -10/3.

Note: The solution includes both positive and negative values for the variables.

The value of K is 2.

Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.

We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.

Using the formula for the surface area, we have:

Initial surface area * (scale factor)^2 = Final surface area

50 * K^2 = 200

Dividing both sides of the equation by 50:

K^2 = 200/50

K^2 = 4

Taking the square root of both sides:

K = √4

K = 2

Therefore, the value of K is 2.

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We can use the trigonometric ratios to solve for the unknown sides and angle:

Since A = π/3, we know that the opposite side (a) is 6 and the adjacent side (b) is unknown.

sin(A) = opposite/hypotenuse

sin(π/3) = 6/c

√3/2 = 6/c

c = 12/√3 = 4√3

cos(A) = adjacent/hypotenuse

cos(π/3) = b/4√3

1/2 = b/4√3

b = 2√3

Finally, we can use the Pythagorean theorem to find the remaining side:

a^2 + b^2 = c^2

6^2 + (2√3)^2 = (4√3)^2

36 + 12 = 48

√48 = 4√3

Therefore, the unknown sides are b = 2√3 and c = 4√3, and the unknown angle is B = π/2 - π/3 = π/6.

4.0 mL of marcaine will be needed to draw up to equal the 1%.

Marcaine is a brand name for the medication bupivacaine, which is a local anesthetic used to numb a specific area of the body during a surgical or medical procedure.

To determine the amount of marcaine that is needed to be drawn up to equal the 1% lidocaine, we can use the following formula:

(Concentration of Lidocaine) / (Concentration of Marcaine) = (Volume of Lidocaine) / (Volume of Marcaine)

In this case, we know that the concentration of lidocaine is 1% and the concentration of marcaine is 0.25%. So we can plug these values into the formula:

1 / 0.25 = (Volume of Lidocaine) / (Volume of Marcaine)

To solve for the volume of marcaine, we can multiply both sides of the equation by the volume of lidocaine:

(Volume of Lidocaine) / (Volume of Marcaine) = 4

Therefore, 4.0 mL of marcaine will be needed to draw up to equal the 1%.

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Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

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

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

Let's call Mindy's height "M". According to the problem, we know that:

Camille's height = 66 inches

Camille's height = 2 * Mindy's height - 20 inches

We can substitute the first equation into the second equation to solve for Mindy's height:

66 inches = 2 * M - 20 inches

We can add 20 inches to both sides of the equation to get:

66 inches + 20 inches = 2 * M

This gives us:

86 inches = 2 * M

To find Mindy's height, we can divide both sides of the equation by 2:

M = 86 inches / 2

So Mindy is 43 inches tall.

Answer:

Mindy is  46 inches

Step-by-step explanation:

Let m = Mindy's height

66 = 2m - 20  Add 20 to both sides

66 + 20 = 2m - 20 + 20

86 = 2m  Divide both sides by 2

\(\frac{86}{2}\) = \(\frac{2m}{2}\)

46 = m

You put in 3 to you piecewise function and 2 to your X value

The equation of the line (y+10)=4(x−3)  or  y=4x−22

We can use the point-slope formula to find an equation for this line.

The point-slope formula states: \((y-y_{1} )=m(x-x_{1} )\)

Where m is the slope and \((x_{1}, y_{1} )\) is a point the line passes through.

Substituting the values from the problem gives:

(y − −10) = 4(x − 3)

(y + 10) = 4(x − 3)

To transform this into the more familiar slope-intercept form we can solve for y:

y + 10 = (4 × x) − (4 × 3)

y + 10 = 4x − 12

y + 10 − 10 = 4x − 12 − 10

y + 0 = 4x − 22

y = 4x − 22

Hence the answer is the equation of the line is (y+10) = 4(x−3)  or  y = 4x−22

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Answer:

(5.5, -1.5)

Step-by-step explanation:

(x, y)midpoint = (x1 + x2)/2 , (y1 + y2)/2

= (6 + 5)/2, (3 - 6)/2

= (11/2, -3/2)

= (5.5, -1.5)

The above image depicts a polygon whose end points are on a cartesian coordinate system.

A system in which the position of a point is specified by coordinates representing its distances from perpendicular lines intersecting at the origin is called the cartesian coordinate system.

The Cartesian plane, named after the mathematician Rene Descartes (1596 - 1650), is a plane with a rectangular coordinate system that assigns a pair of integers to each point in the plane.

The coordinates of the polygon are:
Y (-4, 3)

M (-4, 2)

Q (-2, 0); and

T (0,0).

Cartesian coordinates are also vital tools in most applied geometry fields, such as astronomy, physics, engineering, and many more.

They are the most often used coordinate system in computer graphics, computer-aided geometric design, and other data processing involving geometry.

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Answer: 260

Step-by-step explanation:

Use proportions:

65/25 = x/100

cross multiply the proportions:

25x = 6500

solve your equation:

x = 260

The number is 260.

Let's start by finding the number we're working with.

We know that 25% of the number is 65, so we can set up an equation:

0.25x = 65

To solve for "x", we can divide both sides of the equation by 0.25:

x = 65 / 0.25

x = 260

So the number we're working with is 260.

Next, we need to find 40% of the same number:

0.40(260) = 104

Now we can use this information to find 15% of the same number:

We can set up a proportion:

40% is to 104 as 15% is to x

0.40/104 = 0.15/x

To solve for "x", we can cross-multiply:

0.40x = 104(0.15)

0.40x = 15.6

x = 39

So 15% of the same number is 39.

Answer:

2.73

Step-by-step explanation:

this is because the nunber after 7 which is 2 was less than 5 so it stays the same

number after 2 which was 6 was more than 5 so it rounds up to 3

Answer:

6 and 7

Step-by-step explanation:

The general solution of the differential equation is: y = c1 e^(3t) cos(t) + c2 e^(3t) sin(t), where c1 and c2 are arbitrary constants determined by the initial or boundary conditions.

The given differential equation is a second-order homogeneous linear differential equation with constant coefficients. Its characteristic equation is obtained by assuming a solution of the form y = e^(rt), where r is a constant. Substituting this into the differential equation, we get:

r^2 e^(rt) - 6r e^(rt) + 10 e^(rt) = 0

Dividing both sides by e^(rt) (which is non-zero), we get:

r^2 - 6r + 10 = 0

Solving for r using the quadratic formula, we get:

r = (6 ± sqrt(6^2 - 4(1)(10))) / 2

r = 3 ± i

Therefore, the general solution of the differential equation is:

y = c1 e^(3t) cos(t) + c2 e^(3t) sin(t)

where c1 and c2 are arbitrary constants determined by the initial or boundary conditions.

This solution consists of a linear combination of two functions: the exponential function e^(3t) and the periodic function cos(t) or sin(t), which oscillates between -1 and 1. The exponential function represents the growth or decay of the system, while the periodic function represents the oscillations or vibrations of the system. The constants c1 and c2 determine the amplitude and phase of the oscillations, respectively. The behavior of the system depends on the signs and magnitudes of the real and imaginary parts of the roots, which determine whether the solutions are overdamped, critically damped, or underdamped.

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a). To maximize production within the budget, 600 units of labor and 100 units of capital should be purchased. b). The maximum production under the budgetary constraint is approximately 8,366 units.

a). To maximize production, we need to allocate the budget efficiently between labor and capital. We can calculate the number of units of labor and capital by dividing the budgeted amount by the cost per unit. The budget of $576,000 divided by the cost of labor per unit ($400) gives us 1,440 units of labor. Similarly, dividing the budget by the cost of capital per unit ($2,400) gives us 240 units of capital. However, this allocation does not maximize production within the budgetary constraint.

b). To find the optimal allocation, we can use the partial derivatives of the production function with respect to L and K. Taking the partial derivative of the production function with respect to L, we get 37.5L^(-0.25)K^0.25. Equating this to the budgeted amount of labor (600 units), we can solve for K, which comes out to be 100 units. Similarly, by taking the partial derivative of the production function with respect to K, we get 12.5L^0.75K^(-0.75). Equating this to the budgeted amount of capital (100 units), we can solve for L, which comes out to be 600 units.

By substituting these values into the production function, we can calculate the maximum number of units of production, which is approximately 8,366 units.

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Answer: 14.08

Step-by-step explanation:

You have to do 0.88 times 16

To determine if the yearbook photo is a dilation of the original photo, we need to compare the dimensions and check if there is a consistent scaling factor between the two.

Original photo dimensions: 4 inches by 6 inches.

Yearbook photo dimensions: 6 2/3 inches by 10 inches.

To check if it's a dilation, we can compare the ratios of corresponding sides:

Ratio of width:

Yearbook photo width / Original photo width = (6 2/3) / 4 = (20/3) / (12/3) = 20/12 = 5/3

Ratio of height:

Yearbook photo height / Original photo height = 10 / 6 = 5/3

The ratios of the corresponding sides are equal, with both being 5/3. This indicates that there is a consistent scaling factor of 5/3 between the original photo and the yearbook photo.

Therefore, the yearbook photo is indeed a dilation of the original photo, and the scale factor is 5/3. This means that each dimension of the yearbook photo is 5/3 times the corresponding dimension of the original photo.

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The condition for the first dark fringe through a single slit of width w is given by w sin(θ) = λ/2.

The condition for destructive interference at the first dark fringe can be found using the path difference between the two waves.

For the first dark fringe, the path difference between the two waves that pass through the edges of the slit must be half a wavelength:

Δx = λ/2

where Δx is the path difference and λ is the wavelength of the light.

The path difference Δx can be related to the width of the slit w and the angle θ that the diffracted wave makes with the central axis of the slit by:

Δx = w sin(θ)

Therefore, the condition for the first dark fringe can be expressed as:

w sin(θ) = λ/2

The condition for the first dark fringe through a single slit of width w is given by w sin(θ) = λ/2.

This means that if the width of the slit and the wavelength of the light are known, the angle θ at which the first dark fringe occurs can be calculated.

This condition arises due to the interference of the diffracted waves from the edges of the slit. When the path difference between these waves is equal to half a wavelength, the waves interfere destructively and produce a dark fringe.

The first dark fringe is observed at the angle θ for which the path difference between the waves passing through the edges of the slit is equal to λ/2.

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Answer: -x^10y^15m^5

Explanation:

The term -x^2 is the same as -1*x^2

Raising -1 to an odd number power leads to -1. So this is why the answer has the negative out front.

For each of the variable terms, multiply the inner and outer exponents. For example, (x^2)^5 = x^(2*5) = x^10.

The general rule is (a^b)^c = a^(b*c).

For the term 'm', think of it as m^1

Answer:

D.-2.25 F

Step-by-step explanation:

ayon lang sana makatulong

The purpose of using prefix in the metric system is to properly sale the basis of the unit so large numeric values can be used effectively.

If the metric system is not properly prefixed it can lead to various inconsistencies in the the numeric values. for example if you go to a computer store and you do not know the scale like (kb, mb, gb, tb) you will get quite confused about what is the sales representative saying

Consider you went to a store to get sugar and you do not know the metric system say(gram, kg, mg) you would not know how much sugar you need directly by taking it in your hands.

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Answer:

Step-by-step explanation:

The triangles are similar but NOT congruent.

3 corresponding angles mean the sides are proportional in length but not necessarily equal.

Answer:

The answer is below

Step-by-step explanation:

Let h represent the height of the tree in meters and t represent the number of years after planting.

Initially a tree of height 1.85 m was planted, i.e. at t = 0, h = 1.85. It can be represented in form of (h, t) as (1.85, 0).

After seven years the height of the tree was 5.30 m, it can be represented as (5.30, 7). Hence the equation can be gotten using:

\(t - t_1=\frac{t_2-t_1}{h_2-h_1} (h-h_1)\\\\t-0=\frac{7-0}{5.30-1.85}(h-1.85)\\\\t= 2.03(h-1.85)\\\\t=2.03h-3.75\)

Answer:

her score would be -22

Step-by-step explanation:

20-42=-22

The value of the objective function at this point is Z = 840.  The solution (7, 7) is feasible.

a. Formulation of linear programming model:To solve this problem, the following linear programming model can be used:x1 = Activity 1 (in units)x2 = Activity 2 (in units)Maximize Z = 60x1 + 50x2 subject to30x1 + 126x2 ≤ 4,752 (Acceptable limit)60x1 + 126x2 ≤ 8,436 (Benefit 1)Step-by-step explanation is given below:Function: Linear Programming modelSolution:

a. Formulation of linear programming model:To solve this problem, the following linear programming model can be used:x1 = Activity 1 (in units)x2 = Activity 2 (in units)Maximize Z = 60x1 + 50x2 subject to30x1 + 126x2 ≤ 4,752 (Acceptable limit)60x1 + 126x2 ≤ 8,436 (Benefit 1)  

b. Checking for feasible solutionsWe need to check the following solutions:(x1, 32) (7, 7) (7, 8) (8, 7) (8, 8) (8, 9) (9, 8)Let us substitute the values in the linear programming model for each solution:Solution: (x1, 32)30x1 + 126(32) = 4,752 + 4,032 = 8,784 > 4,752 (Infeasible)Solution: (7, 7)30(7) + 126(7) = 966 < 4,752 (Feasible)60(7) + 126(7) = 1,092 < 8,436 (Feasible)Solution: (7, 8)30(7) + 126(8) = 5,070 > 4,752 (Infeasible)Solution: (8, 7)30(8) + 126(7) = 5,016 > 4,752 (Infeasible)Solution: (8, 8)30(8) + 126(8) = 5,196 > 4,752 (Infeasible)Solution: (8, 9)30(8) + 126(9) = 5,322 > 4,752 (Infeasible)Solution: (9, 8)30(9) + 126(8) = 5,358 > 4,752 (Infeasible)Therefore, only the solution (7, 7) is feasible.

c. Expressing the model in algebraic form:We have,x1 = Activity 1 (in units)x2 = Activity 2 (in units)Maximize Z = 60x1 + 50x2 subject to30x1 + 126x2 ≤ 4,752 (Acceptable limit)60x1 + 126x2 ≤ 8,436 (Benefit 1)The solution x = (7, 7) is feasible and optimal, with Z = 60(7) + 50(7) = 840.d. Using the graphical method:Below is the graph plotted for the above linear programming model:graph{(y-4752)/126<=-(3/2)x+316}The feasible region is given by the shaded region in the graph. The optimal solution is (7, 7), which is at the point of intersection of the two lines. The value of the objective function at this point is Z = 840.

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Among the given options, the only variable that is a discrete random variable is a) the number of patients in a hospital.

a. the number of patients in a hospital

A discrete random variable is a variable that can only take on a finite or countably infinite set of distinct values. In this case, the number of patients in a hospital can only be whole numbers (e.g., 0, 1, 2, 3, etc.), which is a countable set of values. Therefore, it is a discrete random variable.

b. the average amount of electricity consumed

The average amount of electricity consumed is not a discrete random variable but a continuous random variable. It can take on any real number value within a certain range, and it is not restricted to specific distinct values.

c. the amount of paint used in repainting a building

The amount of paint used in repainting a building can be measured in continuous quantities (e.g., liters or gallons). It is not restricted to specific distinct values, and therefore, it is not a discrete random variable.

d. the average weight of female athletes

Similar to the average amount of electricity consumed, the average weight of female athletes is not a discrete random variable but a continuous random variable. It can take on any real number value within a certain range and is not restricted to specific distinct values.

Among the given options, the only variable that is a discrete random variable is a) the number of patients in a hospital.

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