How do I solve
4(x-1) =2(6-2x)​

The vοlume οf the pyramid is 64 cubic centimeters (cm^3).

The vοlume οf a pyramid is given by the fοrmula V = (1/3) Bh, where B is the area οf the base and h is the height.

In this case, the base οf the pyramid is a square with side length s = 8 cm, sο its area is [tex]B = s^2 = 8^2 = 64 cm^2[/tex].

The height οf the pyramid is h = 3 cm.

Therefοre, the vοlume οf the pyramid is:

[tex]V = (1/3) Bh = (1/3) (64 cm^2) (3 cm) = 64 cm^3[/tex]

Hence, the vοlume οf the pyramid is 64 cubic centimetres (cm^3).

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The cost per foot of redwood is $42.37, and the cost per foot of pine is $90.65.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Let's use the variables r and p to represent the cost per foot of redwood and pine, respectively.

From the first purchase, we can set up the following system of equations:

50r + 90p = 292 (equation 1)

90r + 70p = 406 (equation 2)

To solve for r and p, we can use the method of substitution. Solving equation 1 for r, we get:

r = (292 - 90p) / 50

Substituting this expression for r into equation 2, we get:

90[(292 - 90p) / 50] + 70p = 406

Multiplying both sides by 50 to clear the fraction, we get:

162 - 27p + 70p = 4060

Combining like terms, we get:

43p = 3898

Dividing both sides by 43, we get:

p = 90.65

So the cost per foot of pine is $90.65.

To find the cost per foot of redwood, we can substitute this value of p into equation 1 and solve for r:

50r + 90(90.65) = 292

50r = 2118.5

r = 42.37

So the cost per foot of redwood is $42.37.

Therefore, the cost per foot of redwood is $42.37, and the cost per foot of pine is $90.65.

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Answer:25

Step-by-step explanation: easy

Therefore , the solution of the given problem of area comes out to be

option B 864 sq. centimetres is the correct response.

The amount of area it takes to cover the outside is a good indicator of its overall size. When calculating a trapezoidal shape surface, the immediate environs are taken into account. The surface area of something determines its overall measurements. The internal water capacity of a cuboid is the sum of the limits for each of its six rectangular edges. Utilize the following technique to determine the box's dimensions: The area is the same in 2lh, 2lw, but also 2hw (SA). The area is represented by the adaptable shape's face.

Here,

The following algorithm determines a cube's surface area:

=> SA = 6s²

where s represents the cube's edge lengths.

=> S =12 cm in this instance.

The result of substituting into the algorithm is:

=> SA = 6 (12)²

=> 6 (144 )²

=> 864 square centimetres.

The cube's surface size is 864 sq. cm as a result.

B) 864 sq. centimetres is the correct response.

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Answer:

164

Step-by-step explanation:

If a water sample shows 0.37 grams of some trace element for every cubic centimeter of water.  Terrence has collected 841.51 grams of the trace element.

First, we need to find the volume of the cylinder container:

Volume of cylinder = π(radius)² height)

= π(7.9cm)²(11.6cm)

= 2,274.37 cm³

Amount of trace element = concentration x volume

= 0.37 grams/cm³ x  2,274.37 cm²

= 841. 51 grams

Therefore, Terrence has collected  841.51 grams of the trace element.

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e. Affirming the Consequent. The argument takes the form of "If P then Q. Q, therefore P."

Consequent is an outcome or result of an event, action, or decision. It is the result of a cause or premise. Consequents are usually expected and predictable, and can be measured or observed. Consequents are important in the study of cause and effect relationships and can be used to determine the success or failure of certain actions. Consequents can also be used to measure the degree of success or failure of certain objectives. Consequents are often used in decision-making, as well as in research and problem-solving, to help determine the best course of action and the best solution.

In other words, the conclusion (Benji's parents buy him a puppy for Christmas) is based on the premise that Benji learns important care-giving skills.

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The value of the expression 1 / 3x² when x equals 6 is 1/108.

Given the expression in the question;

1 / 3x²

When x = 6, value of expression = ?

The expression 1 / 3x² is a mathematical formula that involves the variable "x".

When we substitute x = 6 into the expression, we are asked to calculate the value of the expression when x is equal to 6.

To evaluate the expression, we simply substitute x = 6 into the expression and simplify:

1 / 3x²

Plug in x = 6

1 / 3(6)²

Raise 6 to the power of 2 and get 36

= 1/(3 × 36)

= 1/108

Therefore, the value of the expression is is 1/108.

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Answer:521.32

Step-by-step explanation:

.3 represents your tenths

the 2 in .32 represents your hundredths

to round, you look at the number next to your two on the right which is 1

since 1 is less than 5 you leave it the same and eliminate the rest of the numbers that follow it

Correct option is D. randomly sampling 50 batteries throughout the day and testing to see if they work would provide the most valid results.

A sample is described as a smaller, more manageable representation of a larger group. a smaller population with characteristics of a larger one. A sample is used in statistical analysis when the population size is too large to include all participants or observations in the test.

The sample may be biased if it is taken from the first 25 batteries made each day (option A) or the last 25 batteries made each day (option B).

The first and final batteries made each day could not be an accurate representation of the total quality of the batteries produced that day if the battery manufacturing process is not consistent throughout the day.

Although battery quality can change during the day, sampling the first 50 batteries produced each day (option C) may also add bias into the sample.

The ideal course of action is to randomly select 50 batteries throughout the day (option D), since this helps to ensure that the sample is reflective of the general caliber of batteries manufactured that day.

Random sampling reduces the possibility of bias into the sample.

A more accurate image of the quality of the batteries manufactured can be obtained using this method, which is also more likely to capture any variations in battery quality over the day.

Therefore, option D would provide the most valid results.

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Answer:

The team was penalized 10 yards on each play.

First three sum 1/10 + 2/10 + 4/10 Proof: When the numbers in the denominator have the same value, fractions can be compute only with the sum of numerator values and the denominator doesn’t change. 1/10 + 2/10 + 4/10 = 1+2+4 / 10 = 7/10 Second three sum 1/10+1/5 + 2/5, Proof: such kind of fractions can be computed as follows: 1/10 + (1+2 )/5 (same denominators). 1/10 + (1+2 )/5= 1/10 + 3/5= 5x1 +10x3 / 5x10 = 5+30 /50 =35/50, by simplifying by 5, 35/50=7/10 The third three sum is 5/10+ 3/15+8/20,it can be computed by using the same method as given above

Hope it helps

Answer:

28

Step-by-step explanation:

you add up all the numbers and divide by the number of numbers there is

16+50+14+20+40=140

140/5=28

Answer: 4/5 is equal to 8/10

Step-by-step explanation:

The simplified forms are;

1) 2x[tex]y^2[/tex]

2) [tex]x^2y^3[/tex]

3) [tex]2xy^3z^5[/tex]

4)[tex]5p^2q[/tex]

5) [tex]5a^3b^5c^3/2[/tex]

6)[tex]4x^4y^5/3z^3[/tex]

7)[tex]7a^3b^3/2[/tex]

8) [tex]x^2y^3z^6[/tex]

9)-4a

10) [tex]3xy^5z^13/2[/tex]

To simplify a surd, you need to find the largest perfect square factor that divides the number under the square root symbol.

We can see that the surds here can be reduced to the simplest forms when we apply the basics of the rules of exponent which have been used to show the simplified forms as shown here.

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hi

here is the answer

i hope it helps

good luck:))

Answer:

Step-by-step explanation:

The cable company offers Erik 3 free months of cable if he signs a contract with them for $40 per month. This means that Erik will pay for (m - 3) months of cable service, since he will get 3 months for free. So the cost of the cable service for (m - 3) months is:

Cost = $40 per month x (m - 3) months

Cost = $40m - $120

We know that Erik spent $680 for the cable television service. So we can set up an equation to relate the cost to the number of months:

$40m - $120 = $680

To solve for m, we can isolate the variable on one side of the equation:

$40m = $800

m = 20

Therefore, Erik will have cable television service for 20 months with this deal.

The given piecewise function is not continuous.

Continuous function is a function such that a continuous variation of the argument induces a continuous variation of the value of the function.

Given is the piecewise function as -

f(x) = {(x² - 2x - 8)/(x + 2)}              x ≠ -2

f(x) = {k}                        x = - 2

At {x} = - 2, the function is not defined and we get -

k = {(-2)² - 2(-2) - 8)/(- 2 + 2)} = {(-2)² - 2(-2) - 8)/0} = ∞

So, the function is not continuous.

Therefore, the given piecewise function is not continuous.

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Answer:

12723.5(cm^2)

Step-by-step explanation:

the area of the circle

S=Tur^2

The sems-circle is s.=1/2 s =1/2Tur^2

The doctor should order a prescription of 0.8906 mL of the 0.9 g/mL solution for each dose.

What is the density?

Density is a physical property of matter that measures the amount of mass per unit volume. It is calculated by dividing the mass of an object or substance by its volume. The resulting number represents the amount of matter, or mass, that is present in a given volume.

The formula for density is:

Density = Mass / Volume

First, we need to convert the weight of the patient from kilograms to pounds, as the recommended dosage is in mg/lb:

72.7 kg x 2.205 lbs/kg = 160.305 lbs

The recommended dosage is 5 mg/lb, so for a 160.305 lbs patient, the total dosage per dose would be:

160.305 lbs x 5 mg/lb = 801.525 mg

Now we need to convert this dosage from mg to mL, using the concentration of the solution, which is 0.9 g/mL:

1 g = 1000 mg, so 0.9 g = 0.9 x 1000 = 900 mg

To convert mg to mL, we can use the density formula:

Density = Mass / Volume

Rearranging the formula to solve for volume, we get:

Volume = Mass / Density

So, the volume of solution needed for each dose would be:

Volume = 801.525 mg / 900 mg/mL

Volume = 0.8906 mL

Hence, the doctor should order a prescription of 0.8906 mL of the 0.9 g/mL solution for each dose.

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Assuming the trend continues, the next 12 animals will include 4 sheep.

Number is a mathematical concept that represents a quantity or amount. It is usually used to identify a specific value or set of values that can be used for calculation and measurement. Numbers are used in many different fields, including mathematics, science, engineering, and economics. They help us to keep track of quantity and count objects, measure distances and time, and even help to solve problems. Numbers are an essential part of our everyday lives and are essential for understanding the world around us.

This is calculated by taking 2 sheep from the initial group of 8 animals and then multiplying that number by the additional 12 animals for a total of 4 sheep.

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Answer:

2.25

Step-by-step explanation:

3/8 or .375

You can find slope by doing rise/run (in fraction form) Rise is counting up or down spaces from one point until you hit the line of the next point. And then the run is counting over to the next point on the line. the number of spaces you counted up or down is the numerator and the run is the denominator.

Answer: Along the shores of Gitche Gumee

Step-by-step explanation:

To determine the domain and range of (g f) (x), we first need to find the composition of the functions f(x) and g(x):

(g f) (x) = g(f(x)) = g(2/(x^2-1)) = 2/(x^2-1) + 1

The domain of f(x) is all real numbers except x = -1 and x = 1, since these values would make the denominator equal to zero. Therefore, the domain of (g f) (x) is also all real numbers except x = -1 and x = 1.

To find the range of (g f) (x), we can start by finding the range of f(x). Since the denominator of f(x) is always positive (except at x = -1 and x = 1), the range of f(x) is all real numbers except 0.

When we add 1 to f(x), we shift the range of f(x) up by 1 unit. So, the range of (g f) (x) is all real numbers except 1.

Therefore, the domain of (g f) (x) is all real numbers except x = -1 and x = 1, and the range of (g f) (x) is all real numbers except 1.

Option B

Answer:

15.

Step-by-step explanation:

Given: simplify 3³- 3²-3

First, write the equation:

3³- 3²-3

Then using BODMAS, complete the 'power of' numbers:

27 - 9 - 3

Then subtract 27 from 9:

18 - 3

Finally subtract 18 from 3:

= 15

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hope it helps! :)

Answer:

Step-by-step explanation:

(a) Since the current entering and leaving the intersection of wires must be equal, we have:

x + y = 18 (current entering the top intersection)

z + w = 18 (current leaving the top intersection)

x + z = 9 (current entering the bottom intersection)

y + w = 9 (current leaving the bottom intersection)

We can solve this system of equations using substitution or elimination. For example, we can eliminate w by adding the first two equations and subtracting the last two equations:

2x + 2y + 2z = 36

2y + 2z - 2x = 0

2z - 2x = 9

Solving for z in terms of x, we get:

z = (x + 9/2)

Substituting this into the first equation, we get:

x + y = 18

Substituting z in terms of x into the second equation, we get:

w = (18 - z) = (18 - x - 9/2) = (27/2 - x)

Therefore, the solution in terms of x, y, z, and w is:

(x, y, z, w) = (x, 18 - x, x + 9/2, 27/2 - x)

(b) To know all of the currents exactly, we need to measure the current in any one wire that is not already determined by the system of equations. From part (a), we see that w is determined in terms of x, y, and z. Therefore, we should measure the current in wire x or y to know all of the currents exactly.

Therefore , the solution of the given problem of trigonometry comes out to be forms an angle with the horizontal of about 11.71 degrees.

A relationships between cubic splines and triangle maths  astrophysics is believed to have been created when the various fields came together. Many metric problems can be solved or the results of their calculation can indeed be determined with the help of precise mathematical methods. Trigonometry is the study of six basic trigonometric calculations. .

Here,

The tangent function, which is referred to as the ratio of the opposite side (the height drop) to the adjacent side, can be used to determine the angle that Highland Drive forms with the horizontal (the horizontal distance).

The angle's tangent in this situation can be written as:

=> tan(θ) = adjacent/opposite = 14.2/70

We can use a computer to determine that the angle's tangent is roughly 0.2029.

By taking the inverse tangent (also referred to as the arctangent) of this number, we can determine the angle itself:

=> 11.71 degrees are equal to theta = arctan(0.2029)

Highland Road thus forms an angle with the horizontal of about 11.71 degrees.

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Answer:

h'(1) = 19

Step-by-step explanation:

if h(x) = f(x) + g(x), and f(x) = x³ and g(x) = 4x⁴,

then h(x) = (x³) + (4x⁴)

h(x) = x³ + 4x⁴

h'(x) is the derivative of h(x), which = 3x² + 16x³. Thus, h'(1) = 3(1)² + 16(1)³ = 19