Write the given equation in standard form.
−7x−5y=3

Answer:

Hey there!

A simple way to think about slope is rise over run. Between any two points on this line, the rise is 3, and the run is -1.

3/-1=-3, so  the slope is -3.

Let me know if this helps :)

Answer: 4b+6a+3c

Step-by-step explanation:

Answer:

22/90.

Step-by-step explanation:

0.24444... * 100 =    24.4444...

0.244444.. * 10   =     2.44444....

Subtract:

0.244444..  * 90    =  22

So the required fraction is 22/90.

Answer:

y = -4x + 1

Step-by-step explanation:

Okay, one way we can find the equation is to plug the x and y values into y = mx + b

We m (slope) is -4 so

y = -4x + b

We want to find b so we plug in x and y (-2 and 9)

9 = -4 (-2) + b

9 = 8 + b

In this case, b is 1

Now we plug this to make our equation,

y = -4x + 1

Hi there!

The question is asking us to find the equation of the line, given that it has a slope of 4, and it passes through (-2,9).

I will go about solving this by using point-slope:

\(\sf{y-y_1=m(x-x_1)}\)

\(\sf{y-9=-4(x-(-2)}\)

\(\sf{y-9=-4(x+2)}\\\sf{y-9=-4x-8}\\\sf{y=-4x-8+9}\\\sf{y=-4x+1}\)

Therefore, the line's equation is y = -4x + 1.

Have a fantastic day!

on the number line the numbers to the left have least value

Answer:

A) 2

Step-by-step explanation:

Because the slope is negative of line 2 the distance is getting smaller

The number of pairs of parallel sides the rotated figure have is 2

Parallel sides or lengths are line segments or lines in the same plane that extend on both sides without intersecting

The shape is given as:

Shape = Rhombus

Rotation= 90 degrees counterclockwise rotation about the vertex G

The rotation transformation is a rigid transformation

This means that when a shape is rotated by 90 degrees counterclockwise about a vertex (in this case, the vertex G), the image of the rotation would have the same properties as the preimage

A rhombus has 2 pairs of parallel sides

This means that the number of pairs of parallel sides the rotated figure have will also be 2 (same as the original shape)

Hence, the number of pairs of parallel sides the rotated figure have is 2

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The internal values of all triangles are worth 180°, so knowing this, just form a 1st degree equation to respond, remembering that the value 180°, will stay after the equal sign of the equation.

The project's payback period is calculated by dividing the initial investment by the annual cash inflows until the cumulative cash inflows equal or exceed the initial investment.

The payback period for Project L is 6.6 years.

The payback period is a simple financial metric used to assess the time required for a project to recover its initial investment. In the case of Project L, the initial outlay is $66,000, and the expected cash inflows are $10,000 per year for 12 years. To calculate the payback period, we divide the initial investment by the annual cash inflows until the cumulative cash inflows equal or exceed the initial investment.

For Project L, the cumulative cash inflows are as follows:

Year 1: $10,000

Year 2: $20,000

Year 3: $30,000

Year 4: $40,000

Year 5: $50,000

Year 6: $60,000

Year 7: $70,000

At the end of the sixth year, the cumulative cash inflows reach $60,000, which is greater than the initial investment of $66,000. Therefore, the payback period for Project L is 6.6 years.

The payback period is a simple measure that provides an indication of how quickly a project can recover its initial investment. It helps organizations assess the liquidity and risk associated with a project. A shorter payback period is generally preferable since it implies a faster recovery of the initial investment.

However, the payback period has some limitations. It does not consider the time value of money or account for the cash inflows beyond the payback period. It also does not take into account the profitability of the project. Therefore, it should be used in conjunction with other financial metrics to make informed investment decisions.

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The solution of the system of equations using Cramer's rule is x = 37/39 and y = 9/39.

The solution of the system of equations using Cramer's rule is calculated as follows;

The given equations are as follows;

9x - 2y = -9

-3x - 8y = 1

The determinant of the coefficient matrix is calculated as;

D = [9      -2]

      [-3     -8]

D = -8(9) - (-3 x - 2)

D = -72 - 6 = -78

The x coefficient is calculated as;

Dx = [-2      -9]

       [ -8       1]

Dx = -2(1) - (-8 x -9)

Dx = -2 - 72 = -74

The y coefficient is calculated as;

Dy = [9      -9]

       [ -3       1]

Dy = 9(1) - (-3 x -9)

Dy = 9 - 27 = -18

The x and y values is calculated as;

x = Dx/D  = -74/-78 = 74/78 = 37/39

y = Dy/D = -18/-78 = 18/78 = 9/39

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The chain rule is a fundamental concept in calculus that allows us to differentiate composite functions, which are functions that are formed by combining two or more simpler functions.

The chain rule states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function with respect to its argument.
In your question,

We have two functions: h(u) and u(x).

The function h(u) depends on the variable u, while u(x) depends on the variable x.

To differentiate h(u) with respect to x, we need to use the chain rule. We can write the chain rule as follows:
dh/dx = dh/du * du/dx
Here, dh/du represents the derivative of the function h(u) with respect to u, while du/dx represents the derivative of the function u(x) with respect to x.

The chain rule tells us that to find the derivative of the composite function h(u(x)), we need to multiply the derivative of the outer function h(u) with respect to its argument u (i.e., dh/du) by the derivative of the inner function u(x) with respect to its argument x (i.e., du/dx).
In other words,

The chain rule allows us to "chain" together the derivatives of the two functions to find the derivative of the composite function.

By applying the chain rule, we can calculate the derivative dh/dx in terms of the derivatives dh/du and du/dx.
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When we apply the chain rule for functions h(u) and u(x), we can express the rate of change of h with respect to x in terms of the rates of change of h with respect to u and u with respect to x. Using the chain rule formula, we have: dh/dx = (dh/du) * (du/dx)

This means that the rate of change of h with respect to x is equal to the product of the rate of change of h with respect to u and the rate of change of u with respect to x. This formula is useful in calculating derivatives in cases where a function is composed of multiple functions nested within each other.

The correct formula should be:

dh/dx = dh/du * du/dx

Now, to answer your question using the chain rule for functions h(u) and u(x), we can follow these steps:

1. Find the derivative of h(u) with respect to u, which is dh/du.
2. Find the derivative of u(x) with respect to x, which is du/dx.
3. Multiply the results of steps 1 and 2 to obtain the derivative of h(u(x)) with respect to x, which is dh/dx.

So, by applying the chain rule to functions h(u) and u(x), we have:

dh/dx = dh/du * du/dx

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A scientific hypothesis is a proposed explanation or prediction based on limited evidence or prior knowledge, which is subject to further investigation and testing.

A guess is a speculative, unsupported statement without any logical basis, whereas a hypothesis is an educated assumption derived from existing knowledge, observations, or theories. Unlike a guess, a hypothesis is testable and can be supported or refuted by evidence gathered through scientific methods.

Scientists need a hypothesis to provide a framework for their research and guide their investigations. It helps them define the specific question they want to answer and provides a starting point for designing experiments or making observations. By formulating a hypothesis, scientists can systematically evaluate and analyze data, ultimately leading to a deeper understanding of the phenomenon under investigation.

There are indeed scientific hypotheses that cannot be directly tested or proven due to practical or ethical constraints. For example, hypotheses related to historical events that occurred in the distant past may not have accessible evidence for direct testing. Additionally, some questions related to consciousness, subjective experiences, or philosophical concepts may lie beyond the scope of scientific inquiry, as they may not be objectively measurable or observable.

While science has its limitations, it is a powerful tool for investigating and understanding the natural world. However, there are questions that fall outside the realm of scientific inquiry and require other methods of investigation, such as philosophical or ethical considerations.

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Answer:

B

Step-by-step explanation:

Area = length x width

Total surface area

=2(8*3) + 2(10*3) + 2(10*8)

=48+60+160

=268

1. Angles BAP and CAP are congruent by the definition of the angle bisector theorem.

2. Segment AP is congruent to itself by the reflexive property.

The angle bisector of a triangle divides a triangle into two parts, from an angle, and the angle is divided into two equal parts.

The bisected angle in this problem is given as follows:

Angle A.

The two new angles are given as follows:

<BAP and <CAP.

Hence they are congruent by the definition of the angle bisector theorem, and congruent is the word that completes the blank for item 1.

For item 2, the reflexive property is the property that states that a segment is always congruent to itself. Hence the reflexive property is the work that completes the blank for item 2.

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To calculate the cost of driving a diesel tractor trailer truck for 175.0 miles, we need to determine the number of gallons of fuel required and then multiply it by the cost per gallon.

Calculate the number of gallons of fuel needed. Given that the truck gets 8.500 miles per gallon, we divide the total distance (175.0 miles) by the fuel efficiency: 175.0 miles / 8.500 miles per gallon

= 20.59 gallons (approximately)

Calculate the cost of the fuel.Since diesel fuel costs $3.599 per gallon, we multiply the number of gallons needed by the cost per gallon: 20.59 gallons x $3.599/gallon = $73.89 (approximately) Therefore, it will cost you approximately $73.89 to drive the diesel tractor trailer truck for 175.0 miles, assuming it gets 8.500 miles per gallon and diesel fuel costs $3.599 per gallon.

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Answer:-3/4

Step-by-step explanation: slope formula (y2-y1)/(x2-x1)

plug everything in

The displacement and distance traveled depend on the given time interval.

To find the displacement, we need to integrate the velocity function from 0 to 5 or 0 to 5π, depending on the given time interval.

If the time interval is [0,5], we have:

Displacement = ∫[0,5] v(t) dt
Displacement = ∫[0,5] 6cos(t) dt
Displacement = [6sin(t)] from 0 to 5
Displacement = 6sin(5) - 6sin(0)
Displacement ≈ 2.785 meters

If the time interval is [0,5π], we have:

Displacement = ∫[0,5π] v(t) dt
Displacement = ∫[0,5π] 6cos(t) dt
Displacement = [6sin(t)] from 0 to 5π
Displacement = 0 - 6sin(0)
Displacement = 0 meters

To find the distance traveled, we need to integrate the absolute value of the velocity function over the given time interval.

If the time interval is [0,5], we have:

Distance = ∫[0,5] |v(t)| dt
Distance = ∫[0,5] |6cos(t)| dt
Distance = ∫[0,π/2] 6cos(t) dt + ∫[π/2,5] -6cos(t) dt
Distance = [6sin(t)] from 0 to π/2 + [-6sin(t)] from π/2 to 5
Distance = 6 - 6sin(5) ≈ 2.215 meters

If the time interval is [0,5π], we have:

Distance = ∫[0,5π] |v(t)| dt
Distance = ∫[0,5π] |6cos(t)| dt
Distance = ∫[0,π] 6cos(t) dt + ∫[π,2π] -6cos(t) dt + ∫[2π,3π] 6cos(t) dt + ∫[3π,4π] -6cos(t) dt + ∫[4π,5π] 6cos(t) dt
Distance = [6sin(t)] from 0 to π + [-6sin(t)] from π to 2π + [6sin(t)] from 2π to 3π + [-6sin(t)] from 3π to 4π + [6sin(t)] from 4π to 5π
Distance = 0 meters

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The double integral for \(3xy^2/x^2+1\) is 8㏑(2).

\(3\int\limits^1_0 \int\limits^2_2 \frac{xy^2}{x^2 + 1} \, dy dx\)  

3* 1/2 (㏑(2) - ㏑(1) ) * 1/3 (8+8)

8㏑(2)

A multiple integral in mathematics is a definite integral of a function with multiple real variables, such as f(x, y), or f(x, y) (x, y, z). In the real-number plane, integrals of functions of two variables over an area are referred to as double integrals, and integrals of functions of three variables over a region in real-number three-dimensional space are referred to as triple integrals.

The Cauchy formula for repeated integration can be used to calculate multiple integrals of a single-variable function.

The double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane that contains its domain, just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis.

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Therefore, the probability of rolling an odd number on the die and flipping a heads on the coin is 1/4.

The probability of rolling an odd number on a fair die is 3/6 or 1/2.

The probability of flipping a heads on a fair coin is 1/2.

Since the die roll and the coin flip are independent events, we can multiply their probabilities to find the probability of both events occurring together:

P(rolling an odd number AND flipping a heads) = P(rolling an odd number) x P(flipping a heads)

P(rolling an odd number AND flipping a heads) = (1/2) x (1/2)

= 1/4

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Okay, here we have this:

Considering the provided functions, we are going to complete the requested table, so we obtain the following:

f(1):

f(x) = −x² + 4x + 12

f(1) = −1² + 4(1) + 12

f(1) = −1 + 4 + 12

f(1) = 15

f(2):

f(x) = −x² + 4x + 12

f(2) = −2² + 4(2) + 12

f(2) = −4 + 8 + 12

f(2) = 16

f(3):

f(x) = −x² + 4x + 12

f(3) = −3² + 4(3) + 12

f(3) = −9 + 12 + 12

f(3) = 15

f(4):

f(x) = −x² + 4x + 12

f(4) = −4² + 4(4) + 12

f(4) = −16 + 16 + 12

f(4) = 12

f(5):

f(x) = −x² + 4x + 12

f(5) = −5² + 4(5) + 12

f(5) = −25 + 20 + 12

f(5) = 7

f(6):

f(x) = −x² + 4x + 12

f(6) = −6² + 4(6) + 12

f(6) = −36 + 24 + 12

f(6) = 0

g(1):

g(x)=x+2

g(1)=1+2

g(1)=3

g(2):

g(x)=x+2

g(2)=2+2

g(2)=4

g(3):

g(x)=x+2

g(3)=3+2

g(3)=5

g(4):

g(x)=x+2

g(4)=4+2

g(4)=6

g(5):

g(x)=x+2

g(5)=5+2

g(5)=7

g(6):

g(x)=x+2

g(6)=6+2

g(6)=8

And now we will proceed to find the solution of f(x)=g(x):

f(x)=g(x)

−x² + 4x + 12=x+2

−x² + 3x + 10=0

-(x+2)(x-5)=0

Then:

x+2=0 or x-5=0

x=-2 or x=5

Finally we obtain that the values that are solution to f(x)=g(x) are -2 and 5. Then the correct answer is the third option.

Answer:

Step-by-step explanation:

diagonal=\(\sqrt{10^2+10^2}\)

diagonal=\(\sqrt{200}\)

diagonal=14.1421356

The desirable heart rate for a 46 year old women is 115.1

Expression means a number, a variable, or a combination of numbers and variables and operation symbols.

Given:

The medical researchers has found the desirable heart rate of the person through the following expression

For men the expression is

r = 165 - 0.75a

For women the expression is

r = 145 - 0.65a

Here r represents the heart rate and a represents the person's age.

Here we need to find the desirable heart rate of the 46 year old women

So, the value of a is 46,

Now we have to apply the value on the given expression in order to solve it,

So,

r = 145 - (0.65 x 46)

r = 145 - 29.9

r = 115.1

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Answer:

26°

Step-by-step explanation:

The angle 123° is on a straight line. All angles on a straight line add up to 180°, so the first thing you should do is subtract 123 from 180.

(180-123)

Now, your answer should be 57°, and that is equal to angle W.

You now know two angles. Angles in a triangle add up to 180°, too, so all you do now is the following:

97 + 57 = 154

180- 154 + 26

And there's your answer!

The percentage of married-couple households with children under 18 has declined steadily from 45% in 1960 to 23.5% in 2000.

The percentage of married-couple households with children under 18 has declined over the years. In 2000, it accounted for 23.5% of all households, compared to 25.6% in 1990 and 45% in 1960.

This decline suggests a shift in family dynamics and societal changes. The trend indicates a decrease in the number of households with married couples and children under 18.

The  answer is that the percentage has decreased over time.

it is worth noting that this decline may be influenced by various factors, such as changing societal norms, an increase in single-parent households, and a rise in childless couples.

In conclusion, the percentage of married-couple households with children under 18 has declined steadily from 45% in 1960 to 23.5% in 2000.

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Answer: $76,244.51

Step-by-step explanation:

You need to use the compound interest formula here.

First of all however, you need to convert the terms to monthly figures because the interest is compounded monthly.

4% in months = 4 / 12 = 4/12%

6 years = 6 * 12 = 72 months

Now use the compound interest formula:

= Amount * (1 + rate) ^ number of years

= 60,000 * ( 1 + 4/12%) ⁷²

= $76,244.51

In order to prove that △VWZ ~ △YXZ by SAS theorem we must have ∠VZW ≅ ∠YZX. Thus, option c is the most appropriate choice.

To prove that △VWZ ~ △YXZ by SAS theorem, we must prove that two sides of each triangle such that the angle between these sides is congruent are also congruent.

now △VWZ ~ △YXZ is to be proved, it implies that -

∠V ↔︎ ∠Y

∠W ↔︎ ∠X

∠Z ↔︎ ∠Z

thus  ∠VZW ≅ ∠YZX should be true.

hence, option c is correct and that automatically strikes out option d.

now the sides involving Z should also be congruent to prove that

△VWZ ~ △YXZ

thus, side WZ ≅ side XZ and side VZ ≅ side YZ

since we don't have such an option- options a and b are not the correct choices for this question.

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The complete question is -

In the diagram, VZ/YZ=WZ/XZ

To prove that VWZ~YXZ by the SAS similarity theorem, Which other sides or angles should be used?

a. WV and XY

b. WV and YZ

c. ∠VZW ≅ ∠YZX

d. ∠VWZ ≅ ∠YXZ

Solve for the unit price of 11.5-ounce package.

Divide the cost by the number of ounce of the package.

$4.24 ÷ 11.5 oz = $0.3690 per ounce

Rounding off to the nearest cent → $0.37 per ounce.

Solve for the unit price of 27.8-ounce package

Do the same as above with its corresponding cost.

$9.98 ÷ 27.8 oz = 0.359 per ounce

Rounding off to the nearest cent → $0.36 per ounce.

Comparing the two, the 27.8-ounce package is much cheaper per ounce than with the 11.5-ounce package, thus the 27.8-ounce package is a better buy.

Answer:

your answer is 2.

Step-by-step explanation:

3+6/2+2-3*2

3+3+2-3*2

3+3+2-6

6+2-6

8-6

2

Basically, follow PEMDAS (parenthesis, exponents, multipulcation, division, addition, and subtraction.) You move from left to right, Always remember that, ok.

0 0

 U

Let the shorter piece be x. The longer piece is 4 times the length of the other, so it is 4x.

4x + x = 160.

5x = 160

x = 32

4x = 128

The length of the shorter piece is x, which is 32.