Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

An employee at a construction company is ordering interior doors for some new houses that are being built. There are 2 one-story houses and 4 two-story houses on the west side of the street, which require a total of 64 doors. On the east side, there are 5 one-story houses and 4 two-story houses, which require a total of 88 doors. Assuming that the floor plans for the one-story houses are identical and so are the two-story houses, how many doors does each type of house have?

Each one-story house has
doors, and each two-story house has
doors.

The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

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I assume the equation is

√(2x - 5) - √(x + 6) = 0

Note the domains for the root expressions:

• √(2x - 5) : 2x - 5 ≥ 0   ⇒   x ≥ 5/2

• √(x + 6) : x + 6 ≥ 0   ⇒   x ≥ -6

So any valid solution we find must be at least 5/2.

Move one term to the other side.

√(2x - 5) = √(x + 6)

Take squares.

(√(2x - 5))² = (√(x + 6))²

2x - 5 = x + 6

Solve for x :

x = 11

Answer:

A. 72°

D. 144°

E. 216°

Step-by-step explanation:

I just answered this.

in short : we rotate each vertex on a circle arc. the center of that circle being P.

so, at the end of every 1/5 of the circle arc there is a vertex of the polygon.

therefore, with every 1/5 of a full circle rotation we move the pentagon visually onto itself.

that is starting at

360/5 = 72°

and then every additional 72°

144°

216°

288°

360°

so, A, D and E are correct

Using the differential equation, the population after 30 years is 760.44.

The population P after t years obeys the differential equation:

Where P(0) = 500 is the initial condition and k is a positive constant.

Using P(0) = 500 gives 500 = Ae⁰.

Furthermore,

The population after 30 years is:

Therefore, using the differential equation, the population after 30 years is 760.44.

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The value of the house was increased by $75420 and the current value of the house is $494420.

A percent is a measurement in hundredths. By dividing the percentage value by 100, percentages can be transformed into decimals and fractions.

Given, A house on the market was valued at 419,000.

Then after several years, the value increased by 18%.

Therefore, The increase in value is,

= (18/100)×41900.

= $75420.

Hence, The current value of the house is,

= $(419000 + 75420).

= $494,420

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Step-by-step explanation:

(f o g)(x)

= f(g(x))

= f(2x - 3)

= |2x - 3|

The linear equation in standard form is g + s + b=104, the relationship between silver to bronze medals is g = s  and the solution is g=46, s=29, b=29

(a) Since the United States won 104 gold (g), silver s, and bronze (b) medals in the 2012 Summer Olympics.

This means the sum of gold (g), silver s, and bronze (b) medals is equal to 104. Thus, the linear equation in standard form is:

g + s + b = 104

(b) Since the United States won 46 gold medals and the same number each of silver and bronze medals. This implies:

g = 46

s = b

Thus, the relationship between the number of silver to bronze medals is s = b

(c) To solve the linear equation, substitute g = 46 and s = b into the equation g + s + b = 104:

g + s + b = 104

46 + b + b = 104

46 + 2b = 104

2b = 104 -46

2b = 58

b = 58/2

b = 29

Also, s = 29        (Remember: s = b)

Thus, g = 46, s =29, b = 29

Therefore, the United States won 46 gold (g), 29 silver (s), and 29 bronze (b) medals in the 2012 Summer Olympics. Select options a., d. and e. for a., b., and c. respectively

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The equation for the tangent plane is 12x - y + 4z - 56 = 0 and the equation for normal line is (x - 6)/12 = (32 - y) = (z - 2)/4

Finding the Equations for Tangent Plane and Normal Line:

The given function is,

f(x, y, z) = x² - y - z² = 0

∂f/ ∂x = 2x

∂f/ ∂y = -1

∂f/ ∂z = 2z

At given point (6, 32, 2),

∂f/ ∂x = 12

∂f/ ∂y = -1

∂f/ ∂z = 4

(a) The equation of tangent plane is given as follows,

(∂f/ ∂x)(x-x₁) + (∂f/ ∂y)(y-y₁) + (∂f/ ∂z)(z-z₁) = 0

12(x - 6) - 1(y - 32) + 4(z - 4) = 0

12x - 72 - y + 32 + 4z - 16 = 0

The required tangent plane is,

12x - y + 4z - 56 = 0

(b) The equation for normal line is given as,

(x-x₁) / (∂f/ ∂x) = (y-y₁) / (y-y₁) = (z-z₁) / (∂f/ ∂z)

(x - 6)/12 = (y - 32)/(-1) = (z - 2)/4

Thus, the required equation of normal line is,

(x - 6)/12 = (32 - y) = (z - 2)/4

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The tax bracket that Monica falls partly into is the $0 - $9,950 bracket. This is because her taxable annual earnings after is less than $9,950. hence she will be paying 10% of what's taxable.

A tax bracket is a tax group into which a person falls into depending on their annual income, number of dependents, and marital status.

It is important to know that tax brackets are reviewed from time to time.

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Answer: The number line that you really want to move is the right side. Then, at that point, the right choice is C.

What is a number line?

A number line alludes to a straight line in science that has numbers organized at customary stretches or divides along its width. A number line is frequently shown on a level plane and can be delayed toward any path.

On the off chance that you are at - 15 on the number line and you needed to push toward the positive numbers

The number line that you need to move in the right side. Then the correct option is C.

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Step-by-step explanation:

Answer:

The answer is 3.5

Step-by-step explanation:

Answer:

A will be the answer hope this will help u

Answer:

the correct option is A. (-5,-7)

like (5,-7) I. e (+,-) lies in the 3rd quadrant and the opposite of 3rd quadrant vertically is the 2nd quadrant.

so, the answer should come as (-,-) according to the 2nd quadrant.

so, answer will be (-5,-7)

I hope it's correct.

Answer:

im gonna guess b

Step-by-step explanation:

sry if wrong

Consider the expression 4(8x + 5)

Complete 2 descriptions of the parts of the expression.

1. The entire expression is the product of 2 factors.

2. On its own, (8x + 5) is a sum with 2 terms.

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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y + 6 = -2(x - 5)

1st unknown: -6

2nd unknown: -2

3rd unknown: 5

The given points: (5, -6) and (-1, 6)

To get the equation in point slope form, we will apply the formula:

First let's find the slope of the line using the given points:

Next we pick any of the points and the slope to get point slope form:

Answer:

1256.63 tiles

Step-by-step explanation:

the question is not quite clear but I assume that it is asking how many tiles of length 70cm is required in order to pave the circular area.

Given,

radius(r) = 14m= 1400cm

Area of the circle= πr²= π×1400²= 6157521.6 cm²=

length of square tile(l)= 70cm

area of square= l²= 70×70= 4900cm²

now,

number of tiles required= area of circle ÷ area of tile

= 6157521.6 ÷ 4900= 1256.63 tiles

Hope this helps.

Answer: Approximately 34.17%.

Step-by-step explanation: Let's divide 41 by 120. Doing so, we get 0.3466666 looping forever. We can simplify that to .3417, and then turn that into a percentage giving us 34.17%

17 and 4, the two y values, are in the wrong place and should be swapped

The coordinates of polygon A'B'C'D' after the rotation of 180º are given as follows:

A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).

The five more known rotation rules are given as follows:

The original coordinates for this problem are given as follows:

A(0,0), B(5,2), C(5,-5), D(0,-3).

Exchanging the sign of each of the coordinates, the coordinates after the rotation are given as follows:

A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).

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The system of equations is.

\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)

And the solutions are y = 50 and x = 10.

Let's define the two variables:

With the given information we can write two equations, then the system will be:

\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)

Now let's solve it.

We can isolate x on the first  to get:

\(\text{x} = 60 - \text{y}\)

Replace that in the other equation to get:

\(15\times(60 - \text{y}) + 10\text{y} = 800\)

\(-2\bold{y} = 900 - 800\)

\(-2\bold{y} = 100\)

\(\text{y} = \dfrac{100}{-2} = \bold{50}\)

Then \(\bold{x=10}\).

Therefore, the solutions are y = 50 and x = 10.

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The area of a triangle with side lengths 17, 18, and 19 in simplest radical form is 18√7770

The area of the triangle is calculated using the formula

Area of triangle = √[s(s – a)(s – b)(s – c)]

s = perimeter o the triangle

a, b and c are the lengths of the triangle

s = a + b + c = 17 + 18 + 19 = 54

Area of triangle = √[54 * (54 – 17)(54 – 18)(54 – 19)]

Area of triangle = √[2517480]

Area of triangle = 18√7770

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Answer:

x =2.8074

Step-by-step explanation:

2^x = 7

Take the log of each side

log (2^x) = log (7)

We know  log a^b = b log a

x log 2 = log 7

x = log (7) / log 2

x =2.80735

To the nearest tenth thousandth

x =2.8074

Answer:

Graph D

Step-by-step explanation:

Graph D is the graph of -2x + y < 5

Point H is the ortho-center of our given triangle and option c is the correct choice.

We have been given an image of a triangle. We are asked to find the term that describes point H.

We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.

We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.

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The answers are 4. a) 15.7 cm, b) 26.25 m, 5. a) 128.74 cm, b) 40.82 mm, c) 45 cm and 6. 777.28 cm

Given are the circles and the circular items we need to find their circumference,

Circumference of a circle = 2π × radius = Diameter × π

4. a) Circumference = 5 × 3.14 = 15.7 cm

b) Circumference = 8.36 × 3.14 = 26.25 m

5. a) Circumference = 41 × 3.14 = 128.74 cm

b) Circumference = 13 × 3.14 = 40.82 mm

c) Circumference = 14.3 × 3.14 = 45 cm

6.

The perimeter of the cloth = circumference of the circular ends plus length in the middle,

= 76 × 2 × 3.14 + 150 × 2

= 477.28 + 300

= 777.28 cm

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Answer:

x = 6.5

Step-by-step explanation:

1.5x - 2.3x + 4 = 1.2

1.5x - 2.3x = -1.2 - 4

-0.8x = - 1.2 - 4

-0.8x = -5.2

divide both sides of the equation by -0.8

x = 6.5   :)

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

5.5 cm

Step-by-step explanation:

Let x be the width of the rectangle.

Since the length is double the width, the length would be 2x.

x can be found by solving the perimeter equation. The perimeter of the rectangle can be found by the equation:

\(p = 2(l + w)\)

\(33 = 2(2x + x)\)

\(33 \div 2 = (2x + x)\)

\(16.5 = 3x\)

\(16.5 \div 3 = x\)

\(5.5 = x\)

Therefore, the width of the rectangle is 5.5 cm.