Write the equation of the line that passes through (4,1) and has a slope of -1/2.

Answer:

Let the value of house before increase be 'x'.

Rate of growth = 7%

So, Amount of growth would be

\(=\dfrac{7}{100}\times x\\\\=0.07x\)

So, Value of house after increase becomes

\(\begin{gathered}x+0.07x\\\\=1.07x\end{gathered}\)

Since Value of house after increase

= $ 749000

it becomes,

\(\begin{gathered}1.07x=749000\\\\x=\dfrac{749000}{1.07}\\\\x=700000\end{gathered}\)

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Answer:

1000 tiles

Step-by-step explanation:

Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.

Answer:

2

Step-by-step explanation:

Answer: 20

Step-by-step explanation:

The number of times of Puerto Rico is 5/6

No earthquake released 10³ of Colombia

From the question, we have the following parameters that can be used in our computation:

The table of values

On the table of values, we have

Colombia = 6.0M

Puerto Rico = 5.0M

This means that

Number of times = Puerto Rico/Colombia

Substitute the known values in the above equation, so, we have the following representation

Number of times = 5/6

Here, we have

Colombia = 6.0M

So, we have

Earthquake = Colombia * 10³

This gives

Earthquake = 6 * 10³

From the table of values, we have no entries with the readings 6 * 10³

Hence, no earthquake released 10³ of Colombia

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Answer: t(x) or total amount

Step-by-step explanation:

Answer:

Step-by-step explanation:

d

Answer:

X= 1/5

Step-by-step explanation:

The value x in the secant line using the Intersecting theorem is 4.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the figure:

First sectant line segment = ( x - 1 ) + 5

External line segment of the first secant line = 5

Second sectant line segment = ( x + 2 ) + 4

External line segment of the second secant line = 4

Using the Intersecting secants theorem:

5( ( x - 1 ) + 5 ) = 4( ( x + 2 ) + 4 )

Solve for x:

5( x - 1 + 5 ) = 4( x + 2 + 4 )

5( x + 4 ) = 4( x + 6 )

5x + 20 = 4x + 24

5x - 4x = 24 - 20

x = 4

Therefore, the value of x is 4.

Option C) 4 is the correct answer.

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Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

The measure of side KL from triangle KLM is 22 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, triangle HIJ is similar to triangle KLM.

From the similar triangles,

JH/MK =HI/KL

31/13.9 =49/KL

31KL=49×13.9

31KL=681.1

KL=681.1/31

KL=21.97

KL≈22

Therefore, the measure of side KL is 22 units.

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For the given polynomial the degree is 1, the leading coefficient is 1, and the constant term is 5.

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

The given polynomial is x+5.

(1) The degree is the highest power of the polynomial.

Degree = 1

(2) The leading coefficient is 1.

(3) The constant term is 5

Therefore, the given polynomial degree is 1, the leading coefficient is 1, and the constant term is 5.

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Answer:

=32÷40%

=32÷0.4

=80

the owner have total 80 stores

Step-by-step explanation:

th

Answer:

80.

Step-by-step explanation:

40 % = 32 stores, so:

10% = 32/4 = 8 stores, and

100% = 8*10 = 80 stores.

The distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

The bearing is defined as the angle measured clockwise from the north direction. A ship is anchored off a long straight shoreline that runs north and south.

From two observation points miles apart on shore, the bearings of the ship are 52 degrees and 134 degrees respectively. To find the distance from the ship to each of the observation points, we can use trigonometry.

Let's call the distance from the north observation point to the ship x, and the distance from the south observation point to the ship y. The bearings from the north and south observation points can be drawn as follows:

[asy]

unitsize(1cm);

pair O = (0,0), N = (-2,0), S = (2,0), A = (-2,1), B = (2,-1);

draw(O--N--A,Arrow);

draw(O--S--B,Arrow);

\(label("$52^\circ$", N + 0.3*dir(52), NE);\)

\(label("$134^\circ$", S + 0.3*dir(134), SE);\)

draw(O--A--B--cycle,dashed);

\(label("$x$", (N+A)/2, W);\)

\(label("$y$", (S+B)/2, E);\)

[/asy]

We can use the tangent function to find x and y, since we have the angle and opposite side.

From the north observation point, we have:

\($$\tan(52^\circ) = \frac{x}{2}$$$$x = 2\tan(52^\circ) \approx 2.95$$\)

From the south observation point, we have:

\($$\tan(134^\circ) = \frac{y}{2}$$$$y = 2\tan(134^\circ) \approx 9.88$$\)

Therefore, the distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

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Answer:

1 ; 1.25 ; 0.25 ; - 0.75 ; - 1.25 ;- 0.5

Step-by-step explanation:

Given the sample observations : 15, 16, 12, 8, 6, 9

Zscore for each sample Observation :

Zscore = (x - mean) / standard deviation

(15 + 16 + 12 + 8 + 6 + 9) / 6 = 11

Mean value (m) = 11

Standard deviation (s) = 5

Sqrt[(x - m)^2 / (n - 1)]

[(15-11)^2 + (16-11)^2 + (12-11)^2 + (8-11)^2 + (6-11)^2 + (9-11)^2] / (6 - 1)

= 80/5 = 16

Sqrt(16) = 4

Zscore = (x - mean) / standard deviation

x = 15

Zscore = (15 - 11) / 4 = 1

x = 16

Zscore = (16 - 11) / 4 = 1.25

x = 12

Zscore = (12 - 11) / 4 = 0.25

x = 8

Zscore = (8 - 11) / 4 = - 0.75

x = 6

Zscore = (6 - 11) / 4 = - 1.25

x = 9

Zscore = (9 - 11) / 4 = - 0.5

To find the number of temperatures in the set, we can divide the sum of the temperatures by the mean temperature.

Number of temperatures = Sum of temperatures / Mean temperature

In this case, the sum of temperatures is given as 2,516 and the mean temperature is given as 74 degrees Fahrenheit.

Number of temperatures = 2,516 / 74

Calculating the division:

Number of temperatures ≈ 34.05

Since we cannot have a fraction of a temperature, we need to round the result to the nearest whole number. Therefore, there are approximately 34 temperatures in the set.

The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

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Step-by-step explanation:

Divide 24 by 4. So, 18 hours. Therefore a light bulb consumes 6840 Watt hours in 4 days and 18 hours.

The approximate surface area of the package is approximately 245.05 square inches.

The best model for the package is a cylinder.

To calculate the approximate surface area of the package, we need to find the lateral surface area of the cylinder and the area of the circular base.

The lateral surface area of a cylinder can be calculated using the formula:

Lateral Surface Area = 2πrh

where r is the radius of the base and h is the height.

The area of the circular base can be calculated using the formula:

Area of Base = \(πr^2\)

Given that the diameter of the bottom is 9 inches, the radius (r) would be half of that, which is 4.5 inches.

Using the given height of 13 inches, we can now calculate the surface area:

Lateral Surface Area = 2πrh = 2π(4.5)(13) ≈ 117.81 square inches

Area of Base = \(πr^2 = π(4.5)^2 ≈ 63.62\) square inches

To find the total surface area, we add the lateral surface area and the area of the base:

Total Surface Area = Lateral Surface Area + 2 × Area of Base = 117.81 + (2 × 63.62) ≈ 245.05 square inches

Therefore, the approximate surface area of the package is approximately 245.05 square inches.

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The area of the right triangle is 27,000 square units. The result is obtained by using the determinant method.

The area of a triangle in coordinate geometry can be found by using the determinant formula.

\(Area \: of \Delta ABC = \frac{1}{2} \left[\begin{array}{ccc}x_{1} &y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right]\)

The vertices of a right triangle are:

Using the determinant formula, the area of the triangle is

\(Area \: of \Delta ABC = \frac{1}{2} \left[\begin{array}{ccc}525 &260&1\\725&260&1\\525&-10&1\end{array}\right]\)

Area of ΔABC = 1/2 |525(260-(-10)) - 725(260-(-10)) + 525(260-260)|

Area of ΔABC = 1/2 |525(270) - 725(270) + 0|

Area of ΔABC = 1/2 |141,700 - 195,750|

Area of ΔABC = 1/2 |-54,000|

Area of ΔABC = 27,000 unit square

Hence, the area of ΔABC is 27.000 square units.

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Answer:

Wouldn't it be 27 dollars?

Step-by-step explanation:

The 4th term of the geometric sequence whose first term is 3 and the common ratio is 2 is 24.

Suppose the initial term of a geometric sequence is a

and the term by which we multiply the previous term to get the next term is r then the sequence would look like

a, ar, ar², ar³,...., arⁿ

Thus, the nth term of such sequence would be aₙ = a₁ × r⁽ⁿ⁻¹⁾ (you can easily predict this formula, as for the nth term, the multiple r would've multiplied with initial terms n-1 times).

Given the first term of the sequence is 3, while the common ratio is 2, therefore, the fourth term of the geometric sequence can be written as,

aₙ = a₁ × r⁽ⁿ⁻¹⁾

a₄ = 3 × 2⁽⁴⁻¹⁾

a₄ = 3 × 2³

a₄ = 24

Hence, the 4th term of the geometric sequence whose first term is 3 and the common ratio is 2 is 24.

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Answer:

(C) Multiply first equation by -2 and second equation by 3, solution (1, 1)

Step-by-step explanation:

Simultaneous equations are set of equations which possess a common solution. The equations can be solved by eliminating one of the unknowns by multiplying each of the equations in a way that a common coefficient is obtained in the unknown to be eliminated.

Given the simultaneous equations:

3x - 5y = -2

2x + y = 3

First step:

Multiply first equation by -2 and multiply second equation by 3,

-6x + 10y = 4

6x + 3y = 9

Second step:

Add the two equations together,

13y = 13

Divide both sides by 13

y = 1

Third step:

Put y = 1 in the first equation

3x - 5(1) = -2

3x - 5 = -2

3x = 5 - 2

3x = 3

Divide both sides by 3:

x = 1

solution (x,y) = (1,1)

Option C

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SOLUTION:

Case: Congruence

Method:

Compare the triangles

Final answer:

The scale factor is not consistent

Hence the given information cannot be used to prove triangle ABC is congruent to triangle EDC.

Answer:

5.6

Step-by-step explanation:

3.5 x 1.6

It all depends on where the parentheses are in the question.

(3) · (1/2) · (1.6)  =  2.4

or

(3-1/2) · (1.6)  =  5.6

Answer:

3 15/17 hour

Step-by-step explanation:

Kim: 11 hours for 1 chapter

Bethany: 6 hours for 1 chapter

Together: x hours to proof a chapter

In 1 hour:

Kim proofs 1/11 of a chapter

Bethany proofs 1/6 of a chapter

Kim and Bethany together proof 1/11 + 1/6 of a chapter

Kim and Bethany together proof 1/x of a chapter

Therefore, 1/11 + 1/6 must equal 1/x

1/11 + 1/6 = 1/x

6/66 + 11/66 = 1/x

17/66 = 1/x

x = 66/17

x = 3 15/17

Answer: 3 15/17 hour

The graph of the translated function is g ( x ) = ( x + 5 )² + 2

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x²

On simplifying , we get

The function is translated 5 units to the horizontal left direction:

And , when the function is translated 2 units in the vertical upward direction:

So , the translated function is

g ( x ) = ( x + 5 )² + 2

Now , the vertex of the function g ( x ) = ( x + 5 )² + 2 is (-5, 2)

Hence , the graph of the function is plotted and g ( x ) = ( x + 5 )² + 2

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Answer:

she uses 10 cups of lemon juice and 30 cups of water for 5 pitchers

Step-by-step explanation:

you multiply the ingredients for one pitcher by 5 because they are making 5 pitchers

The option that best describes X on the scatterplot is;

C: Outlier

Let us first define the terms in the given options before we analyze the scatterplot.

1) Negative correlation is defined as a relationship between two variables whereby one variable increases while the other decreases, and vice versa.

2) A nonlinear relationship is also referred to as nonlinear association, and it exists when a constant change in the independent variable does not result in a constant change in the dependent variable.

3) An outlier is defined as a data point that differs significantly from other observations.

4) Clusters are small populations that a wider population is divided into.

Now, from the scatter plot, we see that X is isolated from the plotted points which tells us that it differs greatly from the other points and as such it fits the definition of an outlier.

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The missing options are;

A. negative correlation

B. nonlinear association

C. outlier

D. cluster