Write an equation perpendicular to x-3y=3 passes through (5,-9)

Answer:

7.8 units

Step-by-step explanation:

(-3,4) and (-8,-2)

d = sqrt [(4 - - 2)^2+ (-3 - - 8)^2

d =sqrt [(4+2)^2 + (-3+8)^2]

d = sqrt (36 + 25)

d = sqrt 61

d = 7.8 units

Answer:

The area of the printed picture is 172.5 square inches.

Step-by-step explanation:

Since a picture is to be printed onto a sheet of paper with dimensions of 81/2 x 11 inches, and a margin of 1 1/2 inches is to be left on all sides of the picture, to determine what is the area of the printed picture the following calculation must be carried out, knowing that the area of a rectangle is equal to the base multiplied by the height:

81/2 = 40.5

1/2 = 0.5

40.5 - 1.5 x 4 = 34.5

11 - 1.5 x 4 = 5

34.5 x 5 = 172.5

Therefore, the area of the printed picture is 172.5 square inches.

Answer:

$0.91

Step-by-step explanation:

Given:

If one pound of Parmesan cheese costs $14.60, to find the cost of a one-ounce portion, simply divide the cost of one pound by 16:

\(\implies \textsf{1 ounce portion}=\dfrac{\$14.60}{16}=\$0.9125=\$0.91\;\sf (nearest \; cent)\)

Therefore, the standard portion cost for a one-ounce portion of Parmesan cheese is $0.91 (nearest cent).

Answer:

The null hypothesis will not be rejected.

Step-by-step explanation:

The hypothesis for the test is:

H₀: There is no difference between the two population means, i.e. d = 0.

Hₐ: There is a significant difference between the two population means, i.e. d ≠ 0.

Consider the Excel output attached.

The mean of the differences is, \(\bar d=-2.75\).

The standard deviation of the differences is, \(S_{d}=4.268\).

Compute the test statistic as follows:

\(t=\frac{\bar d}{S_{d}/\sqrt{n}}=\frac{-2.75}{4.268/\sqrt{8}}=-1.82\)

The degrees of freedom is, n - 1 = 7.

Compute the p-value as follows:

\(p-value=2\cdot P(t_{7}<-1.82)=0.112\)

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

p-value = 0.112 > α = 0.02.

The null hypothesis will not be rejected.

Answer:

If its radius is 9 cm, it’s circumference would be two times radius times pi equal to 18 pi. Also its area is pi R squared which is equal to 81 pi.  Circumference = 18 pi  Area = 81 pi  Area is 4.5 times greater than the circumference. The answer is C.

Answer:

Those two quantities are incommensurate, you can't compare them. The circumference is a length and the area is an area. There is no way to compare the two.

Now if you're talking about the formula Area = circumference squared over 4 times Pi, and if you're just going to go with the numerical values of Area and circumference, then there is an answer.

Step-by-step explanation:

Answer:

A = Length × breath

A = 3 × 7

A = a × 4

A = m × m

The value of side length x in diagram a) is 4.3mm and side length x in diagram b) is 309.7 m.

The figures in the image are right triangles.

A)

angle D = 17 degree

Adjacent to angle D = 14 mm

Opposite to angle D = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( 17 ) = x/14

x = tan( 17 ) × 14

x = 4.3mm

B)

angle Z = 82 degree

Adjacent to angle Z = 43.1 m

Hypotenuse = x

Using trigonometric ratio,

cosine = adjacent / hypotenuse

cos( 82 ) = 43.1 / x

x = 43.1 / cos( 82 )

x = 309.7 m

Therefore, the measure of x is 309.7 meters.

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Answer:

C

Step-by-step explanation:

Your answer is C because got the question right when put C  .

The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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Given the equations a × b = 5742 × 6368, a × c = 5748 × 6362, and c × b = 5738 × 6372, we need to determine the relationship between the three variables a, b, and c.

By comparing the given equations, we notice that the numbers on the right-hand side of each equation are very close to each other, differing only by small amounts. This suggests that a, b, and c are approximately equal.Since a × b, a × c, and c × b involve the same numbers with slight variations, we can conclude that a, b, and c are all very close in value.

Therefore, the inequality we can infer from this information is a ≈ b ≈ c, indicating that a, b, and c are approximately equal.

In simple terms, based on the given equations, it suggests that the values of a, b, and c are very similar or approximately equal to each other.

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Answer:

The Answer is : x= -12

Step-by-step explanation:

\(4x-2(x+1)=3x+10\\4x-2x-2=3x+10\\2x-2=3x+10\\2x-3x=10+2\\-x=12\\x=-12\)

Answer:

\( \huge \boxed{x = - 12}\)

Step-by-step explanation:

\(4x – 2(x + 1) = 3x + 10\)

Expand the terms in the bracket

That's

\(4x - 2x - 2 = 3x + 10 \\ 2x - 2 = 3x + 10\)

Subtract 2x from both sides of the equation

\(2x - 2x - 2 = 3x - 2x + 10 \\ - 2 = x + 10\)

Subtract 10 from both sides of the equation

\( - 2 - 10 = x + 10 - 10 \\ x = - 12\)

We have the final answer as

\(x = - 12\)

Hope this helps you

Answer:

6d+2

Step-by-step explanation:my teacher told me

Answer:

y = csc(x)+2

Step-by-step explanation:

This is the graph of y = csc(x), shown in the attached image, shifted up 2 units.

Step-by-step explanation:

To eliminate x in the system of equations:

1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:

Equation 1: 36x -54y = 90

Equation 2: -36x - 8y = -28

2. Add the two equations together to eliminate x:

(36x - 54y) + (-36x - 8y) = 90 - 28

Simplifying, we get:

-62y = 62

3. Solve for y:

y = -1

4. Substitute y = -1 into one of the original equations, say Equation 1:

4x - 6(-1) = 10

Simplifying, we get:

4x + 6 = 10

5. Solve for x:

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.

Answer:

Her answer should have been x=17/34

Step-by-step explanation:

Answer: \(\dfrac15\)

Step-by-step explanation:

Given : A cloth bag contains 6 cards numbered 1 through 6. Two cards are drawn without replacement.

Favorable outcome: sum of the numbers on the two drawn cards is 7

Since 1+6 = 7 , 2+5=7, 4+3 = 7

So, sum of 7 can be obtained as (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1)

Probability of getting (first 1, second 6) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 2, second 5) = (\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 3, second 4) =\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 4, second 3) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 5, second 2) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 6, second 1) =\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Required probability =\(6\times\dfrac{1}{30}=\dfrac15\)

Hence, the required probability = \(\dfrac15\)

Answer:

1) v = (30 cm)/(0.03 s) = 1000 cm/s = 10m/s

3) The driver is lying. The witness said that the accident happened in a blink of an eye and if the driver was really going at 10 km/hr, he would have only traveled 0.83 m out of the parking lot

The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

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Heya!

2x + 4 > 16

2x > 16 - 4

2x > 12

x > 12 ÷ 6

x > 6

Hope it helps ya!

Answer: (0, 3)

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Answer:

The correct option - Figure A

Step-by-step explanation:

The exact question is as follows :

Given - Royce kept track of the inches of snowfall in his town over a 15-day period. Royce's data is given below.

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

To find - Which box plot shows this data set?

Solution -

Given the data is -

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

Firstly,

Arrange the data from smallest to largest

0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 5, 7

Now,

Find the median

Median is the middle value - i.e. (15 + 1)/2 = 8th value

So, we get Median = 2

Now,

Find the Quartile -

The first quartile is the median of the data points to the left of the median.

i.e. Median of 0, 0, 0, 0, 0, 1, 1

so, we get

Q1 = 0

The third quartile is the median of the data points to the right of the median.

i.e. Median of 2, 2, 2, 3, 3, 5, 7

so, we get

Q3 = 3

Now,

Compute the min and the max

Minimum value = 0

Maximum value - 7

So,

five number summary is -

0, 0, 2, 3, 7

And we draw the box as follows -

So,

The correct option - Figure A

Answer:

x=-5

Step-by-step explanation:

f(x)=-8x

f(x)=40

substitute f(x) with 40 in the first equation

40=-8x

s=-5 (slove)

If Leila makes a dot plot of the heights of the girls in her class to the nearest ¹/₂ inch, the number of different heights that will include on the number line is 5.

A dot plot is a data visualization tool that consists of data points plotted as dots on a graph with an x- and y-axis.

The number of dots plotted on each number line shows the frequency of the data group.

Height    Frequency   Cumulative Frequency

56¹/₂             2                               2

57                 2                               4

57¹/₂             2                               6

58                2                               8

58¹/₂             1                               9

Thus, arranging the heights according to groups, the different heights on the number line can be classified into 5.

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If we both worked together then task will complete in 1/2 hour.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

You can complete one-tenth of a task in an hour.

Your friend can complete two-fifths if the same task in an hour.

So, if we worked together

= 1/10 + 2/5

= (5+ 20)/ ( 10x 5)

= 25/ 50

= 1/2

Hence, if we both worked together then task will complete in 1/2 hour.

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In 6 2/5 hours me and my friend together finish complete the task.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, I can complete one-tenth of a task in an hour.

∴ I can complete the task in 10 hours.

My friend can complete two-fifth of the task in an hour.

∴ My friend can complete the task in 2 and half hours.

So, (1/10) + (1/5/2) is the reciprocal of time together we can finish.

(1/10) + (2/5).

= (1 + 5/)10.

= 6/10.

Or 10/6 which is 6 2/5 hours.

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The integral that represents the area of the shaded region of the figure is area = \(\int\limits^{90}_0\) ( 4 sin ( θ ) )^2 / 2 * dθ

Given :

What is Integral ?

An integral in mathematics is either a numerical value equal to the area under the graph of a function for some interval or a new function, the derivative of which is the original function ( indefinite integral ).

The graph of the polar curve r = 4 sin θ

Now the shaded region lies from

θ = 0 to 90

Thus the integral set up that gives this shaded region area is given by:

Area =  \(\int\limits^{90}_0\) ( 4 sin ( θ ) )^2 / 2 * dθ

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Answer:

\(Rate = 0.2167\ fl\ oz/hour\)

Step-by-step explanation:

Given

\(Rate = \frac{91\ fl\ oz}{2.5\ weeks}\)

Required

Express the rate as per hour

\(Rate = \frac{91\ fl\ oz}{2.5\ weeks}\)

There are 168 hours in  a week;

So, the rate becomes

\(Rate = \frac{91\ fl\ oz}{2.5 * 168\ hours}\)

\(Rate = \frac{91\ fl\ oz}{420\ hours}\)

\(Rate = 0.2167\ fl\ oz/hour\)

Hence;

The equivalent of the given rate is \(0.2167\ fl\ oz/hour\)

Rearrange unknown terms to the left side of the equation

                   \(\boldsymbol{\sf{ 9x > 50.4-9 \ \ \longmapsto \ \ \ [Subtract]}}\)

Calculate the sum or difference.

                                  \(\boldsymbol{\sf{9x > 41.4 }}\)

Convert decimal to fraction.

                                    \(\boldsymbol{\sf{9x > \dfrac{414}{10} }}\)

Reduce the greatest common factor for both sides of the inequality.

                                    \(\boldsymbol{\sf{x > \dfrac{46}{10} }}\)

Reduce the fraction

                         \(\red{ \boxed{\boldsymbol{\sf{\blue{ Answer \ \ \longmapsto \ \ x > \dfrac{23}{5} }}}}}\)

Hello!

Let's solve this inequality for x:

\(\begin{aligned} \sf{\Box\!\!\!\!\!\star{9x+9 > 50.4}\\\sf{9x > 41.4}\\\sf{x > 4.6} \end{aligned}\)

Therefore \(\bold{x > 4.6}\).

Hope that helps! :)

-art lover