A line passes through the point (-6, 9) and has a slope of 4/3. Write an equation in slope-intercept form for this line.

The ratio for the Illustration a+b/a-b=5/3 is 5:4.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

From the information given, the equation is written thus:

a + b / a - b = 5 / 3

Cross multiply

5(a - b) = 3 (a + b)

5a - 5b = 3a + 3b

Collect the like terms

5a - 3a = 3b + 5b

2a = 8b

Divide

a = 8b / 2

a = 4b

Therefore (a + b) / a will be:

= (4b + b) / 4b

= 5b / 4b

= 5/4

= 5 : 4

The ratio is 5:4.

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The statements that must be true if the two quadrilaterals are similar are:

A. m∠K = m∠N

C. HJ/MP = JK/PN

Similar quadrilaterals are quadrilaterals that have the same shape, but not necessarily the same size. This means that their corresponding angles are congruent to each other (congruent angles are angles that have the same measure in degrees), and their corresponding sides are in proportion to each other, or have the same ratio.

Given that quadrilaterals HJKL and MPNQ are similar to each other, therefore:

Also, their corresponding sides are proportional:

HJ/MP = JK/PN = KL/NQ = HL/MQ

Therefore, the statements that must be true are:

A. m∠K = m∠N

C. HJ/MP = JK/PN

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The probability of rolling a 3 on a pair of standard six-sided dice is 1/36.

There is only one way to roll a 3 on a pair of standard six-sided dice: one die must show a 1, and the other die must show a 2.

The number of possible outcomes when rolling two dice is given by the number of combinations of the two dice, which is 6x6 = 36.

The number of outcomes that result in a sum of 3 is 1 (as explained above). Therefore, the probability of rolling a 3 is:

P(rolling a 3) = number of outcomes that result in a sum of 3 / total number of possible outcomes = 1/36.

So the probability of rolling a 3 on a pair of standard six-sided dice is 1/36.

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1. The two main types of software are system software and application software.

2. A desktop computer with a high processing speed and storage capacity.

1. The two main types of software are system software and application software. System software refers to programs that manage and control the computer hardware and operations, such as operating systems and device drivers. Application software refers to programs designed for specific tasks, such as word processing and accounting. Application software is more important to a knowledge worker as it helps them perform their specific job duties and tasks efficiently.

2. For a small startup company, I would recommend a desktop computer with a high processing speed and storage capacity. This would allow for efficient multitasking and the ability to handle complex software programs necessary for business operations. Additionally, a desktop computer can be more cost-effective and easier to upgrade than a laptop or tablet. It also provides a larger display, making it easier to work on spreadsheets, documents, and other business-related tasks.

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Given:

The equation of given line is

\(y=3x-4\)

A line is perpendicular to the given line and passes through the point (9,5).

To find:

The equation of the perpendicular line.

Solution:

We have,

\(y=3x-4\)

On comparing this equation with slope intercept form \(y=mx+b\), we get

\(m=3\)

It means, the slope of the given line is 3.

The product of slopes of two perpendicular lines is -1.

\(m\times m_1=-1\)

\(3\times m_1=-1\)

\(m_1=-\dfrac{1}{3}\)

Point slope form of a line is

\(y-y_1=m(x-x_1)\)

Where, m is the slope.

The slope of perpendicular line is \(-\dfrac{1}{3}\) and it passes through the point (9,5). So the equation of the line is

\(y-5=-\dfrac{1}{3}(x-9)\)

\(y-5=-\dfrac{1}{3}(x)-\dfrac{1}{3}(-9)\)

\(y-5=-\dfrac{1}{3}x+3\)

Adding 5 on both sides, we get

\(y-5+5=-\dfrac{1}{3}x+3+5\)

\(y=-\dfrac{1}{3}x+8\)

Therefore, the equation of required line is \(y=-\dfrac{1}{3}x+8\).

Answer:

if the equation is -1/3x2 =-5/6+1/3y2 and 5y2=25/2-5x2 then the answer is infinitely many

Step-by-step explanation:

hope it helps :D

Answer:

Step-by-step explanation:

Answer:

4×3/4

Step-by-step explanation:

hope it helps!!!!

Answer:

\(\frac{3}{16}\)

Step-by-step explanation:

This can be changed into the following equation:

\(\frac{3}{4}\) ÷ 4 =

\(\frac{3}{4}\)÷\(\frac{4}{1}\)

Step 1 - Flip the second fraction so the numerator is the denominator:

\(\frac{4}{1}\) becomes \(\frac{1}{4}\)

Step 2 - Swap the division sign for the multiplication sign and multiply the two numerators together as well as the two denominators:

\(\frac{3}{4} * \frac{1}{4}\)

\(\frac{3 * 1}{4 * 4}\) = \(\frac{3}{16}\)

This cannot be simplified so the answer is:

\(\frac{3}{16}\)

Hope this helps!

the series 1/(n∛(n)) is divergent.

To determine the convergence or divergence of the series, let's examine the terms of the series and apply the comparison test.

The series in question is:

1/(n∛(n))

We can compare it to the harmonic series, which is known to be divergent:

1/n

Let's compare the terms of the given series to the terms of the harmonic series:

1/(n∛(n)) < 1/n

Since 1/n is a divergent series, and the terms of the given series are smaller than the corresponding terms of the harmonic series, we can conclude that the given series is also divergent.

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The given information is:

- The tank has the shape of a cylinder

- The dimensions of the cylinder are 5 ft long and diameter 2.2 ft.

- The tank is drained at a rate of 2.1 ft^3 per minute.

The volume of the tank is given by the formula:

Where d is the diameter and h is the height.

By replacing the known values we obtain the initial volume:

As the drain rate is 2.1 ft^3 per minute, the time that is needed to empty the tank is:

The answer is 9 minutes.

Answer:

The answer is 127.6

Step-by-step explanation:

To find the volume of something, you multiply.

So:5.5 times 3.2 times 7.25 is equal to 127.6

HOPE THIS HELPS YOU!!!!    :)

Answer:

127.60 square inches

Step-by-step explanation:

Multiply the diameters all together to get your answers.

5.5 x 3.2 x 7.25

Multiply

5.5 x 3.2 = 17.6

Multiply some more

17.6 x 7.25 = 127.6

You can also just multiply like this:

5.5 x 3.2 x 7.25 = 127.6

Hope this helped :)

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The solution to the linear function M(x) = 180 is of x = -5.

The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.

In this problem, the function is defined as follows:

M(x) = 120 - 12x.

M(x) represents the balance remaining on the gift card after x movie tickets priced at $12 are purchased.

The domain of the situation is given as follows:

x ≥ 0. {discrete}

As the number of tickets cannot assume negative neither decimal values.

The equation is:

M(x) = 180.

The solution is calculated as:

120 - 12x = 180

12x = -60

x = -60/12

x = -5.

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Answer :  The lifetime of light bulbs is approximately normally distributed with a mean of 850 hours and a standard deviation of 44 hours.

Explanation:

Given that the mean lifetime of light bulbs is 850 hours with a standard deviation of 44 hours and it is normally distributed. We need to test the hypothesis that 850 hours against the alternative.

Therefore, we need to use a hypothesis test for mean. Let us assume a null hypothesis and an alternative hypothesis for the given data.

Null Hypothesis : The null hypothesis H0 states that there is no significant difference between the mean lifetime of light bulbs and the hypothesized value of 850 hours.                                                                                                               Mathematically, it is expressed asH0: μ = 850    

Alternative Hypothesis : The alternative hypothesis Ha states that there is a significant difference between the mean lifetime of light bulbs and the hypothesized value of 850 hours.                                                                                      Mathematically, it is expressed asHa: μ ≠ 850Here, μ represents the population mean and is equal to 850.                                                We know that Z-score is given as, Z = (x - μ)/σwhere x = Sample Mean, μ = Population Mean, σ = Standard Deviation

Now, we need to find the Z-score for the given data. Z = (x - μ)/σZ = (15 - 850)/44Z = -18.75As we know that the area under the curve at 5% level of significance on each tail is 0.025 and the Z-score corresponding to this is ±1.96. The rejection region is in the left tail of the curve and the right tail of the curve.

Hence the critical value of Z at 5% level of significance for a two-tailed test is ±1.96. Z critical value = ±1.96Since the calculated value of Z is less than the critical value of Z, we fail to reject the null hypothesis. Hence, we can conclude that the lifetime of light bulbs is approximately normally distributed with a mean of 850 hours and a standard deviation of 44 hours.

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The angle sum of a triangle will always 180 degree.

6X degree + 2X degree + X degree = 180 degree

9X degree =  180 degree

X = 180/9 = 20 degree.

X = 20 degree.

While the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it, the interior angles of a triangle always add up to 180°. By deducting the angle of the target vertex from 180°, one can also determine a triangle's exterior angle.

The three angles that make up a triangle's interior are referred to as its interior angles. The total of these three angles is always 180 degrees.

180° is equal to 6X degrees plus 2X degrees plus X degrees.

90 degrees multiplied by 9

X=180/9=20 degrees.

20 degrees for X

A triangle's three inside angles will always add up to 180 degrees. Since the other two angles (180°+0°+0°) would not exist, a triangle cannot have a single angle of 180°.

Triangles fall into one of three categories based on the lengths of their sides: scalene, isosceles, or equilateral. Equilateral.

Three straight sides and three angles make up the two-dimensional shape of a triangle. Three sides, three vertices, and three angles make up a triangle.

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A certain triangle has interior angle measures of (6x°), (2x°), and x°. The value of x is 20 degrees.

The three angles that make up a triangle's interior are referred to as its interior angles. The total of these three angles is always 180 degrees.

180° is equal to 6X degrees plus 2X degrees plus X degrees.

90 degrees multiplied by 9

X=180/9=20 degrees.

20 degrees for X

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Answer:

Step-by-step explanation:

Step 1. Calculate the measures of center (mean and median)

Mean= Average= All data values added together then divided by number of data values.

Median = middle of numbers

So, number of data values = 3+2+5+1+3+8+3+1= 26

Data values added together = 0 + 4+4+4+5+5+5+5+5+5+5+5+6+6+6+7+8+8+8+8+8+9+9+10+10+10= 165

165/26= 6.34615384

Average = 6.3

Median: Arrange numbers from least to greatest and eliminate one on both sides until you get a middle number:

0 , 4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,8,8,8,8,8,9,9,10,10,10

The median is 6.

Step 2: Calculate range, IQR, and MAD

Range: Maximum- minimum

IQR: The IQR is the difference between Q3 and Q1.

Q1 is the middle value in the first half of the data set.

Q3 is the middle value in the second half of the data set.

MAD:

Range: 10-0= 10

IQR: 3

MAD (population) : 1.9378698224852

MAD (sample) : 1.9378698224852

Iliana is painting a picture. She has green, red, yellow, purple, orange, and blue paint. She wants her painting to have four different colors.



If order does not matter, in how many ways can she pick four colors if green must be one of them?

we have a combination problem

C(3,5) ------> because green must be one of them

Applying the formula

Answer:

9.3 ft

Step-by-step explanation:

The formula for compound interest is A = P(1 + r/n)ⁿᵃ, where A is the amount of money accumulated after a years, P is the principal (starting amount), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

To find out how long it will take for $800 to double at a given interest rate, we need to solve for t when A = 2P = $1600.

$1600 = $800(1 + 0.04)ᵃ

2 = 1.04ᵃ

t ≈ 17.67 years

It will take about 17.67 years for $800 to double at 4% annual interest rate compounded once a year.

$1600 = $800(1 + 0.13)ᵃ

2 = 1.13ᵃ

t ≈ 5.85 years

It will take about 5.85 years for $800 to double at 13% annual interest rate compounded once a year.

$1600 = $800(1 + 0.20)ᵃ

2 = 1.20ᵃ

t ≈ 3.81 years

It will take about 3.81 years for $800 to double at 20% annual interest rate compounded once a year.

$1600 = $800(1 + 1.00)ᵃ

2 = 2ᵃ

t = log2(2)

t = 1

It will take 1 year for $800 to double at 100% annual interest rate compounded once a year. However, such a high interest rate is not realistic or sustainable.

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Answer:

Decay with 37% decrease.

Step-by-step explanation:

If an exponential function is,

y = \(a(b)^{x}\)

Where 'b' = growth factor

And 'a' = Initial amount

How to check the exponential function represents a growth or decay;

1). If the growth is positive,

  Value of 'b' will be greater than 1 and the function will represent growth.

  So the function will be in the form of,

  y = a(1 + r)ⁿ

  Where r = growth rate in percent

2). If the growth is negative,

  Value of 'b' will be in decimals and the function will represent the decay.

  And function will be in the form of,

  y = a(1 - r)ⁿ

  From the given function,

  y = 47(0.63)ˣ

  y = 47(1 - 0.37)ˣ

  Therefore, growth rate of the function will be,

  r = 0.37 ≈ 37%

  Therefore, function decay, with 37% decrease.

Answer:

-2xl -2y + 99

Step-by-step explanation:

Answer:

\(-2xl -2y+99\)

Step-by-step explanation:

STEP 1: Subtract 9 from 61.

\(-2xl+52+41-2y+6\)

STEP 2: Add 52 and 41.

\(-2xl+93-2y+6\)

STEP 3: Add 93 and 6.

\(-2xl-2y+99\)

Answer:

It depends on which why you are moving so let's say you have to move the 3 units to the right and 1 up, that would be the answer. I can't really give you the exact answer because you didn't say where they are supposed to go.

Answer:

0.5 kg = 500g. she will buy hook C

Answer:

10 inches

Step-by-step explanation:

If the original figure has a height of 25 inches and it was photocopied at a scale of 40%, we can find the new height of the figure by multiplying the original height by the scale factor:

new height = 25 inches x 0.4

new height = 10 inches

Therefore, the new height of the figure is 10 inches.

Answer:

Wassup

Step-by-step explanation:

By multiplying the initial height by the scale factor, which is 40% or 0.4 in decimal notation, the new height of the image can be calculated.

New height: 25 inches times 0.4 to equal 10 inches.

The figure's revised height is 10 inches as a result.

Step-by-step explanation:

1.

use equation 1

vf = vi + a×t = 5.2 + 2.3×7 = 21.3 m/s

deltax (displacement) not needed

vi = 5.2 m/s

vf = 21.3 m/s

a = 2.3 m/s²

t = 7 s

2.

use equation 4.

vf² = vi² + 2×a×deltax

47² = vi² + 2×4.7×150

2209 = vi² + 1410

vi² = 799

vi = 28.26658805... m/s

deltax = 150 m

vi = 28.26658805... m/s

vf = 47 m/s

a = 4.7 m/s²

t not needed

3.

use equation 2.

deltax = (vf + vi)×t/2

228 = (3.15 + 3.15)×t/2

456 = 6.3×t

t = 456/6.3 = 72.38095238... s

deltax = 228 m

vf = 3.15 m/s

vi = 3.15 m/s

a not needed

t = 72.38095238... s

4.

use equation 5.

deltax = vf×t - 1/2 × a×t²

897 = 0×15.5 - 1/2 × a×15.5² = -1/2 ×a×240.25 = a×-120.125

a = 897/-120.125 = -7.467221644... m/s²

deltax = 897 m

vi not needed

vf = 0 m/s

a = -7.467221644... m/s²

t = 15.5 s

Gazelle vs. Lion.

use equation 2.

deltax = (vf + vi)×t/2

deltax = (18.4 + 0)×3.09/2 = 18.4×3.09/2 =

= 9.2×3.09 = 28.428 m

deltax = 28.428 m

vi = 0 m/s

vf = 18.4 m/s

a not needed

t = 3.09 s

Around 62.47% of the data population is situated between a z-score of -1.5 and 0.5.

Assuming a standard normal distribution, the percentage of the data population that falls between a z-score of -1.5 and 0.5 can be calculated using a standard normal table or a calculator.

Using a standard normal table, we can find the area under the curve between z = -1.5 and z = 0.5.

The area to the left of z = 0.5 is 0.6915, and the area to the left of z = -1.5 is 0.0668. Therefore, the area between z = -1.5 and z = 0.5 is:

0.6915 - 0.0668 = 0.6247

So, approximately 62.47% of the data population falls between a z-score of -1.5 and 0.5.

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Answer:

its not

Step-by-step explanation:

if you do the division euclidiene the rest will be 5 not zero

f(x)=(x-2)(6x+5)+5

Answer:

1

Step-by-step explanation:

12- 8x = 4x -12

-12              -12

-8x=4x -24

-4x   -4x

-12x=-12

___  ___

-12    -12

x=1

The required, 4.5 × 10⁵ as an ordinary number is 450,000.

An ordinary number is a number that is expressed in the usual way, using digits 0-9 without any exponent notation or other mathematical symbols.

4.5 × 10⁵ means 4.5 multiplied by 10 raised to the power of 5. To write this as an ordinary number, we simply need to perform this multiplication:

4.5 × 10⁵ = 4.5 × 100,000 = 450,000

Therefore, 4.5 × 10⁵ as an ordinary number is 450,000.

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