Consider the line -9x-6y=8.
What is the slope of a line perpendicular to this line
What is the slope of a line parallel to this line?
Slope of a perpendicular line:
Slope of a parallel line:

Using the given information, the equation of the circle with radius 2 and center at (-1 , -5) is (x + 1)^2 + (y + 5)^2 = 4.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (-1 , -5)

r = 2

(x - -1)^2 + (y - -5)^2 = 2^2

(x + 1)^2 + (y + 5)^2 = 4

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Line m passes through the point value of k is -1/3.

Now let us find the slope of the equation using the slope equation of line:

y = mx + b,

From the given slope let’s find y,

y-7= -3/2(x+4)

y-7= -3/2x - 6

y= -3/2x + 1

=-1 / (-3/2)

=2/3

As these two lines are perpendicular the product of the slopes is -1.

m= 2/3 , y=-1

Line m is given as  y=2/3 x +b

As the line m passes through the points

(-1, 4) and (5, k)

X=4,

To find b

-1 = 2/3 * 4+b

-1=8/3+b

b=-11/3

By substituting all the values in the formula we get value of k,

Line m : y=2/3*-11/3

When x=5

k=y=2/3*5-11/3

=10/3-11/3

=-1/3

K = -1/3

A perpendicular is a straight line that makes an angle of 90° with any other line. 90° is also known as a right angle and is marked through a little square among two perpendicular lines.

Hence, the value of k is -1/3. The two lines intersect at a right angle, and hence, are stated to be perpendicular to each other.

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Answer: k=8

Step-by-step explanation:

To find the value of k in the equation y-7=-3/2(x+4), we need to determine the slope of the line given by this equation.  

First, let's rewrite the equation in slope-intercept form (y = mx + b),

where m is the slope and b is the y-intercept:  

y - 7 = -3/2(x + 4) y - 7 = -3/2x - 6 y = -3/2x - 6 + 7 y = -3/2x + 1  

Comparing this equation with the general slope-intercept form, we can see that the slope (m) is -3/2.  

Since the line y - 7 = -3/2(x + 4) is perpendicular to line m, we know that the slopes of the two lines are negative reciprocals of each other.  

The negative reciprocal of -3/2 is 2/3.  

Therefore, the slope of line m is 2/3.

We know that line m passes through the points (-1, 4) and (5, k). Using the slope-intercept form, we can write the equation of line m as:

y = 2/3x + b  Substituting the coordinates (-1, 4) into the equation,

we can solve for the y-intercept (b):  4 = 2/3(-1) + b 4 = -2/3 + b 4 + 2/3 = b 12/3 + 2/3 = b 14/3 = b  Therefore, the equation of line m is:  y = 2/3x + 14/3  Substituting the x-coordinate 5 and solving for k:  k = 2/3(5) + 14/3 k = 10/3 + 14/3 k = 24/3 k = 8  Hence, the value of k is 8.

The mean of the probability distribution is 21.35 and the variance of the probability distribution is 51.3275

Given the probability distribution with values of x and corresponding P(x). We need to find the values of [tex]x^2[/tex], x P(x), [tex]x^2[/tex] P(x) to calculate mean and variance.

x       P(x)          [tex]x^2[/tex]      x P(x)      [tex]x^2[/tex] P(x)

7       0.10         49       0.7         4.9

14     0.20        196      2.8         39.2

21     0.25         441     5.25       110.25

28     0.45        784     12.6       352.8

-----------------------------------------------------

∑x P(x) = 21.35

∑[tex]x^2[/tex] P(x) = 507.15

Mean = ∑x P(x) = 21.35

and variance = ∑[tex]x^2[/tex] P(x) - [tex](\sum x\ P(x) )^2[/tex] = 507.15 - 455.8225 = 51.3275

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Dan is left with £66 after the total spending.

An expense is the amount of operations incurred by a business in order to generate revenue.

As for the given question;

The total earning per week is £495.

Spending on rent is 1/5.

1/5 of  £495 = 495/5 = 99

Spending on rent is  £99.

Now, spending on food is 2/3 of  £495.

Food spending = (2/3)×495 = £330

Let the money left is 'x'.

Total expenses = Total income

food cost + rent cost + saving = 495

99 + 330 + x = 495

x = 495 - 429

x = 66

Thus, the savings by the Dan is  £66.

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The probability that the event that the second part is defective will be 0.0564.

From the information, the bin of 50 manufactured parts contains 3 defective parts and 47 nondefective

Therefore, the probability of having a defective and non defective parts will be:

= 47/50 × 3/50

= 0.94 × 0.06

= 0.0564

Therefore, the probability that the event that the second part is defective will be 0.0564.

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The solution of the given rational equation [tex]\frac{x}{x+1}+\frac{3}{x+4}=\frac{x+3}{x+4}[/tex] is x = 0

In this question, we have been given a rational equation.

[tex]\frac{x}{x+1}+\frac{3}{x+4}=\frac{x+3}{x+4}[/tex]

We need to find the solution of the above rational equation.

[tex]\frac{x}{x+1}+\frac{3}{x+4}\\\\=\frac{x(x+4)+3(x+1)}{(x+1)(x+4)}\\\\ =\frac{x^{2}+4x+3x+3 }{(x+1)(x+4)} \\\\=\frac{x^{2} +7x+3}{(x+1)(x+4)}[/tex]

So given equation would be,

[tex]\frac{x^{2} +7x+3}{(x+1)(x+4)}=\frac{x+3}{x+4}\\\\x^{2} +7x+3=(x+1)(x+3)\\\\x^{2} +7x+3=x^{2} +x+3x+3\\\\x^{2} +7x+3=x^{2} +4x+3\\\\7x-4x=3-3\\\\3x=0\\\\x=0[/tex]

Therefore, the solution of the given rational equation [tex]\frac{x}{x+1}+\frac{3}{x+4}=\frac{x+3}{x+4}[/tex] is  x = 0

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The total asset is $4750

The worth of the car is valued at the worth of  has $4000 and you he have a baseball card collection valued at $750.

The capital is also know as the equity which means the net worth.

Liabilities are everything a business owes, now and in the future.

Assets are everything a business owns. Assets may be current or fixed assets

Therefore,

Total Assets - Total Liabilities = Capital

Where

Base ball card collection = $750

Total assets = ?

Capital = $4000

Hence,

Total Assets  =  $4000 + $750

Total Assets  = $4750

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The required number of combinations is 24.

Given that,
To make an outcome tree to show all possible combinations. you have three pairs of shorts four shirts, flip-flops, and sneakers.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,

                                       flip flops                  
         short 1                    short 2                    short 3
Shirt 1                shirt 2                      shirts 3                  shirts 4
Number of combinations = 12
                                         
                                       sneakers
         short 1                    short 2                    short 3
Shirt 1                shirt 2                      shirts 3                  shirts 4
Number of combinations = 12

Total number of combination = 12 + 12 = 24

Thus, the required number of combinations is 24.

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The formula a=m-a represents the actual cost, a, of an item with original price loss m after a coupon for in dollars off is applied.

n = m - a

In light of this:

The formula a = m - n's expression

where;

a = the item's real cost

m = initial cost

n = the monetary value of the coupon

The goal is to figure out how much the coupon is worth.

To calculate the quantity of the coupon, we must subtract n from the above statement, where n is the number of coupons in dollars.

As a result, if a = m - n

a + n Equals m

n = m - a

Profit and loss are expressions used to determine whether or not a sale is economic. we use these expressions frequently. However, the difference between the two is appertained to as profit, If the selling price is advanced than the cost price. However, the difference is appertained to as the loss, If the selling price is lower than the cost price. The cost price of a product is the price at which it's bought.

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The domain, range and  x-intercept of the given function are (-∞,∞), (-∞,∞) and (1,0) respectively.

Given the function in the question;

g(x) = −4x + 4

The domain of the expression is all real numbers except where the expression is undefined.

For -4x + 4, there is no real numbers that makes the expression undefined.

Hence, domain is (-∞,∞).

Also, the range is the set of all valid y-values.

The range is (-∞,∞).

For the x-intercept, substitute 0 in place of y or g(x) in the given function and solve for x.

g(x) = −4x + 4

0 = −4x + 4

4x = 4

x = 4/4

x = 1

Hence, the x-intercept in point form is (1,0)

Therefore, the domain, range and  x-intercept of the given function are (-∞,∞), (-∞,∞) and (1,0) respectively.

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Tessellation in trapezoid is possible only if it is rotated

see the fig, attached.

But tessellation in parallelogram is possible both rotated and non rotated

see the fig, attached.

A tessellation or tiling is the seamless application of one or more geometric shapes, known as tiles, to a surface, frequently a plane. Tessellation in mathematics can be expanded to include other geometries and higher dimensions.

A tiling constructed of materials like cemented ceramic hexagons or squares is referred to as a real-world tessellation. Such tilings may be ornamental designs or serve practical purposes such providing long-lasting and water-resistant pavement, floor, or wall coverings.

Tessellations were historically employed in Islamic art, such as the Moroccan architecture and the ornamental geometric tiling of the Alhambra palace. They were also used in Ancient Rome.

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The evaluation of each expression is 3/2 , 1/2.

What is logarithms:

Logarithms are the other way of writing the exponents. A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation. For example, if 102 = 100 then log10 100 = 2.

Hence, we can conclude that,

Log b x = n  or   bn = x

Where b is the base of the logarithmic function.

This can be read as “Logarithm of x to the base b is equal to n”.

In this article, we are going to learn the definition of logarithms, two types of logarithms such as common logarithm and natural logarithm, and different properties of logarithms with many solved examples.

What is properties of logarithms:

Properties of logarithms functions are used to solve logarithm problems. We have learned many properties in basic math's such as commutative, associative and distributive, which are applicable for algebra. In the case of logarithmic functions, there are basically five properties.

This are as follows:

The product property

The quotient property

Power rule

Change of base rule

Reciprocal rule

Now,

3log₉ 3 = [(9)^x]^3 = 3

[(3^2)^x]^3 = 3

x = 3/2

Second part,

1/4 log₉ 81

= 1/2

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Answer: 23 + 2c

Step-by-step explanation:

     To write an expression, we will look at the wording of the phrase given;

The sum of ➜ addition

twice Chau's height ➜ 2c

The sum of 23 and twice Chau's height.

23 + 2c

The force on one of the ends due to hydrostatic pressure is 332.8lb.

How is a hydrostatic pressure produced?

The force on one of the ends due to hydrostatic pressure is 332.8lb

Data;

Density = 62.4 lb/ft^3

length = 4ft

radius = 2ft

Force Due to Pressure

The force due to hydrostatic pressure can be calculated as

From the attached diagram

F = Pressure * area

density = 62.4 lb/ft³

depth of water = 2- y

pressure  = ( 2- y ) ( 62.4)

                = 124.8 - 62.4

We can proceed as

x² + ( y - 2)² = 2²

x² = 4 - ( y - 2)²

x = ± √4y - y²

this implies that

2x = 2 √4y - y²

The area is given as

δA = ( 2x) * δy

δA = 2√4y - y² δy

The force would be given by

δF = ( 2- y ) ( 62.4) (2 √ 4y - y²)δy

The total force is given by

F = [tex]\int\limits^2_0 {( 2 - y)} \, (62.4) ( 2\sqrt{4y - y^{2} } dy[/tex]

F = 124.8 [tex]\int\limits^2_0 {( 2-y)} \,( \sqrt{4y - y^{2} } dy[/tex]

F = 124.8 [tex][ -\frac{1}{3} y( y- 4 ) ( \sqrt{4y - y^{2} }[/tex]

F = 124.8 [tex][ -\frac{1}{3} (2) ( 2-4) \sqrt{4(2) - 2^{2} }[/tex]

F = 332.8lb

The force on one of the ends due to hydrostatic pressure is 332.8lb

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The total number of penalty kicks is 9+ 2y where the penalties made is x and the penalties missed is y

The given parameters are:

Leroy made 9 more penalty kicks than he missed

Represent the penalties made with x and the penalties missed with y

So, we have

x = 9 + y

The total number of penalty kicks is then calculated as

Total = x + y

This gives

Total = 9 + y + y

Evaluate

Total = 9+ 2y

Hence, the total number of penalty kicks is 9+ 2y where the penalties made is x and the penalties missed is y

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The width of the lake on the scale drawing is 30 cm.

Based on the given conditions, formulate 1500*2/100

Cross out the common factor: 15*2 = 30

Get the result as 30 cm

An object is enlarged in a scale drawing. An expansion increases or decreases the size of an object by multiplying each of its lengths by a scale factor. Typically, a ratio is used to describe the scale of a drawing. a representation of a real thing with correct sizes that have been scaled back or blown up slightly (called the scale). The scale is represented by the length in the drawing, a colon (":"), and then the actual length that corresponds to it.

Hence, the width of the lake on the scale drawing is 30 cm.

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The value in the missing place is 10 after plugging the value of F = 0.833; the answer is 10.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

0.83 = F

0.83 is a repeating decimal

Multiply by 10 on both sides:

10x0.83 = Fx10

8.33 = ? F

Plug F = 0.833

8.33 = ? (0.833)

? = 0.833/0.833

? = 10

8.33 = (10) F

Thus, the value in the missing place is 10 after plugging the value of F = 0.833; the answer is 10.

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Igor has not been skiing in 10 years. however, when he gets on his skis, his body remembers exactly how to ski. the kind of memory that makes it possible for him to remember how to ski is procedural.

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Answer:

4 × 3

Step-by-step explanation:

4 is being added 3 times.

Answer: 13.7

Step-by-step explanation:

First you do 16.6 - 2 = 14.6 then you subtract 0.9 from 14.6, your equation would be 14.6 - 0.9 = 13.7

Hope This Helps!

Answer:

13.7

Step-by-step explanation:

The model for the total number of people in the US Labor force is T = -0.0054t² + 0.087t + 13.559 .

In the given question

the number of men "M" in the US labor force is modelled by the equation ,

M = 0.0016t² + 0.315t + 19.467   ...(i)

and

the number of women "W" in the US labor force is modelled by the equation ,

W= 0.007t² - 0.228t + 5.908   ...(ii)

Let "T" denoted the model for total number of people in the US Labor force.

The total number of people in the US Labor force = Number of Men + Number of Women in US Labor force.

Adding equation (i) and (ii) we get ,

T = (0.0016t² + 0.315t + 19.467) + (0.007t² - 0.228t + 5.908)

Adding the like terms we get ,

T = (0.0016-0.007)t² + (0.315-0.228)t + (19.467-5.908)

T = -0.0054t² + 0.087t + 13.559

Therefore , the total number of people in the US Labor force is modeled by the equation T = -0.0054t² + 0.087t + 13.559  .

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The volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis is V = 8π/3

The volume of a solid, given by the function f(x), over an interval between a and b, is given by:

[tex]V = \pi \int\limits^a_b {f(x)^2} \, dx[/tex]

To find the area, integrate around that area. We're revolving around the x-axis so the area will be a circle;

V = ∫A(x)dx =  ∫(πr²)dr

Then we subtract them from each others.

∫(πr₂² - πr₁²)dr

Now substitute the value and integrate;

∫(π(2)² - π(2x)²)dr

∫(4π - 4πx²)dr

4π∫(1 - x²)dr

Now integrate from 0 to 1 since that's where our boundary is.

V = 4π∫(1 - x²)dr = 8π/3

Therefore, The volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis is V = 8π/3

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Answer:

3.36

Step-by-step explanation:

→ How much is a dozen

12

→ Multiply by 14

168

→ Divide by 50

168 ÷ 50 = 3.36

The expression is written as 2 × 10 =  2 x 10^ 1  = 20

The index form of a number  can be defined as that number written as an exponential expression.

It is also said to be a single number that is  raised to another number.

Given the expression;

2x _____ = 2 x 10^ 1 = ______

Note that a number raised to the power 1 is that same number, so we have;

2 × 10

2 x 10^1 = 2 × 10

2 × 10  = 20

Thus, we have the expression to be written as 2 × 10 =  2 x 10^ 1  = 20

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Answer:

in image

Step-by-step explanation:

The eighth term of the given geometric sequence is:  [tex]\frac{3}{2048}[/tex]

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 24, -6, 3/2, ...

Here, [tex]\frac{-6}{24}=\frac{\frac{3}{2}}{-6} = \frac{1}{-4}[/tex]

Thus, for the given geometric progression, a₁ = 24, and r = -1/ 4.

The nth term of a geometric progression is given by: [tex]a_n=a_1(r^{n-1})[/tex]

For n = 8, a₈ = 24 ( -1/4) ⁷

=> a₈ = [tex]\frac{6}{(-4)^6} = \frac{6}{64\times64}[/tex] = [tex]\frac{3}{2048}[/tex]

Hence, The eighth term of the given geometric sequence is:  [tex]\frac{3}{2048}[/tex].

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Answer:

I think its 3 20.

Step-by-step explanation:

The projectile motion equation [tex]h(t) = - g \cdot {t}^{2} + v_{0}\cdot {t} + h_{0}[/tex], gives;

First part;

Second part;

Third part;

The quadratic equation that represents the projectile motion can be presented as follows;

[tex]h(t) = - g \cdot {t}^{2} + v_{0}\cdot {t} + h_{0}[/tex]

g = 16 ft./s² or 9 m/ s²

First part;

When

[tex] v_{0} = 0 \: and \: h_{0} = 100 \: ft.[/tex]

We have;

h(t) = -16•t² + 100

When the object hits the ground, we have;

h(t) = 0, which gives;

0 = -16•t² + 100

Therefore;

16•t² = 100

t² = 100 ÷ 16 = 25/4

t = √(25/4) = 5/2 = 2.5

Second part;

The direction in which the object is thrown = Upwards

Initial height of the object, [tex] h_{0} = 6 \: ft[/tex]

Initial speed of the object, [tex] h_{0} = 30 \: ft/sec[/tex]

The equation of the projectile motion is therefore;

h(t) = -16•t² + 30•t + 6

Which gives;

When the object is at its starting height of 6 feet, h(t) = 6, which gives;

6 = -16•t² + 30•t + 6

-16•t² + 30•t = 0

A solution to the above equation is t = 0

The other solution is found as follows;

-16•t² + 30•t = 0

-16•t + 30 = 0

30 = 16•t

t = 30/16 = 1.875

Third part;

When the object hits the ground, we have;

h(t) = 0, which gives;

0 = -16•t² + 30•t + 6

Which gives;

t ≈ 2.06

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