Find the value of each variable. For the circle, the dot represents the center.

Answer:

[tex]y-7=-\frac{4}{3}(x+7)[/tex]

Step-by-step explanation:

The slope of the line is [tex]\frac{-9-7}{5-(-7)}=-\frac{4}{3}[/tex].

The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex], so the equation is [tex]y-7=-\frac{4}{3}(x+7)[/tex].

589 in base five is  [tex]4324_{5}[/tex].

Given number:

589

converting to [tex]589_{5}[/tex].

⇒ 5|589

⇒ 5|117|4

⇒ 5|23|2

⇒ 5|4|3

⇒ 5|4|4

Now we write the last digit from last number to first that is,

= [tex]4324_{5}[/tex].

Hence 589 in base five is  [tex]4324_{5}[/tex].

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Answer: 667

Step-by-step explanation:

14.50 x 46

Answer:4/5 : 1/3=4/5 x 3/1=12/5

Step-by-step explanation:

Answer:

12/5

Step-by-step explanation:

If you set it in the calculator 4/5 ÷ 1/3 you get = 12/5

was it helpful?

Answer:

1. I'm $3 in debt, and I spend 4 more dollars. I am now 4 dollars more in debt than I was before.

2. I'm $3 in debt, and I pay back $2 of debt. I am now $1 in debt.

Step-by-step explanation:

-Hope this helped

When the the light's angle is 20° from perpendicular to the wall, and the light is rotating at an angular speed of one rotation in 2 seconds the rate the light projected onto the wall is moving is approximately 60.48 feet/s

Angular speed, ω, is the angle, θ, in radians rotated by a rotating object per second. The unit of angular speed is radians per second, rad/s.

Mathematically;

[tex]\omega = \dfrac{\Delta \theta}{\Delta t}[/tex]

Where;

Δt = The time the object rotates through an angle of Δθ

The distance of the light from the wall, x = 17 feet

Time it takes the light to complete one rotation = 2 seconds

Angle the light makes with the perpendicular wall = 20°

[tex]tan(\theta) = \dfrac{y}{x}[/tex]

The distance the light has moved along the wall, y = x × tan(θ)

Therefore;

The y = 17 × tan(θ)

The angular velocity of the light, ω = θ/t

Therefore, θ = ω × t = ω·t

Which gives; y = 17 × tan(ω·t)

[tex]\omega = \dfrac{2\cdot \pi}{2}\ rad/s = \pi \ rad/s[/tex]

Therefore; x = 17 × tan(·t)

[tex]\dfrac{dy}{dt} = \dfrac{d}{dt} \left(17\times tan(\omega\cdot t)\right) = 17\cdot \omega\cdot sec^2(\omega \cdot t)[/tex]

ω = π rad/s (constant)

ω·t = θ

Therefore;

[tex]\dfrac{dy}{dt}= 17\cdot \omega\cdot sec^2(\theta)[/tex]

Rate the light is moving along the wall, dy/dt when θ = 20°, is therefore;

[tex]\dfrac{dy}{dt}= 17\times \pi\cdot sec^2(20^{\circ}) \approx 60.48[/tex]

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Answer:

f = 4/3

f = 1.3

f = 1 1/3

Step-by-step explanation:

Move all terms that don't contain f to the right side and solve.

Differentiation of f(x) is [tex]-8x^{3} sinx^{4}[/tex].

Given,

f(x) = [tex]cos2x^{4}[/tex]

Now, we will differentiate f(x) with respect to x,

[tex]\frac{d}{dx}cos2x^{4} = (\frac{d}{dx}cos2x^{4})(\frac{d}{dx}2x^{4} )[/tex]

              [tex]= (-sin2x^{4})(2*4x^{3})[/tex]

              [tex]= -8x^{3}sin2x^{4}[/tex]

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Lester's final score from the two Judges is 7.6

The scores of the judges are in percentage and this will be converted to decimal by dividing by 100

impact (worth 40%) = 0.4

composition (worth 30%) = 0.3

lighting (worth 20%) = 0.2

color balance (worth 10%) = 0.1

Average score from the Judges will be used to multiply the percentages

Impact: 8 and 9

= 8.5 * 0.4 = 3.4

Composition: 7 and 7

= 7 * 0.3 = 2.1

Lighting: 8 and 7

= 7.5 * 0.2 = 1.5

Color balance: 5 and 7

= 6 * 0.1 = 0.6

sum of the scores gives Lester's final score as 7.6

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Answer:

1). True

2). x = 16.4 m^2

3). A = 24, h = 4

4). A = 18.39

5). 162

Step-by-step explanation:

I took this quiz on K12 and got everything correct! Brainliest welcome! :)

The equation of the sentence, the square of a number is equal to the square root of that number, is [tex]x^{2} =\sqrt{x}[/tex].

According to the question,

We have the following information:

The square of a number is equal to the square root of that number.

Now, let's take this number to be x.

Now, square of this number will be [tex]x^{2}[/tex] and the square root of this number will be [tex]\sqrt{x}[/tex].

Now, according to the sentence, we will have the following expression:

[tex]x^{2} =\sqrt{x}[/tex]

Hence, the equation of the sentence, the square of a number is equal to the square root of that number, is [tex]x^{2} =\sqrt{x}[/tex].

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The expected mean for a sample of 150 women is 168.5 pounds.

Expected mean can be defined as the mean weight of a number . Based on the given data we were told that the mean weight of the us women was 168.5 pounds which implies that the expected mean is 168.5 pounds.

The formula for expected mean is :

E ( X ) = μ = ∑ x P ( x )

Where:

x = values of the random variable X

P(x) = Corresponding probability

∑ =Sum of all products xP(x)

μ = mean

Therefore the expected mean is 168.5 pounds.

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The estimation of 719 x 26 is 14,000

Making a number simpler so that its value stays near to its original state is known as rounding. Although less exact, the outcome of rounding off a number is simpler to utilise.

Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.

Given:

Estimation of 719 x 26

Now, Round off nearest hundred for 719 which is 700

i.e., Round 719 = 700

Now, Round off nearest hundred for 26 which is 20

i.e., Round 26 = 20

Hence, the estimation is 700 x 20 = 14,000.

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Answer:

a )

[tex]6 ( ? ) = 27[/tex]

b )

? = The amount of rice in each container.

So, 1 container = ( ? ) ounce.

6 containers have = 6 x ( ? ) ounces.

We know that 6 containers have 27 ounces so...

[tex]6 ( ? ) = 27[/tex]

[tex]? = \frac{27}{6}[/tex]

[tex]? = 4.5[/tex]

Final Answer: 4.5 ounces in each container

Hope this helps! :)

Answer:

yes if b is odd then b+6 is odd

Step-by-step explanation:

example

consider a odd number 1,3,5,7,and 9

1+6=7

3+6=9

5+6=11

7+6=13

9+6=15

all answers are odd number

The required value of x is 3 in the given equilateral triangle.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

The triangle given in the figure is an equilateral triangle.

We know that all sides are equal in the equilateral triangle.

As per the given figure,

side AB = side AC

6x - 3 = 3x + 6

6x - 3x = 6 + 3

Apply the arithmetic operation,

3x = 9

x = 9/3

x = 3

Therefore, the required value of x is 3 in the given equilateral triangle.

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Answer: A

Step-by-step explanation :

HE ASKED YOU ABOUT AN EQUALTULAR ( TO EQUALED AND OPPSITE ANGLE )

Answer:

New: $44,840 Original: 47,200

Step-by-step explanation:

You have to multiply 47,200 by 95% or 0.95

The exponential function that can model the amount of medication in Austin's body, y, x hours is of: [tex]y = 180(0.9)^x[/tex]

The definition of the exponential function is presented as follows:

[tex]y = a(b)^x[/tex]

The parameters a and b are listed as follows:

a is the amount when x = 0.

b is the rate of change.

Given that the initial dose was of 180 micrograms, hence the parameter a is;

a = 180.

After one hour, the concentration was of 162 micrograms, hence the parameter b is;

b = 162/180 = 0.9.

Hence the equation is:

[tex]y = 180(0.9)^x[/tex]

After six hours, the concentration is given as;

[tex]y = 180(0.9)^6[/tex]= 96 micrograms.

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P(A∪B)=24/35 when A and B are independent and P(A)=2/5,P(B)=2/7

Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 signifying impossibility and 1 expressing certainty. The greater the likelihood of an occurrence, the more likely it will occur.

Probability theory, which is widely used in domains such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy, has given these concepts axiomatic mathematical formalization.

Given,

P(A)=2/5

P(A)=2/7

P(A∪B)=?

And also given that A and B are independent then,

P(A∩B)=0

P(A∪B)=P(A)+P(B)-P(A∩B)

P(A∪B)=(2/5)+(2/7)-0

P(A∪B)=(14+10)/35

P(A∪B)=24/35

Therefore, P(A∪B)=24/35 when A and B are independent.

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Answer:

B

Step-by-step explanation:

Combine 2x^2 and 3x^2 to get 5x^2.

Combine x and 2x to get 3x.

Add 3 and 1 to get 4.

The meaning of the expression x + 4 as required in the task content is; "four more than the number of questions on test".

It follows from the task content that the word phrase which best represent the algebraic expression; x + 4 is to be determined.

Given; x = the number of questions on test.

It therefore follows that the algebraic expression x + 4 can be interpreted as; "four more than the number of questions on test".

Hence, the meaning of the expression is; "four more than the number of questions on test".

PS: Just like word phrases can be accurately represented by algebraic expressions, the latter can be represented by the former too.

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The paper company can produce 25 notebooks for $285

From the question, the equation of the total cost is given as

Equation = 4x + 185

Rewrite as

Cost = 4x + 185

Express the equation as a cost function

So, we have the following representations

C(x) = 4x + 185

When the total cost is $285, we have

C(x) = 285

This gives

4x + 185 = 285

Subtract 185 from both sides

4x = 100

Divide by 4

x  = 25

Hence, the number of notebooks is 25

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Using division operations and based on the rates of production, given, Machine D works the fastest.

The rate of production can be computed using the division operation, which divides the dividend by the divisor, to obtain the quotient (rate).

The rate of production is the number of goods that can be produced during a given period of time.

The rate of production or production rate also refers to the time consumed in the production of a unit of goods or services.

There are, therefore, two ways of determining production rate.  Firstly, we can divide the total production by the hours consumed.

Secondly, the production rate can be computed by dividing the total production time by the number of goods produced.

                           Units          Production     Rate of

                       Produced          Hours      Production

Machine A        10,000               15             667 cups per hour

Machine B       25,000              20           1,250 cups per hour

Machine C       30,000              30           1,000 cups per hour

Machine D       15,000               10            1,500 cups per hour

Thus, using division operation, Machine D produces at the fastest rate than the other three machines.

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                           Units          Production

                       Produced          Hours

Machine A        10,000               15

Machine B       25,000              20

Machine C       30,000              30

Machine D       15,000               10

Using the monthly payment formula, it is found that:

A. You can afford a car at a price of $13,742.36.

B. The monthly payments are of $109.15.

The monthly payments are given by the equation presented as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

The variables involved in the equation are listed and explained as follows:

For item a, the parameters are given as follows:

A = 250, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60

Hence the maximum value of the car is obtained as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]250 = P\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]

0.0181919241P = 250

P = 250/0.0181919241

P = $13,742.36

For item b, the parameters are given as follows:

P = 6000, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60

(P = 6000 as the 2000 of the down payment are already paid, hence not subjected to interest).

Hence the monthly payments are given as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 6000\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]

A = 6000 x 0.0181919241

A = $109.15.

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x-3=0

so x = 3

-(y-2)=0

so y = 2

vertex = (3,2)

The amount invested in the account that yields 10% simple interest is $1,000.

The amount invested in the account that yields 7% simple interest is $9,000.

The first step is to form a system of equations using the information provided in the question:

a + b = $10,000 equation 1

0.1a + 0.07b = 730 equation 2

Where:

a = amount invested in the account that yields 10% simple interest

b =  amount invested in the account that yields 7% simple interest

The elimination method would be used to solve the equations

Multiply equation 1 by 0.1

0.1a + 0.1b = 1000 equation 3

Subtract equation 2 from equation 3

0.03b = $270

Divide both sides of the equation by 0.03

b = $270 / 0.03

b = 9,000

Substitute for b in equation 1

a + 9,000 = 10,000

a = 10,000 - 9,000

a = 1000

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