What must x equal if a ∥ b? Explain.

We got to use the Secant-Tangent Theorem, here. It says that AC² is equal to the distance BC times the distance from C to the circumference. Let's denote the point in OC where it intercepts the circumference by D, so:

Beucase the radius is equal in all points of the circumference, OA=OB=OD, so BC = OA + OC, and CD = OC - OA. So,

Explanation:

This is the LCM (lowest common multiple) of 3 and 5

3*5 = 15

Eva: 3, 6, 9, 12, 15, 18, 21, ...

Jin: 5, 10, 15, 20, 25, ...

Answer: [tex]4x^{5} y^{6} \sqrt{7y}[/tex]

Step-by-step explanation:

1) Separate the radicals

sqrt(112x^10y^13) = sqrt(112)*sqrt(x^10)*sqrt(y^13)

2) For sqrt(112), rewrite it as the product of a perfect square and some other number.

sqrt(112) = sqrt(16) * sqrt(7)

= 4*sqrt(7)

3) For sqrt(x^10), rewrite it in terms of it being raised to a fraction

[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]

n = 2, so x^(10/2), and when simplified you have x^5

4) For sqrt(y^13), do the same thing.

y^(13/2) = sqrt(y)*(y^6)

5)Combine everything

4x^5y^6sqrt(7y)

The value of the expression −|a + b|/2 − c when a =1 2/3 , b=−1 , and c=−3 is 8/3

From the question, the expression is given as

−|a + b|/2 − c

Also, we have the values of the variables to be

a =1 2/3 , b=−1 , and c=−3

Rewrite a as

a = 5/3

So, we substitute a = 5/3  b=−1 , and c=−3 in −|a + b|/2 − c

This gives

−|a + b|/2 − c  = −|5/3 - 1|/2 + 3

Evaluate the difference in the expression

−|a + b|/2 − c  = −|2/3|/2 + 3

Divide

−|a + b|/2 − c  = −|1/3| + 3

Remove the absolute bracket and solve

−|a + b|/2 − c  = 8/3

Hence, the solution is −|a + b|/2 − c  = 8/3

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The required simplified value of the given expression is 8/3.

As per the given data, an expression −|a+b|/2−c is given when   a=1 2/3, b=−1, and c=−3 the value of the expression is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let the solution be x,
x = −|a+b|/2−c
Substitute value in the above equation,
x = - |1 + 2 / 3 - 1|/2 - (-3)
x = -1/3 + 3
x = -1+9 / 3
x = 8/3

Thus, the required simplified value of the given expression is 8/3.

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The equation of the line perpendicular to x = -4 that passes through the point (-2,5) is y = 5  .

In the question ,

it is given that

the required line is perpendicular to x = -4

the slope of x = -4

x + 4 = 0

0.y = x + 4

slope = 1/0

so the slope of the perpendicular line [tex]=[/tex] 0   .

the equation of the perpendicular line passing through (-2,5) and slope as 0  is

(y - 5) [tex]=[/tex] 0*(x + 2)

y -5 = 0

y = 5

Therefore , The equation of the line perpendicular to x = -4 that passes through the point (-2,5) is y =5  .

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[tex] = 2(4)^{2} - (10 \div 2) \\ = 2(16) - 5 \\ = 32 - 5 \\ = 27[/tex]

THE ANSWER IS OPTION 2. 27

HOPE THIS HELPS

Answer:

Answer is 27                  

    ♬      

⚫    

Answer:

  7/3

Step-by-step explanation:

You want the ratio 3.50 : 1.50 written as a fraction.

A ratio can be written 3 ways. Any of them can be reduced to a ratio of mutually prime integers:

  3.50 : 1.50 = 3.50/1.50 = 3.50 to 1.50

Here, the fraction can be made to be a ratio of integers by multiplying both numerator and denominator by 2:

  3.50/1.50 = (2·3.50)/(2·1.50) = 7/3

The ratio 3.50:1.50 is equivalent to the fraction 7/3.

Insecticides = 14/100 x 5 = 0.7

In the first one, the word increase means you will be add something

+42000

In the second one, the word withdrew means you will subtract something

-40

To calculate the final amount of money at the end of the period, considering that the interest is compounded continuously you have to use the following formula:

Where

A is the accrued amount at the end of the given time

P is the principal amount

r is the annual nomial interes expressed as a decimal value

t is the time period in years

For this investment, the initial value is P= $200

The interest rate is 6%, divide it by 6 to express it as a decimal value

The time is t= 20 years

After 20 years, the amount of money in the account will be $664.02

The original recipe has half of the number of strawberries She wants to use in her salad in this case we will need double the fruits of the recipe given

Bananas

4x2=8 bananas

Apples

3x2=6 apples

Pears

6x2=12 pears

a)

The oven devaluated from $1970 to $270 in 10 years.

Since each year it looses the same value, divide the change in the price over the time interval to find the rate of change of the value with respect to time.

To find the change in price, substract the initial price from the final price:

The change in price was -$1700.

Divide -1700 over 10 to find the change in the price per year:

The initial value of the oven was $1970, and each year it looses a value of $170.

Then, after x years, the value will be equal to 1970-170x.

Then, the linear equation that models the value of the oven, y, after x years of use, is:

b)

To find the value of the oven after 2.5 years, substitute x=2.5:

Then, the value of the oven after 2.5 years is $1545.

c)

To find the y-intercept, substitute x=0:

The y-intercept is the initial value of the oven when 0 years have passed.

d)

The graph of G(x) is symmetric with respect to the y-axis. It also passes through the origin.

Since the graph of F(x) moved 4 units upward, we must add 4 to the right of the equation. Thus, the equation of F(x) is as follows.

The rate of change of the distance between the police car and the truck after 10 minutes is approximately 193.66 m/s

The rate of change of a function is the rate at which the output of the function is changing with regards to the input.

The velocity of the police car = 160 km/h south

The velocity of the truck = 140 km/h east

Distance of the police car from Sioux Falls = 60 km north

Distance of the truck from Sioux Falls = 50 km east

Required;

The rate at which the distance between the vehicles is changing at t = 10 minutes

Solution;

Let d represent the distance between the vehicles, we have;

d² = x² + y²

Where;

x = The distance of the truck from Sioux falls

y = The distance of the police car from Sioux Falls

Which gives;

[tex] \displaystyle{ \frac{d}{dt} d^2= \frac{d}{dt}(x^{2}) +\frac{d}{dt} (y^{2}) }[/tex]

Which gives;

[tex] \displaystyle{ 2 \cdot d \cdot \frac{d}{dt} d=2 \cdot x \cdot \frac{dx}{dt} + 2 \cdot y \cdot\frac{dy}{dt} }[/tex]

After 10 minutes, we have;

y = 60 - (10/60)×160 = 100/3

x = 50 + (10/60)×140 = 220/3

d = √((100/3)² + (220/3)²) = 20•(√146)/3

[tex] \displaystyle{ \frac{d}{dt} d=\frac{2 \cdot x \cdot \frac{dx}{dt} + 2 \cdot y \cdot\frac{dy}{dt} }{2 \cdot d }}[/tex]

Which gives;

[tex] \displaystyle{ \frac{d}{dt} d= \frac{2 \times \frac{220}{3} \times 140 + 2 \times \frac{100}{3} \times 160}{2 \times \frac{20 \times \sqrt{146}}{3}}}[/tex]

[tex] \displaystyle{ \frac{2 \times \frac{220}{3} \times 140 + 2 \times \frac{100}{3} \times 160}{2 \times \frac{20 \times \sqrt{146}}{3}}\approx 193.66}[/tex]

Therefore;

[tex] \displaystyle{ \frac{d}{dt} d \approx 193.66}[/tex]

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To determine a percentage we can use the following formula:

In this case the part is equal to two, the whole is equal to 10, then we have:

Therefore, 2 is 20% of 10

Recall that to expand a binomial we can use the following formula:

The above is known as the square of the binomial.

Answer:

Square of binomial.

STEP - BY - STEP EXPLANATION

What to find?

Rate of change of the given function.

Given:

Step 1

State the formula for rate of change.

Step 2

Choose any two point within the given interval.

(3, 59) and (6, 44)

⇒a=3 f(a) =59

b= 6 f(b)=44

Step 3

Substitute the values into the formula and simplify.

ANSWER

Rate of change = -5

Kevonta, this is the solution:

Time of departure : 11:49

Time of travel : 4:32

In consequence, the estimated arrival time if the train departs in the morning is:

11 + 4 = 15 hours

49 + 32 = 81 minutes

81 minutes = 1 hour + 21 minutes

4:21 pm

If the train departs at night, the estimated time of arrival is:

4:21 am

infinite numbers

Explanation

An Irrational Number is a real number that cannot be written as a simple fraction,for example Pi()

Step 1

between 0 an 6 we have 6 integers numbers :(1,2,3,4,5,6)

Step 2

Now check this

a number for example

so, the answer is infinite numbers

The probability of selecting the integer 361 from the random generator is 0.

It should be noted that probability simply has to do with the likelihood that a particular thing will take place.

In this case, a random number generator is used to select an integer from 1 to 50 .

The probability of selecting the integer 361 from the random generator will be 0. This is because the numbers given are from 1 to 50.

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Answer:

Domain: (-∞, ∞)

Range: (-∞, -9]

Step-by-step explanation:

Area of rectangle = Length x Width

. = 14.3 x 13.9

. = (13.9+ 0.4) x 13.9

. = 13.9^2 + 5.56

. = 13•14 +( 1.4)•8 + 5.56

. =198.77 cm2

The price of gasoline before the 15% increase is $4.75/gallon.

What is gasoline?
Petroleum-derived clear flammable liquid known as gasoline or petrol is the primary fuel for the majority of spark-ignited internal combustion engines (also known as petrol engines). It mostly comprises of organic compounds made from petroleum fractional distillation that have been improved with various additions. In the United States, refineries typically create 19 to 20 gallons of gasoline, 11 to 13 gallons of distillate fuel, the majority of which is sold as diesel fuel, and 3 to 4 gallons of jet fuel from a barrel of crude oil. The crude oil test and oil refinery processing determine the product ratio. 42 US gallons, or around 159 litres or 35 imperial gallons, is the standard measurement for the volume of an oil barrel.

How can we calculate the price before the 15% increase?

Overnight the price of gasoline increased by 15% to settle at a price of $4.90 per gallon.

15÷100+x = $4.90/gallon

0.15+x = $4.90/gallon

Therefore, x = $4.90/ gallon - 15÷100

 x = $4.90/gallon - 0.15

x = $4.75/gallon.

Hence , the price of gasoline before the 15% increase is $4.75/gallon.
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Answer:

g(8 + x) = - 2(8 + x)

Step-by-step explanation:

substitute x = 8 + x into g(x)

g(8 + x) = - 2[tex]\sqrt{(8+x)^2}[/tex] = - 2(8 + x)

Given:

Salesman A earn = 65 per sale.

Salesman B earn = 40 per sales and 300weekly salary.

Salesman C earn = 900 weekly salary

Let "x" represent the number of sales each man

Salesman A earn is:

Salesman B earn is:

So total sales is 12 then.

S=0 For Zero week

For S=1

For s=10

Answer:

the answer is C

Step-by-step explanation:

25% of 150 is 37.5 so 150-37.5 is 112.5

Answer:

Area = 4πr²

Step-by-step explanation:

- We know that a moon revolves around its orbit as per Keplar. The moon is not a perfect sphere, so we shall take an assumption;

Assume the moon is a perfect and regular sphere

[tex]{ \tt{volume \: of \: moon = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \boxed{ \tt{ \: v = \frac{4}{3} \pi {r}^{3} }}}[/tex]

- From engineering mathematics (rates of change), we know that volume is first order integral of area and area is the first order derivative of volume;

[tex]{ \tt{area = \frac{d(volume)}{dr} }} \\ \\ { \tt{volume = \int area \: dr}}[/tex]

- So, from our formular;

[tex]{ \tt{area = \frac{dv}{dr} = \frac{4}{3}\pi ( \frac{d ({r}^{3} )}{dr} ) }} \\ \\ { \tt{area = \frac{4}{3}\pi(3 {r}^{2}) }} \\ \\ { \boxed{ \rm{area = 4\pi {r}^{2} }}}[/tex]

[tex]{ \boxed{ \mathfrak{DC}}}{ \underline{ \mathfrak{ \: delta \: \delta \: creed}}} \\ [/tex]

We have the following information:

• At a sale, a sofa is being sold for ,67% of the regular price

• The sale price is $469

And we need to determine the regular price.

To find it, we can proceed as follows:

1. Let x be the regular price. Then we have:

2. Now, we have to solve for x as follows:

Therefore, in summary, the regular price is $700.