If GF is a midsegment of CDE, find CD.

A. 3.4

B. 6.8

C. 13.6

D. 14

Answer:

102 ≤ heart rate ≤ 183.6

Step-by-step explanation:

... lower limit ≤ heart rate ≤ upper limit

Put 16 where "a" is and do the arithmetic.

... lower limit = 0.5(220 -16) = 102

... upper limit = 0.9(220 -16) = 183.6

Then the inequality is ...

... 102 ≤ heart rate ≤ 183.6

_____

Comment on the problem

There is nothing to "solve" here. One only needs to evaluate the limits.

In this Compound Inequality question, The recommended heart rate range for a 16 year old person, according to the provided formulas, is between 102 and 183.6 beats per minute.

Given that the age 'a' is represented by 16 years, we can simply substitute this value into the two given formulas to find the recommended heart rate range.

The lower limit of the heart rate is given by the formula 0.5 x (220 - a) and the upper limit is given by the formula 0.9 x (220 - a).

For the lower limit, substituting a = 16, we get 0.5 x (220 - 16) = 102 beats per minute. Similarly, for the upper limit, we get 0.9 x (220 - 16) = 183.6 beats per minute.

Therefore the range of the heart rate for a 16 year old person is 102 to 183.6 beats per minute.

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x³y⁴

The Lowest Common Denominator of fractions is the Least Common Multiple of their denominators. That is, you want to find the LCM of ...

Find the highest power of each of the factors, and multiply those together.

The highest power of x is x³. The highest power of y is y⁴. So, the LCM of these expressions is ...

... x³y⁴

_____

Then the two fractions are ...

... 3y³/(x³y⁴) . . . and . . . 7x²/(x³y⁴)

Answer:

A is the right one

Step-by-step explanation:

it is right on edge

We find angle B by using the pythagorean theorem to find BC then solve the equation tanB=8/BC

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

BCD is a right angle triangle

We have to find the angle B from the triangle

BD is the hypotenuse which is √89

DC is the opposite side of angle B

We can find angle B by using sine function.

Or we can find the length of BC by using pythagorean theorem

then find the tanB function

tanB=8/BC

Hence, we find angle B by using the pythagorean theorem to find BC then solve the equation tanB=8/BC

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Answer:

2<x<∞

Step-by-step explanation:

The arrow has a filled in circle at around the 2.5 mark which allows us to deduce that the number 2 is not included in the inequality but almost all the numbers after 2 i.e. (2.1,2.2,2.3,2.4,2.4... etc ) are included. This gives us our lower bound.

The arrow goes to positive infinity. Which gives us our upper or left bound.

Answer:

r>(greater than or equal to)2.5

Step-by-step explanation:

Answer:

there are 49 passengers

Step-by-step explanation: 35%=0.35

0.35*140= 49

Answer:

Step-by-step explanation:

Since the given expression represents the account balance, the initial amount (when x=0) is $500 in Account A, and $100 in Account B. (Less money was invested in account B.)

The growth rate of each account is $1.03 per year.* (The growth rate ($/year) is identical for each account.)

The total of the initial amounts invested is $500 +100 = $600.

_____

* Comment on growth rate

Since the account balance is shown as greater than or equal to the given expression, there appears to be the possibility that adjustments are made to the account balance by some means other than the growth predicted by this inequality. For example, if the balance in Account A is $900 at the end of 1 year, the inequality will still be true, but the extra $398.97 will be in addition to the $1.03 growth predicted by this expression.

This means we really cannot say what the growth rates of the accounts might be, except that it is a minimum of $1.03 per year in each account.

_____

Comment on the expressions

More usually, we would expect to see an account balance have the equation a = 400·1.03^x. That is, the interest rate would be 3% and it would be compounded annually. The expression 400 + 1.03x is very unusual in this situation.

The correct classification for each function is as follows:

1. [tex]\( y = 5x + 1 \)[/tex] - Linear

2. [tex]\( y = 23 \)[/tex] - Linear

3. [tex]\( y = 1 - 2x^2 \)[/tex]- Nonlinear

A linear function is one that can be written in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] and [tex]\( b \)[/tex] are constants, and [tex]\( x \)[/tex] is the independent variable. The graph of a linear function is a straight line.

1. For the function [tex]\( y = 5x + 1 \)[/tex], we can see that it is already in the form of a linear equation with [tex]\( m = 5 \)[/tex] and [tex]\( b = 1 \)[/tex]. Therefore, this function is linear.

2. The function [tex]\( y = 23 \)[/tex] is a constant function. Although it does not have an [tex]\( x \)[/tex] term, it can still be considered linear because it can be written as [tex]\( y = 0x + 23 \)[/tex], where the slope [tex]\( m = 0 \)[/tex] and the y-intercept [tex]\( b = 23 \)[/tex]. The graph of this function is a horizontal line, which is a special case of a linear function.

3. The function [tex]\( y = 1 - 2x^2 \)[/tex] contains an [tex]\( x^2 \)[/tex] term, which makes it a quadratic function. Quadratic functions are nonlinear because their graphs are parabolas, not straight lines. The presence of the [tex]\( x^2 \)[/tex] term means that the rate of change of [tex]\( y \)[/tex] with respect to [tex]\( x \)[/tex] is not constant, which is a key characteristic of nonlinear functions. Therefore, this function is nonlinear.

Answer:

I believe it would still be considered 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

feb

When the number of cars needed to be sold to meet fixed plus variable expenses is subtracted from the number of cars projected to be sold, the result is negative for all months listed except February. In that month, Barney covers is expenses.

We have computed ...

... (expected car sales) - (needed car sales)

where ...

... (needed car sales) = (variable expenses + fixed expenses)/(income per car sold)

For January, this calculation gives ...

... 32 - (2600 +3100)/175 = 32 -32.571 = -0.571

That is, Barney does not project he will sell enough cars to pay his January expenses.

In February, the result is 0, which means he will sell enough cars in February to pay all his monthly expenses.

[tex]\theta=\dfrac{3\pi}{4}=\pi-\dfrac{\pi}{4}\\\\y=\tan\theta x\\\\y=\left(\tan\dfrac{3\pi}{4}\right)x\\\\y=\left(\tan\left(\pi-\dfrac{\pi}{4}\right)\right)x\\\\y=\left(\tan\left(-\dfrac{\pi}{4}\right)\right)x\\\\y=\left(-\tan\dfrac{\pi}{4}\right)x\\\\y=-1x\\\\\boxed{y=-x}\to\boxed{D.}[/tex]

Answer:

If you are doing it on edge it is x+y=0

Step-by-step explanation:

x+y=0 when you solve for y it equals -x( y=-x)

Answer:

d. $425.65

Step-by-step explanation:

The total value of Ralph's stuff is ...

... 150 + 60 + 100 + 80 + 200 + 100 + 40 + 20 + 850 + 200 + 600 + 175 = 2575

The premium is 16.53% of that, so is ...

... 0.1653 × 2575 = 425.65

Answer:

The insurance company charges an annual premium of $425.65 .

Option (d) is correct .

Step-by-step explanation:

As given

Ralph wants to purchase a renters insurance policy for his new apartment.

His insurance company charges an annual premium of 16.53% of the approximate value of the items he owns and is keeping in his apartment.

Total amount of the items he owns and is keeping in his apartment = TV cost + VCR cost + DVD Player cost + Stereo cost + Sofa cost + Entertainment centre cost  +  Microwave cost + Coffee Maker cost +  Computer cost + Bicycle cost  +  Coin Collection cost  + Pictures/Posters cost

Putting all the values in the above

Total amount of the items he owns and is keeping in his apartment = $150 + $60 +$100 + $ 80 + $200 + $100 + $40 + $20 + $850 + $ 200 + $ 600 + $ 175

Total amount of the items he owns and is keeping in his apartment = $ 2575

16.53 % is written in the decimal form .

[tex]= \frac{16.53}{100}[/tex]

= 0.1653

Insurance company charges an annual premium = 0.1653 × Total amount of the items he owns and is keeping in his apartment .

                                                                                   = 0.1653 × 2575

                                                                                   = $ 425.65 (Approx)

Therefore the insurance company charges an annual premium of $425.65 .

Option (d) is correct .

Answer:

4 years

Step-by-step explanation:

The exponent of 0.5 is 1 when t=4. So, half the original amount will be remaining when t=4.

Answer:

37.5 g

Step-by-step explanation:

The final solution will contain 3% × 100 g = 3 g of solute. This amount of solute will be found in w grams of 8% solution, where ...

... 3 = 0.08 × w

... 3/0.08 = w = 37.5 . . . . . grams of 8% solution

Answer:

37.5 grams

Step-by-step explanation:

;)

Final answer:

To find the value of x in a rectangle with a length of 4 inches, set up the equation 2(4 + x) = 4x and solve for x. The value of x is 4 inches.

Explanation:

To find the value of x, we need to set up an equation using the given information. The perimeter of a rectangle is equal to twice the length plus twice the width. The area of a rectangle is equal to the length times the width. So, we can set up the equation: 2(4 + x) = 4x. Next, solve the equation for x:

8 + 2x = 4x

8 = 4x - 2x

8 = 2x

4 = x

Therefore, the value of x is 4 inches.

Answer: that would be 3 months.

Step-by-step explanation:

The given formula is f(x) = 20(1.2)^x

The formula is the starting amount multiplied by 1 + the percentage raised to the number of weeks.

A) the percent increase is 20% ( 1.2 in the formula is 1 +20% as a decimal)

B) the original amount is $20

C) for 2 weeks, replace x with 2 and solve:

20(1.2)^2

20(1.44) = $28.80

After 2 weeks the coupon is $28.80

D)  To solve for the number of weeks (x) set the equation equal to $100:

100 = 20(1.2)^x

Divide both sides by 20:

5 = 1.2^x

Take the natural logarithm of both sides:

ln(5) = ln(1.2^x)

Use the logarithm rule to remove the exponent:

ln(5) = x ln(1.2)

Divide both sides by ln(1.2)

x = ln(5) / ln(1.2)

Divide:

X = 8.83

At 8.83 weeks the coupon would be $100, so after 9 weeks the coupon would be greater than $100

The answer is 9 weeks.

The solution of the expression 3a+2b/2 is -13 when a = -3 and b = -4

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculation

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

Given the expression as :

⇒ 3a + 2b/2

when a = -3 and b = -4

Substitute the values of a and b

⇒ 3 × (-3) + 2 × (-4/2)

⇒ -9 - 4

⇒ -13

Hence, the solution of the expression 3a+2b/2 is -13 when a = -3 and b = -4

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Answer:

d  31 degrees

Step-by-step explanation:

We can use the formula

<C = 1/2 (arc AE - arc BD)

Let substitute in what we know

ARC AE = 120

ARC BD = 58

<C = 1/2 (120 - 58)

<c = 1/2(62)

<c = 31

Answer:

9

Step-by-step explanation:

Otf the 15 that have a view of the river, 6 have both selections.

The remaining 9 only have a view of the river.

Answer: The volume is 603.19, so whichever answer doesn't equal that.

Step-by-step explanation:

V= πr^2h

V= π(8)^2(3)

V= 603.19

Volume = 192πunits³

Work is provided in the image attached.

Multiply the total number of questions by the percent:

50 questions x 90% =

50 x 0.90 = 45

She answered 45 questions correctly.

Answer:

BC = EF = 8

Step-by-step explanation:

Assuming you mean BC ≅ EF, then ...

... 3z +2 = z +6

... 2z = 4 . . . . . . . . add -2-z

... z = 2 . . . . . . . . . divide by 2

BC = EF = 2+6 = 8

The question is about finding the measures of given sides and angles in similar triangles. By setting up a proportion between the given sides BC and EF, we can solve for the variable 'z'. This 'z' can then be used to find the sides and angles of the triangles.

In the case of the problem, we're dealing with the concept of similar triangles in geometry. Since △ABC is similar to △DEF, this means that the corresponding sides are in proportion, and corresponding angles are equal.

Given that BC = 3z + 2 and EF = z + 6, we can write a proportion: BC/EF = 3z+2 / z+6, because the lengths of the corresponding sides of these two similar triangles should be in ratio.

Then you can solve this equation for the variable 'z', which will give us the values for sides BC and EF. If necessary,  you can also find the measure of the angles using the values of 'z'.

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Step-by-step explanation:

f(x) = 15(b)x

f(4) = 1215

15(b)4 = 1215

(15)(4)b = 1215

60b = 1215

60b / 60 =  1215 / 60

b = 20.25

Check the answer

15 * 20.25 * 4 = 1215

Answer:

3

Step-by-step explanation:

if you did this on prepworks its 3.

1215=15(b)4  

121515=(b)4

81=b4

92=b4

(32)2=b4

34=b4

b = ±3

Answer: y=54

Step-by-step explanation: so 24/4 is 6 soooo 9*6=54 ez

Answer:

y =54

Step-by-step explanation:

We can use the equation y =kx

If we know y and x we can solve fork

24 = k*4

24/4 = k

6 =k

y = 6x

Substitute in 9

y =6*9

y =54

Answer:

Parker is 6 years old

Step-by-step explanation:

Parker is 6 years old

Let q, p, k represent the ages of Quinn, Parker, and Karl, respectively.

... q = 2k . . . . . . Quinn is twice as old as Karl

... q = p+4 . . . . . Quinn is 4 years older than parker

... q + p + k = 21 . . . . the sum of their ages is 21

_____

We can use the first two equations to find Karl's age in terms of Parker's.

... p+4 = q = 2k

... (p+4)/2 = k

Now, we can substitute for q and k in the last equation.

... (p+4) +p +(p+4)/2 = 21

... 5/2p +6 = 21 . . . . . . collect terms

... p = (2/5)(21 -6) . . . . subtract 6, multiply by 2/5

... p = 6 . . . . . . Parker is 6 years old

Answer:

1728

Step-by-step explanation:

You could write it like this

5.4 * 10^5 * 3.2 * 10^-3  

You could do this by multiplying the numbers first

5.4 * 3.2 = 17.28

Now work with the powers of 10

10^5 * 10^-3 = 10^(5 - 3) = 10^2

10^2 = 100

So the answer is 17.28 * 100 = 1728

Answer:

as discriminant = 9, it has two real solutions.

Step-by-step explanation:

for eqn ax^2 + bx + c, discriminant = b^2 - 4ac

y = 4x^2 - 5x + 1

discriminant = (-5)^2 - 4(4)(1)

= 25 - 16

= 9

as discriminant > 0, it has two real solutions.

Answer:

Discriminant = 9 and the equation has two real solutions

Step-by-step explanation:

For a quadratic equation in the form of y = ax^2 + bx + c, its discriminant is equal to b^2 - 4ac.

If discriminant < 0, then the equation has two imaginary solutions. If it is 0, then the equation has 1 real solution and if it is > 0, 2 real solutions.

In this case, y = 4x^2 - 5x + 1.

So its discriminant = -5^2 - 4*4*1

= 9 so it has two real solutions.

Answer:

2 is a factor 5 times

Step-by-step explanation:

2 x 2 x 2 x 2 x 2 =32

The Diameter of Hydrogen Atom in Scientific Notation is :

✿  1.06 × 10⁻¹⁰ Meters

Answer:

Step-by-step explanation: I just solve it.