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:
;)
Write 2^100 as an exponent with a base of 32.
Answer:
2 is a factor 5 times
Step-by-step explanation:
2 x 2 x 2 x 2 x 2 =32
Convert theta= 3pi/4 to rectangular form.
A. y= -1
B. y= 1
C. y= x
D. y= -x
E. x= -1
[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)
Find the discriminant and determine how many solutions the equation has and if they are imaginary or real. Please show all work.
y = 4x^2 - 5x + 1
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.
please help me asap!
Answer:
2968.30 cm cube.
Step-by-step explanation:
Given is a cone and top of it is a hemisphere of radius 9 cm.
Cone has height as 17 and radius same 9 cm.
We have to find the volume of the compound shape
We find that the volume would be the sum of that of hemisphere of radius 9 cm and cone of height 17, and radius 9 cm.
Volume of compound shape = volume of cone+Volume of hemisphere
= [tex]\frac{1}{3} \pi r^{2} h+\frac{2}{3} \pi r^{3}[/tex]
substitute for h and r in the equation
Required volume =
[tex][tex]\frac{1}{3}\pi r^{2} (h+2r) = \frac{1}{3}\pi 9^{2} (17+2(9))\\= 1441.99+1526.31\\=2968.30[/tex][/tex]
So answer is 2968.30 cm cube.
=
△ABC @ △DEF. Find the measures of the given angles or the lengths of the given sides
BC = 3z + 2, EF = z + 6
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.
Explanation: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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Math true or false
Septima investing money into two different accounts at the same time. the system of inequalities represent the balance of each account where x represents the number of years the money has been invested.
Math! Please help! Please explain your answers.
Answer:
FalseFalseTrueStep-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.
Barney works as a car salesman and earns $175 for every car that he sells. He has fixed expenses of $3100 every month. He has laid out his projected variable expenses as well as his projected car sales for the first 6 months of next year.
. EXPENSES VARIABLE CARS SOLD
january 2,600 32
feb 3,200 36
march 1,600 26
may 800 22
which month will barney sell enough cars to pay for all his monthly expenses ?
feb
Step-by-step explanation: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.
Ming is given the following function and asked to find b. f(x)=15(b)x If f(4) = 1215, what is one possible value of b?
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
Select Linear or Nonlinear for each function. Function Linear Nonlinear y=5x+1 y=23 y=1−2x2
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.
In an airplane 35% of the passengers are children they’re 140 children on the airplane how many passengers are on the airplane
Answer:
there are 49 passengers
Step-by-step explanation: 35%=0.35
0.35*140= 49
The amount, A, in milligrams, of radioactive material remaining in a container can be modeled by the exponential function A(t)=5(0.5)^0.25t where T is time, in years. Based on this model how many years does it take for half of the original radioactive material to be left remaining?
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.
On the main street, the tourists walked for s km with a speed of v km/hour. On the side road, the tourists walked twice the distance that they covered on the main street. How much time t (in hours) did the tourists spend if it is known that on the side road they walked with a speed that was 2 km/hour less than their speed on the main road? Find t when s=10, v=6.
Answer:
6 2/3 hours
Step-by-step explanation:
We assume the time of interest is the total time spent on the main road and side road.
In each case, ...
... time = distance/speed
On the main road, ...
... tmain = s/v
On the side road, ...
... tside = (2s)/(v -2)
Then the total time spent is ...
... ttotal = tmain + tside
... = s/v + (2s)/(v -2)
For s=10 and v=6, this is ...
... ttotal = 10/6 + 2·10/(6 -2) = 5/3 + 20/4 = 5/3 + 5 . . . . hours
... ttotal = 6 2/3 hours
Answer:
6 hr 40 min
Step-by-step explanation:
A rectangle has a length of 4 inches and a width of x inches. The value of the perimeter of the rectangle is equal to the value of the area of the rectangle. What is the value of x?
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.
Quinn is twice as old as karl and four years older than parker. The sum their ages is 21. How old is Parker
Answer:
Parker is 6 years old
Step-by-step explanation:
Parker is 6 years old
Step-by-step explanation: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
Tiffany answered 90% of the questions on her math test correctly. There were 50 questions on the test. how many questions did Tiffany answer correctly?
Multiply the total number of questions by the percent:
50 questions x 90% =
50 x 0.90 = 45
She answered 45 questions correctly.
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. Below is a list of items Ralph made of the items he has in his apartment that he would like to be insured with his policy. What will Ralph’s annual renters insurance premium be? Ralph's Stuff Value TV $150 VCR $60 DVD Player $100 Stereo $80 Sofa $200 Entertainment Center $100 Microwave $40 Coffee Maker $20 Computer $850 Bicycle $200 Coin Collection $600 Pictures/Posters $175 a. $17.88 b. $35.48 c. $214.58 d. $425.65 Please select the best answer from the choices provided A B C D Mark this and return
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 .
Which relation is displayed in this table? x y
5 5
A. {(5, 5), (6, −6), (8, 7), (−9, 9)} 8 7
6 -6
-9 9
B. {(5, 5), (−6, 6), (7, 8), (9, −9)}
C. {(−5, 5), (−6, 6), (−8, 7), (−9, 9)}
D. {(5, −5), (6, −6), (8, −7), (9, −9)}
A. {(5, 5), (6, −6), (8, 7), (−9, 9)}
Step-by-step explanation:Compare the table contents to the ordered pairs in each relation. The first pair of table values, (5, 5) matches relations A and B, but not C or D.
The second pair of table values (8, 7), matches relation A, but not B. Since all pairs of table values show up in relation A, and we have rejected relations B, C, and D as inappropriate choices, the answer is A.
What is one method to find the measure of angle B?
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
What is Trigonometry?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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What isn't the volume of the cylinder below? Radius 8 height 3
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.
Evaluate the expression 3a+2b/2 when a = -3 and =-4
The solution of the expression 3a+2b/2 is -13 when a = -3 and b = -4
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
What are Arithmetic operations?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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suppose y varies directly with x. if y= 24 when x = 4, what is y when x = 9?
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
If GF is a midsegment of CDE, find CD.
A. 3.4
B. 6.8
C. 13.6
D. 14
Answer:
C
Step-by-step explanation:
Triangle CGF and triangle CED are similar. Hence, the ratio of their corresponding sides are equal. Thus we can write:
[tex]\frac{5x+4}{2x+3}=\frac{CD}{3x+0.8}[/tex]
We can now cross multiply and solve for CD:
[tex]\frac{5x+4}{2x+3}=\frac{CD}{3x+0.8}\\(5x+4)(3x+0.8)=(2x+3)(CD)\\15x^2+4x+12x+3.2=(2x+3)(CD)\\15x^2+16x+3.2=(2x+3)(CD)\\CD=\frac{15x^2+16x+3.2}{2x+3}[/tex]
Since GF is a midsegment of CDE, CD is double of CF. So we can write:
[tex]CD=2CF\\\frac{15x^2+16x+3.2}{2x+3}=2(3x+0.8)\\\frac{15x^2+16x+3.2}{2x+3}=6x+1.6\\15x^2+16x+3.2=(6x+1.6)(2x+3)\\15x^2+16x+3.2=12x^2+18x+3.2x+4.8\\15x^2+16x+3.2=12x^2+21.2x+4.8\\3x^2-5.2x-1.6=0[/tex]
By using quadratic formula [tex]\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex] and with a=3, b= -5.2, and c= -1.6, we find the value of x to be:
[tex]\frac{5.2+-\sqrt{(-5.2)^2-4(3)(-1.6)} }{2(3)}=2[/tex]
Since the expression for CD is [tex]\frac{15x^2+16x+3.2}{2x+3}[/tex] , we plug in [tex]x=2[/tex] into this expression to find value of CD:
[tex]\frac{15(2)^2+16(2)+3.2}{2(2)+3}=13.6[/tex]
The correct answer is C
Answer:
C. 13.6
Step-by-step explanation:
We have been given that GF is a mid-segment of CDE.
Since we know that mid-segment of a triangle is half the length of its parallel side.
We can see that ED is parallel to GF , so measure of GF will be half the measure of ED. We can represent this information as:
[tex]GF=\frac{1}{2}ED[/tex]
Let us substitute given value of GF and ED to find our x.
[tex]2x+3=\frac{1}{2}(5x+4)[/tex]
Multiply both sides of equation by 2.
[tex]2*(2x+3)=2*\frac{1}{2}(5x+4)[/tex]
[tex]2*(2x+3)=5x+4[/tex]
[tex]4x+6=5x+4[/tex]
[tex]6=5x+4-4x[/tex]
[tex]6=x+4[/tex]
[tex]6-4=x[/tex]
[tex]2=x[/tex]
We can see that triangle CFG is similar to triangle CDE, so we will use proportions to find length of CD.
[tex]\frac{CF}{GF}=\frac{CD}{ED}[/tex]
Substitute given values.
[tex]\frac{3x+0.8}{2x+3}=\frac{CD}{5x+4}[/tex]
Upon substituting x=2 in our equation we will get,
[tex]\frac{3*2+0.8}{2*2+3}=\frac{CD}{5*2+4}[/tex]
Let us simplify our equation.
[tex]\frac{6+0.8}{4+3}=\frac{CD}{10+4}[/tex]
[tex]\frac{6.8}{7}=\frac{CD}{14}[/tex]
[tex]14*\frac{6.8}{7}=CD[/tex]
[tex]2*6.8=CD[/tex]
[tex]13.6=CD[/tex]
Therefore, CD equals 13.6 and option C is the correct choice.
Abby buys 1 sheet of stickers. 5 strips of ten and 9 singles. How many stickers did she buy?
Eric is 6 1/6 feet tall and his brother is 5 3/4 feet tall. Eric is how many feet taller than his brother?
A. 1/5 feet
B. 5/12 feet
C. 7/12 feet
D. 3/4 feet
Answer:
B. 5/12 feet
Step-by-step explanation:
We know that Eric is [tex]6\frac{1}{6}[/tex] feet tall while his brother is [tex]5\frac{3}{4}[/tex] feet tall. We are supposed to find out how many feet is Eric taller than his brother.
So basically we have to find the difference between the height of the two brothers.
First, let's just change the mixed numbers to improper fractions:
[tex]6\frac{1}{6}[/tex] = [tex]\frac{37}{6}[/tex]
[tex]5\frac{3}{4}[/tex]= [tex]\frac{23}{4}[/tex]
Now taking their difference:
[tex]=\frac{37}{6} -\frac{23}{4}\\\\=\frac{148-138}{24}\\\\=\frac{10}{24}\\\\=\frac{5}{12}[/tex]
Therefore, Eric is 5/12 feet taller than his brother.
A plant has a initial height of 1 inch and grows at a constant rate of 3 inches each month. A second plant that also grows at a constant rate has an initial height of 4 inches and is 28 inches taller after 1 year. After how many months are the plant the same height?
Answer: that would be 3 months.
Step-by-step explanation:
I forgot how to this can someone help please
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
As a promotion, a clothing store draws the name of one of its customers each week. The prize is a coupon for the store. If the winner is not present at the drawing, he or she cannot claim the prize, and the amount of the coupon increases for the following week's drawing. The function f(x) = 20 (1.2)^x gives the amount of the coupon in dollars after x weeks of the prize going unclaimed. {{ x is the exponent on (1.2). }}
(A) What is the percent increase each week?
(B) What is the original amount of the coupon? (the initial value)
(C) What is the amount of the coupon after 2 weeks of the prize going unclaimed?
(D) After how many weeks of the prize going unclaimed will the amount of the coupon be greater than $100?
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.
Three hundred people were asked to choose their favorite of the following ice cream flavors: vanilla, chocolate, or strawberry. Which of the following fractions is the best estimate for the number of people that chose vanilla?
1/3 1/4 1/10 1/2
Answer:
I believe it would still be considered 1/2
Step-by-step explanation:
Answer:
1/2Step-by-step explanation:
The table shows formulas for the recommended heart rates during exercise for a person who is "a" years old. Write and solve a compound inequality to determine the heart rate range for a 16 year old person.
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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For what values of x does the following hold true:
a. (5x+3)^2=5(x+3)
b. (3x+10)^2=3(x+10)
c. (3x−8)^2=3x^2−8x
a. x ∈ {-1.2, 0.2}
b. x ∈ {-4 2/3, -1 2/3}
c. x ∈ {2 2/3, 4}
Step-by-step explanation:For this sort of exercise, I find a graphing calculator to be very handy. While the one shown in the attachment (Desmos) can solve the equation as written, I find it convenient to recast the equation to the form f(x) = 0. The calculator finds the values of zero crossings very nicely. Some, like my TI-84, will show the value to 8 or 10 significant digits. Here, 4 digits is sufficient to determine the exact solution.
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If you want to work these by hand, you rewrite them to standard form, then use factoring, completing the square, or the quadratic formula to solve them.
a. 25x² +30x +9 -5x -15 = 0 . . . . subtract the right side
... 25x² +25x -6 = 0 . . . . . . . . . . . collect terms
... (5x+6)(5x-1) = 0 . . . . . . . . . . . . . factor (the graphing calc helps here)
... x = -6/5, 1/5
b. 9x² +60x +100 -3x -30 = 0 . . . . subtract the right side
... 9x² +57x +70 = 0 . . . . . . . . . . . . collect terms
... (3x +14)(3x +5) = 0 . . . . . . . . . . . factor
... x = -14/3, -5/3
c. 9x² -48x +64 -3x² +8x = 0 . . . . . subtract the right side
... 6x² -40x +64 = 0 . . . . . . . . . . . . collect terms
... 3x² -20x +32 = 0 . . . . . . . . . . . . factor out 2
... (3x -8)(x -4) = 0 . . . . . . . . . . . . . . factor
... x = 8/3, 4