According to the given data we have the following function:
f(x)=3x-6
To determine f(8) we would have to plug in into the equation the 8 and then proceed to calculate it, so:
If f(x)=3x-6
Then, f(8)=3(8)-6
f(8)=24-6
f(8)=18
Let f(t) = 3 + 2, g(x) = -x^2?, andhe) = (x - 2)/5. Find the indicated value:24. h (g(5))
The Solution to Question 24:
Given the function below:
[tex]\begin{gathered} g(x)=-x^2 \\ h(x)=\frac{x-2}{5} \end{gathered}[/tex]We are asked to find the value of h(g(5)).
Step 1:
We shall find g(5) by substituting 5 for x in g(x).
[tex]g(5)=-5^2=-25[/tex]So that:
[tex]h(g(5))=h(-25)[/tex]Similarly, we shall find h(-25) by substituting -25 for x in h(x).
[tex]h(-25)=\frac{-25-2}{5}=\frac{-27}{5}[/tex]Therefore, the correct answer is
[tex]\frac{-27}{5}[/tex]What is x in x/4=1.8/5
Answer:
x = 1.44
Step-by-step explanation:
Multiply both sides by 4 to get rid of the denominator on the LHS(Left hand Side) of the equation and you get x
(x/4) x 4 = 1.8/5 x 4
x = 1.44
4) The half-life of a medication is the amount of time for half of the drug to be eliminated from the body. The half-life of Advil or ibuprofen is represented by the equation 2 ) 5 . 0 ( t M R = , where R is the amount of Advil remaining in the body, M is the initial dosage, and t is time in hours.
Based on the half-life, 35.36 mg will remain at 6:00P PM in the body
The amount of the medication that will remain at 6:00P PM?The details that complete the question are added as an attachment
From the question, we have
Initial dosage = 200 mg
This means that
M = 200
Also, we have
Initial time =1 : 00 pm
This means that the number of hours, is
n = 6pm - 1pm
n = 5
Recall that the function is given as
R = M(0.5)ⁿ/²
So, we have the following equation
R = 200 x (0.5)⁵/²
Evaluate the quotient of the exponents
So, we have the following equation
R = 200 x (0.5)².⁵
Evaluate the products
R = 35.36 mg
Using the above computation as a guide, we have the remaining amount to be 35.36 mg
Hence, the amount of the medication that will remain at 6:00P PM is 35.36 mg
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Which expression is equivalent to (2-3x) (2+3x) ?
Answer:
[tex]4-9x^{2}[/tex]
Step-by-step explanation:
in the first parenthesis, multiply the FIRST number (2 - 3x) by the numbers in the OTHER parenthesis. (2 + 3x)
[tex](2-3x)(2+3x)[/tex]
it would look like:
[tex]2(2) = 4\\2(3x) = 6x[/tex]
Next, multiply the SECOND number (2 - 3x) by the numbers in the OTHER parenthesis. (2 + 3x)
[tex]-3x(2) = -6x\\-3x(3x) = 9x^2[/tex]
Now, add like terms. Your answer should either be:
[tex]4+6x-6x+9^2[/tex] OR [tex]4 -9x^2[/tex]
Soue se compound inequality and give your answer in intentel notation- 10 AND-80-72-1
S= (-4, 1 ]
1) Solving that compounded inequality
4x +6 > -10 and -8x+7 ≥ -1
2) Let's start by 4x +6 > -10
4x +6 > -10 Subtracting 6 from both sides
4x > -10-6
4x > -16 Dividing both sides by 4
x > -4
And with -8x+7 ≥ -1
-8x+7 ≥ -1 Subtract 7 from both sides
-8x ≥ -1 -7
-8x ≥ -8 Multiply by -1
8x ≤ 8
x ≤ 1
3) Graphing the solution interval:
So the solution is the interval S= (-4, 1 ] not including x= -4 and including the value x = 1
A circle has a circumference of 10 inches. Find its approximate radius, diameter and area
Answer:
Radius = 1.59 in
Diameter = 3.18 in
Area = 7.94 in²
Explanation:
The circumference of a circle can be calculated as:
[tex]C=2\pi r[/tex]Where r is the radius of the circle and π is approximately 3.14. So, replacing C by 10 in and solving for r, we get:
[tex]\begin{gathered} 10\text{ in = 2}\pi r \\ \frac{10\text{ in}}{2\pi}=\frac{2\pi r}{2\pi} \\ 1.59\text{ in = r} \end{gathered}[/tex]Then, the radius is 1.59 in.
Now, the diameter is twice the radius, so the diameter is equal to:
Diameter = 2 x r = 2 x 1.59 in = 3.18 in
On the other hand, the area can be calculated as:
[tex]A=\pi\cdot r^2[/tex]So, replacing r = 1.59 in, we get:
[tex]\begin{gathered} A=3.14\times(1.59)^2 \\ A=3.14\times2.53 \\ A=7.94in^2 \end{gathered}[/tex]Therefore, the answer are:
Radius = 1.59 in
Diameter = 3.18 in
Area = 7.94 in²
4. A stone nudged off the Royal Gorge Bridge near Cañon City, Colorado, falls 1053 feet before hitting water. Because its speed increases as it falls, the distance ittravels each second increases. During the first second, it drops 16 feet. During the next second, it drops an additional 48 feet. During the third second, it drops another80 feet. The distances traveled each second form an arithmetic sequence:16, 48, 80,...Part 1: How far does the stone fall during the 5th second? Find and use the explicitformula.a. What is the first term of the sequence?b. What is d, the common difference?c. Write the explicit formula in function notation. Use f(n) = f(1) + (n - 1)d, wheref(1) represents the first term.d. Use the explicit formula to find the distance the stone travels in the 5th second.Part II: The table below shows the values in the sequence you already know. Use the explicit formula or the common difference to complete the table for the first 7 seconds. Time (s) 1 2 3 4 5 6 7 Distance (ft) 16 48 80 | | 144 | | | | Part ||| : Use the table from part 2 to answer the questions a. The values in the table form a(n)___ sequence and the term numbers are shownb. The term values are shown in the in the____row, and the term numbers are shown in the ___ row. c. This sequence is associated with a(n)___function d. The domain of the function is the set of time values:___
The formula for determining the nth term of an arithmetic sequence is expressed as
f(n) = f(1) + (n - 1)d
Where
f(1) represents the first term
d represents the common difference
n represents the number of terms
From the information given,
f(1) = 16
d = 48 - 16 = 80 - 48 = 32
a) The first term of the sequence is 16
b) the common difference is 32
c) The explicit is
f(n) = 16 + 32(n - 1)
d) To find the distance the stone travels in the 5th second, it means that n = 5
Thus
f(5) = 16 + 32(5 - 1)
f(5) = 16 + 32 * 4
f(5) = 144
the distance the stone travels in the 5th second is 144 feet
a bottle of ketchup holds 0.95 liters how maney milliliters does it hold?
Explanation:
The relation between liters and milliliters is:
[tex]1\text{ liter}=1000\text{ milliliters}[/tex]we have to multiply the liters by 1000
Answer:
The answer is 950 milliliters
What is the slope of this line? :(
Answer:
y=1/4x+1
Step-by-step explanation:
Answer:
m=1/4
Step-by-step explanation:
Got it correct
In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the probability that a randomly selected student will be taller than 71 inches tall, to the nearest thousandth?
The probability that a randomly selected student will be taller than 71 inches tall is 0.010.
We use z score formula to calculate :
z = (x-μ)/σ
where,
z = standard score
x = observed value
μ = mean of students height
σ = standard deviation of students height
x = 63 inches
μ = 70 inches
σ = 3 inches
For x shorter than 63 inches we calculate
Z = (x - μ)/σ
then put the given values in above equation.
= (63 - 70)/3
= -2.33333
Probability value is :
P(x<63) = 0.0098153
Approximately to the nearest thousandth = 0.010
The probability that a randomly selected student will be taller than 71 inches tall is 0.010.
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Refer to the diagram below to prove that the exterior angle equals the
To prove that the sum of the remote interior angles and the exterior angle have the same value, we recall 2 things:
1.- the inner angles of a triangle add up 180 degrees
2.- angle 3 and angle 4 are supplementary which means that they add up 180 degrees.
[tex]\begin{gathered} \measuredangle1+\measuredangle2+\measuredangle3=180^{\circ} \\ \measuredangle3+\measuredangle4=180^{\circ} \\ \Rightarrow \\ \measuredangle1+\measuredangle2+\measuredangle3=\measuredangle3+\measuredangle4 \\ \Rightarrow \\ \measuredangle1+\measuredangle2=\measuredangle4 \end{gathered}[/tex]Answer:
They are linear pair and therefore supplementary.
Triangle sum theorem.
Substitution.
Subtraction property of equality.
factor out 2x^4 = 9x^2
Solution
Step 1
Rearrange the equation
[tex]2x^{4\text{ }}-9x^2=0[/tex]Step 2
factorise the equation
[tex]x^2(2x^2-9)=0[/tex]Hence by factorization, the answer is
x^2(2x^2 - 9) = 0
Determine the period
I hate acellus
Answer:
my answer i got is y=2x+9
Answer:
5
Step-by-step explanation:
They are asking for the Period. The Period goes from one peak to the next (or from any point to the next matching point). To me it looks like that value is 5 for this graph.
A restaurant offers a $12 dinner special that has 4 choices for an appetizer, 11 choices for an entree, and 3 choices for a dessert. How many different meals are available when you select an appetizer, an entree, and a dessert?
-1514,2 – 30r2y3 + 45ryjent of517is 3(x^3)y + 6x(y^2) - 3.1. Whe3(x^3)y - 6x(y^2) +9Res-3(x^3)y + 6x(y^2) - 33(x^2)y + 5x(y^2) - 93(x^3)y + 5x(y^2) + 3
To find the quotient of the first part, we can start by noticing that all the factors on the denominator are present in all terms of the numerator, so we can factor those out and cancel with the denominator ones:
[tex]\frac{15x^4y^2-30x^2y^3+45xy}{5xy}=\frac{5xy\cdot3x^3y+5xy\cdot(-6xy^2)+5xy\cdot9}{5xy}=\frac{5xy\cdot(3x^3y-6xy^2+9)}{5xy}=3x^3y-6xy^2+9[/tex]So, the first dropdown option is
[tex]3x^3y-6xy^2+9[/tex]Also, this is the quotient, so we will use it for the second part.
The second part says that if we divide by one of the options (let's call it a), we will get:
[tex]\frac{3x^3y-6xy+9}{a}=x^3y-2xy^2+3[/tex]As we can see, no terms on the final result has fractional coefficient, so the number a has to be a common factor of all the terms coefficients. the coefficients are 3, -6 and 9, so the only common factors are 1 and 3, so the answer should be 3:
[tex]\frac{3x^3y-6xy+9}{3}=\frac{3(x^3y-2xy+3)}{3}=x^3y-2xy^2+3[/tex]So, the second dropdown option is 3.
Use the quadratic formula to solve the problems. Then state whether the roots are real number roots or complex number roots.
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
Solving the quadratic equation using the quadratic formula, we have that:
From the solution above, we can see that the roots are complex.
[tex]\begin{gathered} \text{The roots of the equation are:} \\ x\text{ = }\frac{-5}{4}\text{ + i }\frac{\sqrt[]{31}}{4}, \\ x\text{ =}\frac{-5}{4}-i\frac{\sqrt[]{31}}{4} \end{gathered}[/tex]A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 12.5 ft by 13.5 ft by 13 ft. The container is entirely full. If, on average, its contents weigh 0.18 pounds per cubic foot, and, on average, the contents are worth $7.18 per pound, find the value of the container’s contents. Round your answer to the nearest cent.
The volume of a right rectangular prism is given by
[tex]V=\text{height}\times length\times width[/tex]From the given information, we know that
[tex]\begin{gathered} \text{ height=13.5 ft} \\ \text{ length=13 ft} \\ \text{width = 12.5 ft} \end{gathered}[/tex]So, the volume is given by
[tex]V=13.5\times13\times12.5ft^3[/tex]which gives
[tex]V=2193.75ft^3[/tex]Now, since the content weigh 0.18 pound per cubic foot and worth $7.18 per pound, the value of the container is given by,
[tex]\text{ Value=}2193.75\times0.18\times7.18[/tex]Therefore, by rounding to the nearest cent, the answer is:
[tex]\text{Value}=\text{ \$2835.20}[/tex]Daylyn wants to win headphones . In addition to his grandmother and uncle, some friends of his agree that each one will give him a $5 donation . Some other friends agree that each one will pay him $0.25 for every correct answer. The number of friends who donate $ 5 to Daylyn is 3 times the number who pays him for correct answers. Write and solve an equation to find the number of friends who must pay him $0.25 for each correct answer in order for Daylyn to meet his goal
Let
x ------> number of friends of his agree that each one will give him a $5 donation
y -----> the number of friends who must pay him $0.25 for each correct answer
so
to win headphones-------> $350
we have that
x=3y -------> equation A
5x+0.25y=350 -------> equation B
substitute equation A in equation B
5(3y)+0.25y=350
solve for y
15y+o.25y=350
15.25y=350
y=22.95
therefore
the answer is 23 friends who must pay him $0.25 for each correct answerIn a charity triathlon, Mark ran half the distance and swam a quarter of the distance when he took a quick break to get a drink of Gatorade he was just starting to bite the remaining 12 miles what was the total distance of the race?
Exam Content
Question 25
Approximately how many years would it take money to grow from $5,000 to $10,000 if it could earn 6% interest?
It would take 16.66 years to grow from $5,000 to $10,000 if it could earn 6% interest.
Time it would take money to grow from $5,000 to $10,000
The prinicipal amount is $ 5000
The total amount is $ 10000
The rate of interest is 6%
Interest = Amount - principal
interest = 10000 - 5000 = 5000
By putting the simple interest formula
SI = prt/100
where p is the principal, r is the rate of interest and t is the time period
SI = 5000 x 6% x t/100
5000 = 5000 x 6 x t / 100
5000 x 100= 5000 x 6 x t
t = 100/6
t = 16.66
Therefore, it would take 16.66 years to grow from $5,000 to $10,000 if it could earn 6% interest.
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How would you use the Pythagorean Theorem to find the missing length in the triangle shown? Find the missing length.
The given triangle is a right angle triangle. The pythagorean theorem is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the diagram,
hypotenuse = AB = c
one leg = BC = 9
other leg = AC = 12
By applying the pythagorean theorem, we have
[tex]\begin{gathered} c^2=9^2+12^2\text{ = 81 + 144} \\ c^2\text{ = 225} \\ c\text{ = }\sqrt[]{225} \\ c\text{ = 15} \end{gathered}[/tex]The missing length is 15 cm
Victoria, Cooper, and Diego are reading the same book for theirlanguage arts class. The table shows the fraction of the bookeach student has read. Which student has read the leastamount? Explain your reasoning.
Given:
Completion of reading in fractions:
[tex]\text{Victoria}=\frac{2}{5};\text{Cooper}=\frac{1}{5};\text{Diego}=\frac{3}{5}[/tex]Since the denominators,
[tex]\text{The least value of the three given values is }\frac{1}{5}[/tex]Therefore, Cooper has read the least amount.
Which of the following is a perfect cube?118481
From the options given we will have that a perfect cube is:
[tex]1^3=1\ast1\ast1=1[/tex]So, 1 is the perfect cube.
7-Which beans are the better deal? Kidney Beans $1.18 per lb O Lima Beans $213 for 2 lbs 76-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 or .00, so if answer is 43 cents, its 0.43 or.43, if there is a dollar amount like 1.50, do not add zeros in front).
Given :
Two kinds of Beans :
1. Kidney Beans $1.18 per lb
The unit price = $1.18
2. O Lima Beans $213 for 2 lbs
The unit price = 2.13/2 = 1.065
Rounding to the nearest hundredth
So,
The unit
The question is in the picture, couldn’t fit the last graph so sent it in a separate picture
Explanation:
Concept:
To figure out if a graph is a function, we will use the vertical line test below
The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.
From the first graph we can see that the vertical line cuts the points at on intersection
The Second graph is given below as
Its has two intersections on both sides of the graph
The third graph is given below as
It has two intersections on the ride hand side of the graph
The Fourth graph ios given below as
Its has two intersection on the right hand side of the graph
In conclusion,
A graph is said to be a function if one value of x has a separate value of y
Therefore,
The final answer is
The FIRST OPTION is the correct answer
Two students measured a box in class. They used a digital scale and found that the mass was 400 grams. They then measured the box found the length is 2cm, the width is 2cm, and the height is 1cm. What is the density of the object
Explanation
Step 1
the density of an object is given by:
[tex]\begin{gathered} density=\frac{mass_{object}}{volume_{object}} \\ \end{gathered}[/tex]Let
mass: 400 grams
length's box=2 cm
width´s box= 2 cm
height's box= 1 cm
Step 2
find the volume of the box
[tex]\begin{gathered} \text{Volume}=\text{ length}\cdot width\cdot height \\ \text{replacing} \\ \text{Volume= 2 cm }\cdot\text{ 2 cm }\cdot\text{ 1 cm} \\ \text{Volume}=\text{ 4 cubic cm} \end{gathered}[/tex]Step 3
finally, replace the values of mass and volume in the density equation
[tex]\begin{gathered} density=\frac{mass_{object}}{volume_{object}} \\ density=\frac{400\text{ grm}}{4cm^3} \\ \text{density}=100\frac{gr}{cm^3} \end{gathered}[/tex]I hope this helps you
Which of the following is only true sometimes? A. The sum of a rational number and a rational number is rational. B. The sum of a rational number and an irrational number is irrational. C. The product of an irrational number and an irrational number is irrational. D. The product of a nonzero rational number and an irrational number is irrational.
The sum of a rational number and a rational number is rational. ALWAYS
The sum of a rational number and an irrational number is irrational.
The product of an irrational number and an irrational number is irrational. SOMETIMES
For example, the product of multiplicative inverses like √2 and 1/√2 will be 1
The product of a nonzero rational number and an irrational number is irrational.
In the equation y = 2x, y represents the perimeter of a square.What does x represent?Ahalf the length of each sideBthe length of each sideСtwice the length of each sideDtwice the number of sides
Given:
An equation that represents the perimeter of a square:
[tex]y=2x[/tex]To find:
What x represents.
Solution:
It is known that the perimeter of the square is equal to four times the side of the square.
Let the side of the square be s. So,
[tex]\begin{gathered} y=P \\ 2x=4s \\ x=\frac{4s}{2} \\ x=2s \end{gathered}[/tex]Therefore, x represents twice the length of each side.
In the diagram, m/ACB = 55°.
E
What is mZECD?
90°
O 55°
180°
D
O 125°
C
B
80
Answer:
55°
Step-by-step explanation:
Angle ACB and angle ECD are alternate exterior angles and alternate angles have same angle measurements:
If angle ACB = 55°
then angle ECD is also = 55°
m(25+2)(x-7)(4%-8)"y =
From the figure we can obtain 2 equations:
[tex](2y+2)+(4x-8)=180[/tex]and
[tex](9x-7)+(4x-8)=180[/tex]first lets simplify both equations:
for the first;
[tex]2y+4x=186[/tex]and for the second one:
[tex]9x+4x=195\Rightarrow13x=195\Rightarrow x=\frac{195}{13}=15[/tex]Now we have that x=15 and we can substitute x for 15 in the first equation to find y:
[tex]2y+4(15)=186\Rightarrow2y=126\Rightarrow y=63[/tex]so the final answe is: x=15 and y=63
