Simplified form of the given radical will be,
⇒ ± √-38 = ± i√38
What is imaginary unit?
The imaginary unit is use to find solutions of many equations that do not have real number solutions.
The radical is given is,
± √-38
Now, Simplify the given radical as,
We can rewrite the radical as;
± √-38 = ± √-1 x √38
= ± i√38
( Since, √-1 = i )
Hence, Simplified form of the given radical will be,
± √-38 = ± i√38
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In your own words, describe what transformations are possible in a linear function and what in the equation causes these movements.
The transformations that is possible in a linear function is: g(x) = (x - 3)².
What in the equation causes these movements?if the function of the g (x) is known to be the original function, then one can say that:
g(x) = (x - 3)²
= g(x) = x²
This is one that is shifted by 3 unit to the right because in the above, one need to substitute x for x - 3.
Hence , it functional graph can be said to be a parabola with a vertices that is known to be opening at (3,0)
Therefore, based on the above, the example of the transformations that is possible in a linear function is: g(x) = (x - 3)².
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A cup of cereal has 12 grams of fiber, which is 40% of the amount of fiber jared’s doctor recommends he consume each day. how much fiber does jared’s doctor recommend he consume each day?
The amount of fiber asked by the doctor to be consumed is 30 grams .
Method to calculate percentages :
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100 .
Let the amount of fiber asked by the doctor to be consumed be x .
According to question ,
40 % of x = 12
Solving the equation ,
( 40 / 100 ) * x = 12
x = 1200 / 40
x = 30
Hence , the amount of fiber asked by the doctor to be consumed is 30 grams .
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Answer:
30
Step-by-step explanation:
Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and zeros of 2 and 3+ i
The polynomial function of least degree with only real coefficients is y = x³ - 8 · x² + 22 · x - 20.
What is the polynomial function of least degree with real coefficients?
The statement indicates that the polynomial has a leading coefficient of 1 and zeros of 2 and 3 + i. By algebra of quadratic equations, equations with real coefficients with complex roots are α + i β and α - i β. Then, all the roots of the polynomial function of least degree are 2, 3 + i and 3 - i. The complete expression is shown below:
y = 1 · (x - 2) · (x - 3 - i) · (x - 3 + i)
y = (x - 2) · [x² - 3 · x - i · x - 3 · x + i · x + (3 + i) · (3 - i)]
y = (x - 2) · (x² - 6 · x + 9 - i²)
y = (x - 2) · (x² - 6 · x + 10)
y = x³ - 6 · x² + 10 · x - 2 · x² + 12 · x - 20
y = x³ - 8 · x² + 22 · x - 20
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The radius of a circle measures 16 yd.. What is the circumference of the circle? Use 3.14 for pi , and do not round your answer. Be sure to include the correct unit in your answer.
Fawzia owns a small business selling used books. She knows that in the last week 45 customers paid cash, 10 customers used a debit card, and 64 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a debit card as a decimal to the nearest hundredth.
Answer:
0.08
Step-by-step explanation:
[tex]\frac{10}{45+10+64}[/tex] The numerator is the number of times a customer used a debit card. The denominator is the total of all the ways that customers have paid.
[tex]\frac{10}{19}[/tex] = 0.08403361344
This rounded to the nearest hundredths is
0.08
Answer:
0.08
Step-by-step explanation:
45 cash, 10 debit card, and 64 credit card.
= 45+10+64=119
There were a total of 119 customers. 10 paid with a debit card.
Probability the next customer will pay with a debit card:
10/119
=0.084033...
≈0.08
A car travels 560 miles In 8 hours(driving at a constant speed) how long did it take the car to go 200 miles
Answer:
see below
Step-by-step explanation:
RATE is 560 mi / 8hr = 70 mi/hr
Rate * time = distance
then
time = distance / Rate = 200 mi / 70 mi/hr = 2.857 hr ( or 2 hr 51 min)
help pls no clue where to start
Answer:
[tex]P_{rofit}=13x-50\\C_{ost}(70)=960\\P_{rofit}(70)=860\\C_{ost}(100)=1350\\P_{rofit}(100)=1250\\For\ a\ profit\ of\ \$1100\ one\ must\ sell\ 89\ stuffed\ animals.[/tex]
Step-by-step explanation:
I would suggest starting with 1 and working to 4, as it is set up for you like that.
I would start by writing down what you know, then what you need as follows:
[tex]Givens:\\ C_{ost}=13x+50;\\ R_{evenue}=36x;\\P_{rofit}=R_{evenue}-C_{ost};\\ x=N_{umber\ of\ animals}\\[/tex]
[tex]Find:\\1.\ Profit\ equation\\2a.\ C_{ost}\ to\ make\ 70\ animals\\2b.\ P_{rofit}\ from\ selling\ 70\ animals\\3a.\ C_{ost}\ to\ make\ 100\ animals\\3b.\ P_{rofit}\ from\ selling\ 100\ animals\\4.\ N_{umber}\ of\ animals\ needed\ to\ produce\ P_{rofit}\ of\ \$1100[/tex]
Now you can read it easier. Given that Profit is Revenue minus Cost, plug the equations for Cost and Revenue into the Profit equation as follows:
[tex]P_{rofit}=36x-(13x+50)\\NOTE:\ Do\ NOT\ forget\ to\ put\ the\ C_{ost}\ equation\ in\ parenthesis\ as\ you\ \\must\ subtract\ the\ entire\ C_{ost}.\\\\Distribute\ the\ negative:\ P_{rofit}=36x-13x-50\\Combine\ like\ terms:\ P_{rofit}=13x-50[/tex]
With the Profit equation, it is now easier to solve 2b, 3b, and 4.
[tex]C_{ost}\ for\ 70: C_{ost}=13(70)+50=(700+210)+50\\NOTE:\ I\ used\ the\ fact\ that\ 13*70=(10+3)*70=10*70+3*70\\C_{ost}=910+50=960\\This\ could\ also\ be\ written\ more\ clearly\ as\ C_{ost}(70)=960\\\\P_{rofit}(70) = 13(70)-50\\P_{rofit}(70)=(700+210)-50\\P_{rofit}(70)=910-50\\P_{rofit}(70)=860\\\\C_{ost}(100)=13(100)+50\\C_{ost}(100)=(1300)+50\\C_{ost}(100)=1350\\\\P_{rofit}(100)=13(100)-50\\P_{rofit}(100)=(1300)-50\\P_{rofit}(100)=1250\\[/tex]
Problem 4 will involve using the (now) known amount for profit, $1100 to find the unknown number of animals. This will involve a little bit more "algebra" compared to the prior questions.
[tex]P_{rofit}(x)=1100=13x-50\\1100=13x-50\\[/tex]
Because 13x - 50 is 1100, 13x will be 1100 + 50, just as
[tex]5*2+10 = 20\\5*2=20-10\\[/tex]
So, add 50 to both sides:
[tex]1100+50=13x-50+50\\1150=13x\\[/tex]
Because 13x is 1150, x will be 1150÷13, just as
[tex]5*2=10\\5=\frac{10}{2}[/tex]
So, divide 13 from both sides:
[tex]\frac{1150}{13}=\frac{13x}{13}\\\\\frac{1150}{13}=x[/tex]
Because 1150/13 is not an integer, use a calculator, or simplify the improper fraction to obtain...
x=88.5 (Approximately)
But, because you cannot sell half an animal, you would have to sell 89 in order to profit $1100, for bonus points, what is the actual profit accrued by selling 89 animals?
Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?
acute, because 62 + 102 < 122
acute, because 6 + 10 > 12
obtuse, because 62 + 102 < 122
obtuse, because 6 + 10 > 12
The given triangle whose sides are 6cm, 10cm, and 12cm is an obtuse triangle and it can be determined by using Pythagorean theorem which is the correct option (C).
What is Pythagoras theorem?Pythagoras theorem states that a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
The given triangle whose sides are 6cm, 10cm, and 12cm
Now, applying Pythagorean's theorem:
⇒ 6² + 10² = 12²
⇒ 36 +100 = 144
⇒ 136 = 144
Here, it is clearly observed that 136 < 144 therefore, the triangle is obtuse.
Therefore, the given triangle whose sides are 6cm, 10cm, and 12cm is an obtuse triangle
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The table below gives the annual sales (in millions) of a product. year 1998 1999 2000 2001 2002 2003 2004 2005 2006 sales 222 276 318 348 366 372 366 348 318 What was the average rate of change of annual sales a) Between 2003 and 2004 millions of dollars/year b) Between 2003 and 2006 millions of dollars/year
Using it's concept, the average rate of change is given as follows for the intervals:
a) -6 millions of dollars per year.
b) -18 millions of dollars per year.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
For item a, we have that:
In 2003, the amount is of 372 million sales.In 2004, the amount is of 366 million sales.Hence:
r = (366 - 372)/1 = -6 millions of dollars per year.
For item b, we have that:
In 2003, the amount is of 372 million sales.In 2006, the amount is of 318 million sales.Hence:
r = (318 - 372)/3 = -18 millions of dollars per year.
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An empty shipping box weighs 250 grams. The box is then filled with t-shirts. Each t-shirt weighs 132.5 grams.
The equation W=250+132.5t represents the relationship between the quantities in this situation, where W is the weight, in grams, of the filled box and is the number of shirts in the box.
If the company ships 100 t-shirts in a box, how much will the box weigh?
________ grams
========================================================
Explanation:
t = number of t-shirts
t = 100 shirts are in the box
Plug this into the equation and simplify to find W
W = 250+132.5t
W = 250+132.5(100)
W = 250+13250
W = 13500
The box weighs 13500 grams
This is equivalent to 13500/1000 = 13.5 kg
a family is comparing different car seats. one car seat is designed for a child up to and including lb. another car seat is designed for a child between lb and lb. a third car seat is designed for a child between lb and lb, inclusive. model those ranges with compound inequalities. which car seats are appropriate for a -lb child?
According to the given statement the following car seats are adequate for a 32-pound child:
car seat suited for a youngster weighing between 15 and 40 pounds, andcar seat intended for children weighing 30 to 85 poundsWhat is an interval notation?Interval notation tells which part of the number line, from left to right, is included in the solution (i.e., which part of the number line is shaded). Parentheses are written next to endpoints which are NOT included in the solution while brackets are written next to included endpoints.
According to the given statement:The Inequality car seat is intended for children weighing up to 30 pounds.
let the child's weight = x
x ≤ 30
Inequality for a car seat built for a child weighing between 15 and 40 pounds;
15 < x < 40
Inequality for a car built for a youngster weighing between 30 and 85 pounds;
30 < x < 85
According to the given statement the following car seats are adequate for a 32-pound child:
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The given question is not complete.
A family is comparing different car seats. One car seat is designed for a child up to and including 30 lb. Another car seat is designed for a child between 15 lb and 40 lb. A third car seat is designed for a child between 30 lb and 85 lb, inclusive. Model these ranges on a number line. Represent each range of weight using interval notation. Which car seats are appropriate for a 32-lb child?
Please help me find ABCD!!
Alexia landed her plane. The plane's elevation relative to the ground (in meters) as a function of time (in seconds) is graphed. How high was the plane after 1000 seconds?
A) 8500 meters
B) 1500 meters
C) 3500 meters
D) 5 meters
find the difference. (6d+5)-(2-3d)
Solving the Question
[tex](6d+5)-(2-3d)[/tex]
We subtract algebraic expressions exactly as we would integers, or as we would in a 'normal' subtraction sentence. First, we must open up the brackets:
[tex]= 6d+5-2+3d[/tex]
Now, combine like terms:
[tex]= 9d+5-2\\= 9d+3[/tex]
Answer9d+3
Pls help, and answer both questions I will try to give you brainly.
Answer: J(2,2) K(1,-1) thats all I got
Step-by-step explanation:
Determine whether the following statement is true or false. Explain.
The graph of y = |x-2|- 2 is a translation two units to the right and two units upward of the graph of y = |x|.
Choose the correct answer below.
A. True, because the graph of y = f(x - h) + k is the translation of the graph of y = f(X) |k| units upward if k= 0 or downward if k < 0, and h units to the right if h> 0 or to the
left if h < 0.
B. True, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) In| units upward if h = 0 or downward if h < 0, and k units to the right if k> O or to the
left if k < O
C. False, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) |k| units to the right if k>0 or to the left if k < 0, and h units upward if h downward if h < 0.
D. False, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) h units to the right if h > 0 or to the left if h < 0, and k units upward if k>downward if k < 0.
Answer:
Determine whether the following statement is true or false. Explain.
The graph of y = |x-2|- 2 is a translation two units to the right and two units upward of the graph of y = |x|.
Choose the correct answer below.
A. True, because the graph of y = f(x - h) + k is the translation of the graph of y = f(X) |k| units upward if k= 0 or downward if k < 0, and h units to the right if h> 0 or to the
left if h < 0.
B. True, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) In| units upward if h = 0 or downward if h < 0, and k units to the right if k> O or to the
left if k < O
C. False, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) |k| units to the right if k>0 or to the left
(x + 1)3 − x (x − 2)2 − 1
Answer:
x = -0.27 or 3.77
Step-by-step explanation:
explanation in pic
Answer:
This simplifies to 7x^2 - x.
Step-by-step explanation:
(x + 1)3 − x (x − 2)2 − 1
= x^3 + 3x^2 + 3x + 1 - x(x^2 - 4x + 4) - 1
= x^3 + 3x^2 + 3x + 1 - x^3 + 4x^2 -4x - 1
= 7x^2 - x
The function g(x) is a transformation of the cube root parent function,
f(x)=√x. What function is g(x)?
5-
N
-5-
g(x)
f(x)
-5
O A. g(x)=√x+2+1
B. g(x)=√x-1+2
C. g(x)=√x-2+1
O D. g(x)=√x+1+2
Using translation concepts, function g(x) is given as follows:
C. [tex]g(x) = \sqrt[3]{x - 2} + 1[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, the parent function is given by:
[tex]f(x) = \sqrt[3]{x}[/tex]
The translations for g(x) are as follows:
One unit up, hence g(x) = f(x) + 1.Two units right, hence x -> x - 2.Thus the rule is:
C. [tex]g(x) = \sqrt[3]{x - 2} + 1[/tex]
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A package of 4 pairs of insulated socks costs $21.96. What is the unit price of the pairs of socks?
The unit price is $ per pair of socks.
Answer: $5.49
Step-by-step explanation:
Unit price = 21.96/4 = 5.49
20pts. Please help ASAP!
Answer:
given
Step-by-step explanation:
When doing a two-column proof, you usually begin with what you are given.
PLEASE HELP WILL MARK WHAT IS 25-29
Help jwhsiwoeodjdjdjiejf
Help my cousin
Answer:
I. 1) 32124, 32456, 32532, 32934, 32983
2) 62279, 62312, 62345, 62387, 62398
3) 89123, 90246, 89345, 89534, 89923
4) 19087, 19216, 19312, 19432, 19910
5) 31821, 31839, 31861, 31876, 31890
II. 1) 58240, 58204, 58042, 58024
2) 10908, 10809, 10098, 10089
3) 85703, 85370, 85307, 85073
4) 98705, 98570, 98507, 98057
5) 41810, 41108, 41081, 41018
Step-by-step explanation:
ALGAE A scientist has a fish tank in the shape of a rectangular prism. The tank is 18 inches high, 14 inches wide, and 30 inches long. After one month, the scientist found that the sides and bottom of his fish tank were covered with algae. The scientist wants to run tests on the algae to help determine why it started to grow. How much algae is there for the scientist to test?
the algae that is present with the scientist to research upon covers a surface area of 2004 inches² in the rectangular prism.
The dimensions of the rectangular prism is given by:
Height = h = 18 inches
Width = w = 14 inches
Length = l = 30 inches
Now, we have to calculate the surface area of the tank excluding the top of the tank to find out how much algae has been present there for the scientist to test.
So, the formula for surface area will become:
A = 2(w l + h l + h w) - l w ( as the top has to be excluded)
Now substituting the values of l, w and h, we get that:
A = 2 [ (14) (30) + (18) (30) + (18) (14) ] - (30) (14) inches²
A = 2 [ 420 + 540 + 252 ] - 420 inches²
A = 2 [ 1212 ] - 420 inches²
A = 2424 - 420 inches²
A = 2004 inches²
Therefore, we get that, the algae that is present with the scientist to research upon covers a surface area of 2004 inches² in the rectangular prism.
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Gabriella's school is selling tickets to a choral performance. On the first day of ticket sales the
school sold 14 senior citizen tickets and 14 child tickets for a total of $252. The school took in
$154 on the second day by selling 9 senior citizen tickets and 7 child tiekets. Find the price of a
senior citizen ticket and the price of a child ticket.
The ticket price of
A Senior citizen = $14
A Child = $4
First day of ticket sales :
Senior citizen tickets (s) = 14
Child tickets (c) = 14
Total price of both tickets = $252
14s + 14c = 252 eq. (1)
Second day of ticket sales :
Senior citizen tickets (s) = 9
Child tickets (c) = 7
Total price of both tickets = $154
9s + 7c = 154 eq. (2)
Multiplying equation 2 with 2, we get
18s + 14c = 308 eq. (3)
Now, we will subtract eq. (1) from eq. (3)
18s + 14c = 308 eq. (3)
-14s - 14c = -252 eq. (1)
____________________
4s = 56
s = 56/4
s = 14
We get the ticket price of one senior citizen which is 14 Dollars.
Now, we will put s = 14 in eq. 2,
So, 9s + 7c = 154
(9×14) + 7c = 154
7c = 154 - 126
c = 28 / 7
c = 4
Ticket price of one child is 4 Dollars.
Hence, the ticket price of a senior citizen and a child is $14 and $4, respectively.
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i don't Know how to solve this please help
Answer:
f(0) = 0
f(-2) = 0
f(5) = 15
f(-10) = 16
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
[tex]f(x)=\begin{cases} \begin{aligned}-2x-4 & \;\;\textsf {if }\;x < 0\\3x & \;\;\textsf {if }\;x\geq 0\\\end{aligned}\end{cases}[/tex]
Therefore, the function has two definitions:
[tex]\textsf{$f(x)=-2x-4$ when $x$ is less than zero}.[/tex][tex]\textsf{$f(x)=3x$ when $x$ is more than or equal to zero}.[/tex]When graphing piecewise functions:
Use an open circle where the value of x is not included in the interval.Use a closed circle where the value of x is included in the interval.Use an arrow to show that the function continues indefinitely.First piece of the function
Substitute zero into the first function:
[tex]\implies f(0)=-2(0)-4=-4[/tex]
Place an open circle at point (0, -4).
To help graph the line, find another point on the line by inputting another value of x that is less than zero into the same function:
[tex]\implies f(-2)=-2(-2)-4=0[/tex]
Place point (-2, 0) and draw a straight line from the open circle at (0, -4) through (-2, 0). Add an arrow at the other endpoint to show it continues indefinitely as x → -∞.
Second piece of the function
Substitute zero into the second function:
[tex]\implies f(0)=3(0)=0[/tex]
Place an closed circle at point (0, 0).
Again, to help graph the line, find another point on the line by inputting another value of x that is more than zero into the same function:
[tex]\implies f(2)=3(2)=6[/tex]
Place point (2, 6) and draw a straight line from the closed circle at (0, 0) through (2, 6). Add an arrow at the other endpoint to show it continues indefinitely as x → ∞.
See attached for graph.
To find the given functions, decide which function to use based on the given value of x, then solve.
f(0) means to find the value of the function when x = 0.
Therefore, input x = 0 into the second function as x ≥ 0.
[tex]\implies f(0)=3(0)=0[/tex]
f(-2) means to find the value of the function when x = -2.
Therefore, input x = -2 into the first function as x < 0.
[tex]\implies f(-2)=-2(-2)-4=0[/tex]
f(5) means to find the value of the function when x = 5.
Therefore, input x = 5 into the second function as x ≥ 0.
[tex]\implies f(5)=3(5)=15[/tex]
f(-10) means to find the value of the function when x = -10.
Therefore, input x = -10 into the first function as x < 0.
[tex]\implies f(-10)=-2(-10)-4=16[/tex]
Your height in the portrait measures 3 1/2 inches, if the company uses a scale where 1 inch on the portrait represents 20 inches on the wall decal, find the height on the wall decal
- - - - - - - - - - - - - - - - - - - - - - - -
Work below!
- - - - - - - - - - - - - - - - - - - - - - - -
Simply multiply the inches by 20 (the scale per inch), and you have your answer!
3.5 x 20 = 70
The height is 70 inches.
- - - - - - - - - - - - - - - - - - - - - - - -
Good luck! :)
(Consider leaving a Brainliest if this helped!)
~pinetreee
Answer:
70
Step-by-step explanation:
If you multiply 3.5 times 20 you get 70
THERE ARE 2 DECKS OF PLAYING CARDS
Answer:
100 cards?
Step-by-step explanation:
The endpoints of AB are -4 and 6. Find the coordinate of Point P that partitions the segment in a 2:3 ratio.
Answer: 0
Step-by-step explanation:
Since it is 10 units total from -4 to 6,
4/10 and 6/10 would give a ratio of 2:3
4 units from -4 would be at 0, which is also 6 units away from the 6
4 units to 6 units equals a ratio of 2:3
A single hamburger costs $5.00. French fries cost $3.00. If you buy them as a combo the cost is $6.50. What is the savings, expressed in percent if you order the combo?
The the savings, expressed in percent if you order the combo is 18.75%, if the combo is bought at $6.50
What is the amount saved when combo is ordered?
The amount saved when ordering for combo instead of ordering hamburger and French fries is the difference between the total cost cost when for individual orders and the cost of the combo
total cost for individual orders=$5.00+$3.00
total cost for individual orders=$8.00
combo cost=$6.50
savings on combo=total cost for individual orders-combo cost
savings on combo=$8.00-$6.50
savings on combo=$1.50
% savings on combo=$1.50/$8.00
% savings on combo=18.75%
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Find FH .
FH = {Blank}
Answer:
26
Step-by-step explanation:
[tex]FH=7+19=26[/tex]
Answer:
FH = 26
Step-by-step explanation:
The equation will be,
→ FH = FG + GH
Then the value of FH will be,
→ FH = 19 + 7
→ [ FH = 26 ]
Hence, the value of FH is 26.