Evaluate the function. f(x) = -x^2+6x-18
Find f(−3)
Answers
Answer:
\({ \tt{f(x) = - {x}^{2} + 6x - 18}}\)
• when f(x) is f(-3), then x is -3. Substitute for x as -3:
\({ \sf{f( - 3) = - {( - 3)}^{2} + 6( - 3) - 18 }} \\ \\ { \sf{f( - 3) = - 9 - 18 - 18}} \\ \\ \dashrightarrow \: { \boxed{ \tt{f( - 3) = - 45}}}\)
Related Questions
Which expression is equivalent to RootIndex 3 StartRoot 256 x Superscript 10 Baseline y Superscript 7 Baseline EndRoot? 4 x squared y (RootIndex 3 StartRoot x squared y cubed EndRoot) 4 x cubed y squared (RootIndex 3 StartRoot 4 x y EndRoot) 16 x cubed y squared (RootIndex 3 StartRoot x y EndRoot) 16 x Superscript 5 Baseline y cubed (RootIndex 3 StartRoot y EndRoot)
Answers
Answer:
B
Step-by-step explanation:
edg 2021
Answer: b
Step-by-step explanation:
I need 23 questions answered
Answers
The surface area of a rectangular prism is 48 5/6 mi².
How to calculate the surface area of a rectangular prism?In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:
Surface area of a rectangular prism = 2(LH + LW + WH)
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;
Surface area of rectangular prism = 2[6 × 2 1/3 + (1 1/4 × 6) + (1 1/4 × 2 1 /3)]
Surface area of rectangular prism = 2[14 + 15/2 + 35/12]
Surface area of rectangular prism = 48 5/6 mi².
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Find the product. 128 x 17 =
Answers
Answer:
Step-by-step explanation:
128*17=2176
Rewrite using a single positive exponent.
6^5\6^-2
Answers
Answer:
\( \frac{ {6}^{5} }{ {6}^{ - 2} } = {6}^{5 - ( - 2))} = {6}^{5 + 2} = {6}^{7} \)
Since we have the equation 6^5/6^-2, we have to decide what would make this a positive exponent and also cancel out the division.
If we move the -2 up to the 5, it will make it a positive seven. It wouldn’t work the other way because it would make it a -7 instead.
Move the -2 up to the 5 on the top, and cancel the division
Your answer will be 6^7
How much do amber and John earn how many hours it take then and how to they earn all together
Answers
(a)
Let Wj be the wages of John and Tj be the time in hours.
If wages and time are proportional, then the relation between them can be expressed as,
\(W_j=kT_j\)Here, k is a constant
Rewriting the above equation,
\(k=\frac{W_j}{T_j}\)If the ratio of wages to hours is a constant, then the wages of John is proportional to time.
Taking the ratio of Wj to Tj, we get
\(\begin{gathered} k_{}=\frac{18}{2}=9 \\ _{}k=\frac{27}{3}=9 \\ k=\frac{36}{4}=9 \end{gathered}\)Since the ratio of wages to time is a constant, John's wages are proportional to time.
The constant k is the the unit rate. Therefore, the unit rate at which John works is $9/h.
(b)
The graph plotted with Amber's wages against hours worked is a straight line. Therefore, Amber's wages are proportional to time.
The slope of the graph gives the unit rate.
Hence, the unit rate at which Amber work is given by,
\(\begin{gathered} \text{Unit Rate=Slope} \\ =\frac{\Delta y}{\Delta x} \\ =\frac{16-0}{2-0} \\ =\text{ \$8/h} \end{gathered}\)Therefore, the unit rate at which Amber work is $8/h
need to Graph y≥13x−3.
Answers
The dοtted line is the line y=13x3, and the shaded area is abοve it.
what the slοpe οf the line?As is well knοwn, the equatiοn fοr a straight line is y = mx + c. Where 'c' is the y-axis intercept and 'm' is the slοpe οn the y-axis. The fοrmula fοr a hοrizοntal line is y = 3.
In οrder tο graph the inequality y≥13x−3, we can first plοt the line y=13x3
(which has a slοpe οf 13 and a y-intercept οf -3) as a dοtted line.
Since the inequality is y≥13x−3, we must shade the area abοve the line.
The dοtted line is the line y=13x3, and the shaded area is abοve it.
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1 decigram (dg) = ______ grams (g)?
A. 0.01
B. 0.1
C. 0.001
D. 10
Answers
Answer:
B) 0.1
Step-by-step explanation:
The prefix "deci-" means "tenth", so a decigram would be one-tenth of a gram (or 0.1 grams). Therefore, option B is correct.
A line with a slope of 0 passes through the point (10, 6). What is its equation in slope-intercept form?
Answers
Answer:
The slope is 0, then the line is horizontal.
y = 6
Step-by-step explanation:
Is x^3x^3x^3 equivalent to x^3^3^3
Answers
Answer:
No they aren't equivalent.
Step-by-step explanation:
x^3x^3x^3=x^3^3^3
\((x)^{3x^{3x^3\)=\(x^{3^{3^3\)
\(x^{3x^{9x}\)=\(x^{3^{9}\)
\(x^{27x^{2} }\)=\(x^{27}\)
Apply log on both sides
27\(x^{2}\)logx=27logx
27\(x^{2}\)logx/27logx=1
\(x^{2}\)=1
This is true if x=1 , -1.
The values are equivalent if x=1 and -1 , otherwise no they aren't equivalent.
Use the following to answer Sean takes two 250 mg chewable calcium tablets each day,
6) How many milligrams of calcium will Sean take in a week?
7) How many grams of calcium will Sean take in a week?
Answers
Petra jogs 6 miles in 42 minutes. At this rate, how long would it take her to jog 8 miles?
Answers
Distance 1 / Time 1 = Distance 2 / Time 2
Using the information given:
6 miles / 42 minutes = 8 miles / Time 2
To solve for Time 2, we can cross-multiply and then divide:
6 miles * Time 2 = 8 miles * 42 minutes
6 * Time 2 = 8 * 42
6 * Time 2 = 336
Now, we divide both sides by 6 to isolate Time 2:
Time 2 = 336 / 6
Time 2 = 56 minutes
Therefore, it would take Petra 56 minutes to jog 8 miles at the same rate.
Answer:
56 minutes
Step-by-step explanation:
We can use proportions to solve.
6 miles 8 miles
------------ = ------------------
42 minutes x minutes
Using cross products.
6x = 42 *8
Divide each side by 6
x = 42/6 * 8
x = 7*8
x = 56
A deep-sea diver dives from the surface to 131 feet below the
surface and then swims up 8 feet, down 18 feet, down another
28 feet and then up 23 feet. Find the diver's depth after these
movements.
Answers
Answer:
146 feet below the surface
Step-by-step explanation:
\(-131+8-18-28+23=-146\)
5.3 MATHEMATICS HOLIDAY PACKAGE-TERM 2(2023) Instructions: Attempt ALL items 1. Your family has seven siblings; peter, John, Sarah, Joy, Ali, Mary and Ivan. There is an interval of 2 years between the ages of the children from Ivan to peter. Ivan is three years old. Task: Using an arrow diagram, explain the information about your family.
Answers
a butcher prepared 120 sausages using 3/8 pound of meat for each, How many pounds did he use?
Answers
Answer:
45 pounds of meat.
Step-by-step explanation:
= 120 ( 3/8)
= 360 / 8
= 45
If you borrow $60.00 at 10% interest, how much will you pay in one month?
Answers
Answer:
In one month we have to pay an interest of $0.5.
Step-by-step explanation:
We are given that you borrow $60.00 at 10% interest and we have to find how much we have to pay in one month.
Let the Principal sum of money = P = $60
the rate of interest = R = 10%
Time period = T = \(\frac{1}{12}\)
Assuming the interest is simple interest, so the formula for simple interest is given by;
Amount = Principal + Simple interest
A = P + ( \(\frac{\text{P}\times \text{R}\times \text{T}}{100}\) )
A = \(60 + \frac{60 \times 10 \times 1}{100 \times 12}\)
A = 60 + 0.5 = $60.5
So, in one month we have to pay an interest of $0.5.
A town's population is 47,750 . About 100 people move out of the town each month. Each month,175 people on average move into town. A nearby town has a population of 50,500. It has no one moving in and an average of people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question.
Which equation models the situation?
Answers
The equation that models the given situation is; 175x - 100x + 47750 = 50500 - 200x
The number of months it will take the populations to be equal is 10 months
How to model the equation of the word problem?Let us suppose after x months the population of both town's will be equal.
From the given directions, we have;
The population of the first town after x months is given by;
175x - 100x + 47750
The population of the second town after x months is given by;
50500 - 200x
Now, In order to the population of the both town's to be equal, we have;
175x - 100x + 47750 = 50500 - 200x
275x = 50500 - 47750
x = 2750/275
x = 10
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What is the meaning proportion between 3 and 27?
Answers
Answer:
you mean the mean not the meaning right?
The mean proportional of 3 and 27 = +√3×27 = +√81 = 9.
The average rate of growth for human hair is about 0.3 millimeters per day. How many days will it take a hair that is 12 millimeters long to grow to be 16.5 millimeters?
Answers
It will take 15 days for the hair to grow from 12mm to 16.5mm
What do you mean by average rate?By "average rate" in this context, we mean the typical or usual amount of hair growth per unit of time, which is often measured in millimeters per day. This rate can vary slightly depending on factors such as age, gender, genetics, diet, and overall health.
Let's first find out how much the hair needs to grow by subtracting its initial length (12mm) from its target length (16.5mm):
16.5mm - 12mm = 4.5mm
Now we can divide this growth by the average rate of hair growth to find the number of days it will take to grow this much:
4.5mm ÷ 0.3mm/day = 15 days
Therefore, it will take 15 days for the hair to grow from 12mm to 16.5mm.
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HELPPP PLEASE. So I have figured out the first one however I cannot seem to figure out the rest as my answers are wrong. How do solve this problem? Please help!
Answers
Answer:
it seems as it is adding .15 every time so the next 3 would be .05 .20 and .65
6. Convert 3−i into polar form and hence evaluate
\( {(3 - i)}^{7} \)
Answers
9514 1404 393
Answer:
≈ 1000√10∠-129.04464° = -1992 -2456i
Step-by-step explanation:
3 -i = √(3³+(-1)²)∠arctan(-1/3) ≈ √10∠-18.4349°
Then (3-i)^7 = 10^(7/2)∠(7×-18.4349°) = 1000√10∠-129.04464°
= 1000√10(cos(-129.04464°) +i·sin(-129.04464°))
= -1992 -2456i
Geometry Help!
Please only answer if you know the answer. Look at the image below to answer the question.
Be sure to show all of your work and explain your thinking.
I posted 3 of these, so if you understand it, please go and check them out.
If you do not know the answer use the comment section, don't answer my question with a comment. Thanks, Good Luck!
Answers
Answer:
x = 8.8Step-by-step explanation:
To solve this you need the Law of sines
sin A / a = sin B / b = sin C / ca, b, c are the sides opposite to angles A, B and C respectively
Applied to the given triangle we have one side given, the opposite angle to be found.
sin 28 / x = sin (180 - 28 - 126) / 8.2sin 28 / x = sin 26 / 8.2x = 8.2 sin 28 / sin 26x = 8.8 (rounded)Which problem can be solved by performing this multiplication?
3/4×8/9
Responses
Evan practiced piano this week for 3/4 hour. Last week he practice for8/9 hour. How much longer did Evan practice last week than this week?
Jada rode her bike 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike. How far did Sarah ride her bike?
Amelie drove 3/4 mile. She then drove another 8/9 mile. How many miles did she drive in all?
Three out of 4 containers hold lemonade. Each container holds 8/9 quart of lemonade. How much lemonade do the containers all hold?
Answers
The multiplication 3/4×8/9 can be used to address the problem in response (B). which is the correct answer that would be an option (B).
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
As per option (B),
Jada rode her bike for 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike.
Sarah rides her bike = Sarah rode (8/9) of the (3/4) that Jada rode.
Sarah rides her bike = 3/4 × 8/9
Therefore, this problem can be solved by performing the above multiplication.
Hence, the correct answer would be an option (B).
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What is the vertical displacement of the basic graph to produce a graph of
OA Sunits down
B. 2 units down
OC units down
OD
units up
SUBMIT
Answers
The vertical displacement is of 2 units down, the correct option is B.
What is the vertical displacement?Remember that for a function f(x), a vertical displacement of N units is written in general form as:
g(x) = f(x) + N
If N > 0, the translation is upwards.
if N < 0, the translation is downwards.
Here we assume that we start with the parent cosine function:
y = cos(x)
And the transformed function is:
y = -2 - cos(x - π)
So we have some transformations, but the vertical translation is of 2 units down. So the correct option is B.
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Bookwork code: N84
Look at the poster below showing the price of pencils in a stationery shop.
Annabel wants to buy exactly 76 pencils. What is the lowest amount she can
pay?
Give your answer in pounds (£).
spar
..
Pencils for sale!
30p each
Pack of 10
pencils for £2
Answers
Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20
How is the lowest amount determined?The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.
Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.
If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).
If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].
Pencils for sale
30p each
Pack of 10 pencils for £2
Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.
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3. MODELING REAL LIFE An apple growing on a tree
has a circumference of 6 inches. (See Example 2.)
a. The apple has a density of 0.46 gram per cubic
centimeter. Find the mass of the apple.
b. The radius of the apple increases inch per week
for the next five weeks. How does the volume
change during the five-week period? Explain
Answers
a. The mass of the apple is approximately 33.879 grams.
b. The volume of the apple increases by approximately 1.454 cubic inches during the five-week period.
a. To find the mass of the apple, we need to calculate its volume first. The circumference of the apple can be used to determine its radius.
The formula for the circumference of a circle is C = 2πr,
where C is the circumference and r is the radius.
Rearranging the formula, we have r = C / (2π).
Plugging in the given circumference of 6 inches.
we get r = 6 / (2π) ≈ 0.955 inches.
Now, we need to convert the radius from inches to centimeters since the density is given in grams per cubic centimeter.
Since 1 inch is approximately 2.54 centimeters, the radius in centimeters is \(0.955 \times 2.54\) ≈ 2.427 cm.
Next, we can calculate the volume of the apple using the formula for the volume of a sphere: V = (4/3)πr³.
Plugging in the radius in centimeters, we get
V ≈ (4/3)π(2.427)³ ≈ 73.682 cm³.
Finally, we can find the mass of the apple by multiplying the volume by the density:
mass = volume \(\times\) density
= 73.682 cm³ \(\times\) 0.46 g/cm³
≈ 33.879 grams.
Therefore, the mass of the apple is approximately 33.879 grams.
b. The volume of a sphere increases with the cube of its radius.
Since the radius increases by 1/8 inch per week for five weeks, the change in radius would be\((1/8) \times 5 = 5/8 inch.\)
Now, let's calculate the change in volume during the five-week period. The formula for the volume of a sphere is V = (4/3)πr³.
Initially, the radius was 0.955 inches.
After five weeks, the radius would be 0.955 + 5/8 inches.
To compare the change in volume, we can calculate the new volume and find the difference:
Change in Volume = New Volume - Initial Volume
Initial Volume = (4/3)π(0.955)³
New Volume = (4/3)π(0.955 + 5/8)³
By subtracting the initial volume from the new volume, we can determine how the volume changes during the five-week period.
Please note that the exact calculation will depend on the precise values used for π and the measurements provided.
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a = 2, b = 3, c =4 than find the value of ab bc ca
Answers
To find the values of ab, bc, and ca, we simply need to multiply the corresponding variables.
ab = 2 * 3 = 6
bc = 3 * 4 = 12
ca = 4 * 2 = 8
Therefore, ab = 6, bc = 12, and ca = 8.
3 • 4=12
4 • 2=8
ab=6
bc=12
ca=8
Sagar sold a watch at Rs.400 that he had purchased at Rs.500.what is his
percentage loss?
a. 15%
b. 20%
c.25%
d. 30%
Answers
Explanation:
Original price (OP): $500
Selling price (SP): $400
Percentage loss:
= (OP - SP)/OP x 100%
= (500-400) / 400 x 100%
= 100/400 x 100%
= 1/4 x 100%
= 25%
The loss percentage is 20%.
We have the following information available from the question is:
Saggar sold a watch at Rs.400 that he had purchased at Rs.500.
We have to find the Percentage loss.
Now, According to the question:
Cost price of watch is (CP): $500
Selling price of watch is (SP): $400
Loss percentage= Loss/CP x 100.
Loss = C.P. - S.P.
Loss = 500 - 400
Loss = $100
Plug all the values in the formula of loss percentage.
Loss percentage = 100/500 x 100
Loss Percentage is 20%
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Sara's mother bought 8 large oranges for $12.00. Sara said there was a ratio of 12 to 8, so the unit rate was $1.50 per orange. Sara's friend Daniel said he thought the ratio would be 8:12, so the unit rate would be of an orange per dollar.
Explain how both Sara and Daniel might have found their unit rates and how both could be correct.
Answers
The unit rate of orange could be found by Sara and Daniel by ratio to be $1.50
Further explanation on how they could be correctIf Sara's mother bought 8 large oranges for $12.00
Sara may have thought of it like if $12 is for 8 oranges the how much is for 1
12 : 8 then X : 1
12/8 then x/1
12/8 = x/1
x = $1.50
Daniel would have taken this method, if 8 oranges costs $12 then 1 orange would cost ?
8 oranges : $12 then 1 orange : ?
8 : 12 = 1 : ?
8/12 = 1/?
8 * ? = 1 * 12
? = 12/8
? = $1.5
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Divide and simplify 9/7 + 9/2
Answers
Answer:
5.78571428571
Step-by-step explanation:
9/7 = 1.28571428571
9/2 = 4.5
And if you add it you get 5.78571428571
hopes this helps..
The fist three steps in determining the solutions set of the system of equations y=-x^2-2x+8 and y=2x+11, algebraic ally are shown in the table
Answers
The solutions set of the system of equations y=-x^2-2x+8 and y=2x+11 are as x = -3 , -1 and y = 5, 8.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The system of equations
\(y = -x^2 - 2x + 8\)
and
y = 2x + 11,
We can put the value of y in the first equation
\(y = -x^2 - 2x + 8\\\\2x+11 = -x^2 - 2x + 8\\\\2x + 2x + 11 - 8 +x^2 = 0\\\\4x + 3 + x ^2 = 0\)
The factors are;
\(x^2 +4x + 3 = 0\\\\(x+3)(x+ 1)\)
Or x = -3 , -1
Now substitute to find y;
y = 2x + 11
y = 2(-1) + 11
y = 8
y = 2x + 11
y = 2(-3) + 11
y = 5
Or y = 5, 8
Thus, the solutions set of the system of equations y=-x^2-2x+8 and y=2x+11 are as x = -3 , -1 and y = 5, 8.
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