The value of the function f(1) and f(3) is 11 and 1 when the function is f(x)= -2x² + 3x + 10
Given that,
The function is f(x)= -2x² + 3x + 10
We have to find f(1) and f(3).
What is function?The core concept of mathematics' calculus is functions. The functions are special types of relations. In mathematics, a function is represented as a rule that produces a distinct result for each input x.
Take the function
f(x)= -2x² + 3x + 10
Take x as 1
f(1)= -2(1)² + 3(1) +10
f(1)= -2+3+10
f(1) = 11
Now, Take x as 3
f(3)= -2(3)² + 3(3) +10
f(3)= -18+9+10
f(3) = 1
Therefore, The value of the function f(1) and f(3) is 11 and 1 when the function is f(x)= -2x² + 3x + 10
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HELP!! Simply the expression
Answer:
[tex]\frac{2x\sqrt{3y}}{{3y}}[/tex]
Step-by-step explanation:
Apply fractional law for squares:
[tex]\sqrt{\frac{4x^2}{3y}} = \frac{\sqrt{4x^2}}{\sqrt{{3y}}}[/tex]
Then simply:
[tex]\frac{2x}{\sqrt{{3y}}}[/tex]
Rationalize denominator:
[tex]\frac{2x}{\sqrt{{3y}}} \cdot \frac{\sqrt{{3y}}}{\sqrt{{3y}}} = \frac{2x\sqrt{3y}}{{3y}}[/tex]
An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 100 grams of an alloy containing 35% copper with 60 grams of an alloy containing 55% copper.
Answer the questions below. Do not do any rounding.
(a) How many grams of copper are in the resulting mixture?
(b) What percentage of the resulting mixture is copper?
Answer:
(a) 68 grams
(b) 42.5%
Step-by-step explanation:
You mix 100 g of 35% copper with 60 g of 55% copper to form an alloy. You want to know the number of grams and the percentage of copper in the mixture.
CopperThe total amount of copper is ...
0.35·(100 g) +0.55·(60 g) = 35 g + 33 g = 68 g
There are 68 grams of copper in the resulting mixture.
PercentageThe percentage of copper in the mixture is ...
(68 g)/(100 g + 60 g) × 100% = 68/160 × 100% = 42.5%
The resulting mixture is 42.5% copper.
The functions and are defined as follows.
Find the value of .
The expression we get from the given functions r and s defined for all real numbers x.
r( s(-3))= -38
Given that,
All real numbers x are defined by the functions r and s.
r(x) =2x+1
s(x) =-2x²-2
We have to find the expression
r( s(-3))
Take the functions,
r(x) =2x+1
s(x) =-2x²-2
Now, Take
r( s(-3))
Substitute s function first
r(-2(-3)²-2)
r(-2(9)-2)
r(-18-2)
r(-20)
Now substitute r function
2(-20)+2
-40+2
-38
Therefore, The expression we get from the given functions r and s defined for all real numbers x.
r( s(-3))=-38=
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PLEASE HELP ASAP, PLEASE HELP ASAP
Need done soon pls! Super easy
Answer:
choose 3rd option
Step-by-step explanation:
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The inequality - 3(2x - 5) < 5(2 - x) is x > 5 represents a line with an open circle at x = 5 and going indefinity to positive infinity.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, inequality is - 3(2x - 5) < 5(2 - x).
∴ - 6x + 15 < 10 - 5x.
- 6x + 5x < 10 - 15.
- x < - 5.
x > 5 (think of moving x to the other side to make it positive.
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Find the accumulated value of an investment of $20,000 for 7 years at an interest rate of 4% if the money is a.
compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.
Part a; compounded semiannually (n = 2); CI = $6,390.
Part b: compounded quarterly ( n = 4) ; CI = $6,425
Part c: compounded monthly (n = 12): CI = $6,450
Part d: compounded continuously; CI = $6,467.
What is known as the term compound interest?Compound interest is computed as interest on the base principal plus any interest income from prior periods. The frequency plan for compounding interest can be set to be continuous, daily, or yearly.The compound interest is calumniated by formula.
A = P(1 + r/100n)∧nt
In which,
A = amount after compounding
P = principal amount ($20,000 )
n = number of time principal amount compounded in a year.
t = total time in years (7 years)
r= rate of interest (4%)
Part a; compounded semiannually (n = 2)
A = P(1 + r/100n)∧nt
A = 20,000(1 + 4/200)∧(2x7)
A = 26390
CI = A - P
CI = 26,390 - 20,000
CI = $6,390.
Part b: compounded quarterly ( n = 4)
A = 20,000(1 + 4/400)∧(4x7)
A = 26425
CI = A - P
CI = 26,425 - 20,000
CI = $6,425
Part c: compounded monthly (n = 12)
A = 20,000(1 + 4/1200)∧(12x7)
A = 26450
CI = A - P
CI = 26,450- 20,000
CI = $6,450
Part d: compounded continuously.
P = P₀e∧rt
P = (20,000)(2.72)∧(0.04 x 7)
P = 20,000 x 1.32
P = 26,467
CI = 26,467 - 20, 000
CI = $6,467.
Thus, the for compounded continuously is $6,467.
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While charting, a nurse notes that a patient has a medication infusing at 40.5 mL/hr. The label on the IV bag says 400 mg in 250 mL. How many mcg/min is the patient receiving?
The conversion factor you will need for this question is: 1 mg equals 1000 mcg
The amount that the patient is receiving, in mcg/min, using proportions, is of:
1008 mcg/min.
What is a proportion?A proportion represents a unit rate relative to a total amount, and this unit rate is used along basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.
Considering than an hour has 60 minutes, the amount infused each minute is given as follows:
40.5/60 = 0.675 mL/min.
The rate of milligrams per milliliters is given as follows:
400/250 = 1.6 mg per mL.
Hence the number of mg received per minute is:
1.6 x 0.675 = 1.08 mg per minute.
1 mg equals 1000 mcg, hence the number of mcg received per minute is:
1.08 x 1000 = 1008 mcg/min.
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Today only, a table is being sold for $333. This is 74% of its regular price. What was the price yesterday?
Ballentine Company expects sales for June, July, and August of $56,000, $62,000, and $52,000, respectively. Experience suggests that 45% of sales are for cash and 55% are on credit. The company collects 60% of its credit sales in the month following sale, 35% in the second month following sale, and 5% are not collected. What are the company's expected cash receipts for August from its current and past sales?
The company's expected cash receipts for August from its current and past sales is $126220.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, the sales for June, July, and August are $56000, $62000, and $52000 respectively.
The company collects 45% of sales in cash, therefore, for June month the cash collected by the company is,
June = 56000×45%
June =56000×45/100
June =25200
Therefore, the credit amount for June is,
56000 - 25200
=30800
The cash collected by the company for July is,
= 62000×45%
= 62000×45/100
= 27900
The company will also collect 60% of its credit from June sales in July, therefore, the total collected cash in July is,
July = 27900 + 60% of 30800
July = 27900 + 60×30800/100
July = 46380
The remaining credit after July is,
62000-27900
= 34100
The cash collected for August is,
52000×45%
= 52000×45/100
= 23400
The company also collects cash credits in June and July. Therefore, The net cash collected by the company is,
August = 23400 + 30800×35% + 34100×60%
August = 23400 + 30800×35/100 + 34100×60/100
August = 23400 + 10780 + 20460
= 54640
Therefore, the total cash collected by the company for august from its current and past sales is,
June + July + August
= 25200 + 46380 + 54640
= 126220
Hence, the company's expected cash receipts for August from its current and past sales is $126220.
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IXL Please Help Fast!
Answer:
Step-by-step explanation:
so we need slope intercept form, which is y=mx+b ... just memorize this, you'll need it many many times
next we are told to find a line perpendicular to y= [tex]\frac{1}{8}[/tex]x+10
recall that the reciprocal of the slope will give us a perpendicular line with a sign change also.
then the slope m is:
m = -8
and we are given the point P(x1,y1) = ( -1,1)
now use the point-slope formula to find the equation to the line in the slope intercept form.
y-y1 = m(x-x1)
plug in our given info.
y-1 = (-8)(x-(-1))
y-1 = -8(x+1)
y-1= -8x -8
y = -8x -8+1
y=-8x-7
there is your slope intercept form of the equation :)
The area of a parallelogram is 780sq cm if the length of one side is 26cm find the corresponding height.
20 points
Step-by-step explanation:
area of parallelogram = length × height
780 = 26 × height
height = 780/26 = 30cm
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the estimated value of each expression with its position on the number line.
Order of the tiles D, C, E, A
The square root of a number:
A square root of a number is a value of a number(other than the original number) that when multiplied by itself gives the original number. A square root of a number will be in the form of a².
Here are some examples of the square root of a number
√4 = 2 [ since 2 × 2 = 4 ]
√9 = 3 [ since 3 × 3 = 9 ]
Here we have
1. √90 - √40
2. (√35 - √42) / (√5 - √6)
3. 2√27 - √48
4. (√54 -√24)/√18 - √8
Each problem can be solved as given below
1. √90 - √40
= √9 × 10 - √4 × 10
= 3√10 - 2√10
= √10 = 3.16227
2. (√35 - √42) / (√5 - √6)
= (√5 × √7 - √7 × √6 ) / (√5 - √6)
= √7 [√5 - √6 ] / (√5 - √6)
= √7 = 2.64575
3. 2√27 - √48
= 2√9×3 - √16×3
= 6 √3 - 4√3
= 2√3 = 3.46410
4. (√54 -√24)/√18 - √8
= (√9×6 - √4×6)/√9×2 - √4×2 )
= (3√6 - 2√6)/3√2 - 2√2 )
= (√6) / √2 )
= 1.73205
The resultant decimal numbers are
3.16227, 2.64575, 3.46410, and 1.73205.
And the order of the decimal numbers is
1.73205 < 2.64575 < 3.16227 < 3.46410
Therefore,
Order of the tiles D, C, E, A
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What is the area of this triangle? O 18 square units O 20 square units O 21 square units 024 square units
The area of this triangle is 21 square units.
From the graph:
The length of the base = 4 + 3 units
= 7 units
The length of the height = 3 + 3
= 6 units
Area of the triangle = 1/2 b *h
= 1/2*7*6
= 1*42/2
= 42/2
= 21 square units.
Therefore the area of this triangle is 21 square units.
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Does this table represent a function? Why or why not? X 2 3 4 5 5 A y 1 4 4 2 5 A. No, because two of the y-values are the same. OB. Yes, because there is the same number of x-values as y-values. OC. No, because one x-value corresponds to two different y-values. D. Yes, because every x-value corresponds to exactly one y-value.
Answer:no
Step-by-step explanation:
No because 2 5's in x
For f(x) = 9x + 8 and g(x) = 7x, find the following composite functions and state the domain of each.
(a) fog
(b) gof
(c) fof
(d) gog
For the given composite function, then values of
(a) 63x + 8
(b) 63x + 56
(c) 81x + 80
(d) 49x
Composite functions:
An operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)) is known as composite functions.
Given,
Here we have the functions f(x) = 9x + 8 and g(x) = 7x
Now, we have to find the composite function of each.
(a) The composite function is written as,
=> f(g(x)) =f(7x)
=> f(7x) = 9(7x) + 8
=> f(g(x)) = 63x+ 8
(b) The composite function is written as,
=> g(f(x))
=> g(f(x)) =g(9x + 8)
=> g(9x + 8) = 7(9x + 8)
=> g(9x + 8) = 63x + 56
(c) The composite function is written as,
=> f(f(x))
=> f(9x +8) = 9(9x + 8) + 8
=> f(9x + 8) = 81x + 72 +8
=> f(9x + 8) = 81x + 80
(d) The composite function is written as,
=> g(g(x))
=> g(7x) = 7(7x)
=> g(7x) = 49x
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hellloppppppp ILL MARK BRAINLIEST!!!!
Answer:
x=47
Step-by-step explanation:
Sum of all three angles of a triangle is 180 degrees
We know one angle which is 51 degrees
The second is 73 degrees since it’s corresponding angle is 73 degrees
73+51=124
Now subtract this from 180
180-124=56
We can set x+9 equal to this
X+9=56
-9. -9
x=47
Hopes this helps please mark brainliest
By the Factor Theorem, what can be said about the polynomial function s(x) if s(−5)=−4 ?
a) x+5 is not a factor of s(x)
b) s(x) has no real zeros
c) x+5 is a factor of s(x)
d) s(x) has 5real zeros
The polynomial function s(x) if s(−5) = −4 is a) x+5 is not a factor of s(x) is the correct option.
Given:
polynomial function s(x) if s(−5)=−4 .
x = -5 when substitute in s(x) the output is -4 which is not equal to zero so
x+5 is not a factor of s(x) is correct.
The factor theorem tells you that a polynomial f(x) has a factor (x - k) only when f(k)=0 . So if s(-5) is not 0, we can draw the conclusion that (x+5) is not a factor of s(x).
Therefore the polynomial function s(x) if s(−5) = −4 is a) x+5 is not a factor of s(x) is the correct option.
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Complete the equation of the line through (3, -8) and (6, -4).
Use exact numbers.
y =
akis bicycle designs has determined that when x hindered bicycles are built the average cost
The bicycles which the shop should build to minimize the average cost per bicycle is 25 bicycles
How to find number of bicycles that will minimize average cost?Average cost function:
C(x) = 0.2x² - 0.1x + 3.799This is a quadratic function, So
a = 0.2b = -0.1c = 3.799Average cost is minimum when
x = - b / 2a
= -(-0.1) / 2(0.2)
= 0.1 / 0.4
x = 1/4
Number of bicycles which should to minimize average cost per bicycle = minimum average cost × total cost
= 1/4 × 100
= 25 bicycles
Therefore, the number of bicycles which will minimize the average cost function is ,25 bicycles.
Complete question:
Aki's bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.2x^2-0.1x+3.799, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?
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X
-5
0
The table of ordered pairs shows the coordinates of the two points on the graph of a line. Which equation
describes the line?
y
2
7
a. y=x+7
b. y=x-7
A
C
Please select the best answer from the choices provided
c.
d.
Mark this and return
y = -5x +2
y = 5x + 2
Save and Exit
Next
Submit
The equation of the line that best describes the given table of ordered pair is y = x + 7
Equation of the line:
By using the slope and y intercept of the point, we can calculate the equation of the line as
y = mx + c
here m refers the slope and c refers the intercept.
Given,
Here we have the table of ordered pairs shows the coordinates of the two points on the graph of a line.
Now, we need to find the equation of the line that best suits this one.
In order to find the equation of the table, first we have to calculate the slope and the y intercept of the given table.
But in order to calculate the slope we need the points.
So, the point take has been taken by the table are
=> (-5, 2) and (0,7)
Now, the slope of the line is,
=> m = (0 - (-5))/ (7-2)
=> m = 5/5
=> m = 1
By looking into the point we have identified that the y intercept is 7,
Therefore, the equation of the line is
=> y = 1x + 7
=> y = x + 7
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Find the equation of the line with slope -1 and y-intercept (0,-3)
The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 65% pure fruit juice?
Please help this is due soon
Answer:
Okay, so let's make the variable x the 60% juice.
The equation:
0.60(x) + 1(120-x) = 0.7(120)
Multiply both sides by ten for easier calculation:
6x + 1200 - 10x = 840
Put x on one side and the numbers on the other:
-4x = -360
the negatives cancel out...
4x = 360
define x
x = 90
Step-by-step explanation:
Kala the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 3 clients who did Plan A and 5 who did Plan B. On Thursday there were 9 clients who did Plan A and 7 who did Plan B. Kala trained her Wednesday clients for a total of 6 hours and her Thursday clients for a total of 12 hours. How long does each of the workout plans last?
Kala the trainer lasted 0.75 hours for each of the work out.
How to find out how long each of the work out lastedLet A represent plan A and B for plan B
On Wednesday there were 3 clients who did Plan A and 5 who did Plan B for a total of 6 hours. this is represented mathematically as
3A + 5B = 6 hours
On Thursday there were 9 clients who did Plan A and 7 who did Plan B for a total of 12 hours. this is represented mathematically as
9A + 7B = 12 hours
hence we have two system of equations with two unknown
9A + 7B = 12 hours
3A + 5B = 6 hours
solving the equation gives that A = B = 0.75 hours = 45 minutes
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Six car batteries weigh 46.2 pounds. Fourteen car batteries weigh 107.8 pounds. Does this represent a proportional relationship? If so, state the constant of proportionality.
The relationship of the battery represent a proportional relationship and the constant is 7.7 pounds.
How to calculate the constant of proportionality?From the information, 6 car batteries weigh 46.2 pounds. The weight per battery will be:
= 46.2 / 6
= 7.7 pounds
Also, rourteen car batteries weigh 107.8 pounds, the weight per battery will be:
= 107.8 / 14
= 7.7 pounds
The constant of proportionality is 7.7.
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A line of best fit was drawn to the plotted points in a data set below. Based on the line of best fit, for what y-value does x=16x=16?
Answer:yes its 15
Step-by-step explanation:
2 2/3 + 1 5/8
How do you solve this
How do you change the denominator so you can solve
Answer:25/.2
Step-by-step explanation:
i think this is right
Answer:
The answer would be 4 7/24
Step-by-step explanation:
We can obtain common denominators by multiplying both numerator (top) and denominator (bottom) by the same amount.
The LCM (least common multiple) for your question would be 24, so you would multiply in order to get the fractions to have a common denominator of 24, while keeping the same value.
NO LINKS!! Use the diagram below, describe the relationship as parallel, intersection, or skew
Answer:
a) Intersecting lines.
b) Parallel lines.
c) Skew lines.
d) Intersecting planes.
e) Parallel planes.
Step-by-step explanation:
A prism is a polyhedron that has:
Two bases that are congruent and parallel to each other.Lateral sides that are parallelograms and link the two bases.Height that is the distance between the two bases.From inspection of the give diagram, the figure appears to be a triangular prism with triangular bases ADE and BCF.
Lines
Parallel lines are lines on a plane that never meet and are the same distance apart.Intersecting lines cross each other in a plane and share a common point called the point of intersection.Skew lines are a pair of non-coplanar lines that do not intersect, and are not parallel to each other.Planes
A plane is a flat, two-dimensional surface that extends into infinity.
A plane can be named by the letters naming three non-collinear points in the plane.
Parallel planes are planes that never intersect. Intersecting planes are not parallel and always intersect along a line.a) AB and BC are intersecting lines as they share the common point B.
b) AE and BF are parallel lines because they both lie on the plane ABF, do not intersect and are the same distance apart.
c) EF and AD are skew lines because the do not lie on the same plane, they do not intersect and they are not parallel.
d) Plane ABC and plane ABF are intersecting planes as they intersect along line AB.
e) Plane AED and plane BFC are parallel planes as they are the bases of the prism and never intersect.
Laura jogs at an average rate of 5.6 miles per hour for 2 hours. Priya
jogs the same distance but takes 13 hours. Write an expression you can use
to find Priya's average rate, using a decimal value or an operation symbol
(+,-, x, ) to fill in each box.
5.6 x 2.6
The expression to represent the average rate of Priya is (5.6×2)÷13 and the average rate is approximately 0.86 miles per hour .
Laura jogs for 2 hours at the rate of 5.6 miles per hour.
Distance travelled = speed × time
= 5.6 × 2
= 11.2 miles
Priya jogs the same distance in 13 hours.
Now to calculate the average rate of Priya we haver to divide the total distance travelled by the total time taken to complete the journey.
Average rate of Priya:
= 11.2 / 13
= 0.86153
≈ 0.86 miles per hour
You will be better able to appreciate the pace of a journey if you are aware of average speed. The speed may occasionally fluctuate while travelling. The need of determining the average speed then increases in order to estimate how quickly the trip will be completed.
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Tyshawn took a taxi from his house to the airport. The taxi company charged a pick-
up fee of $2.50 plus $3.50 per mile. The total fare was $79.50, not including the tip.
Which equation could be used to determine m, the number of miles in the taxi ride?
3.5m + 2.5 = 79.5 is the equation that could be used to determine m, the number of miles in the taxi ride.
Given in question,
Pick-up fee = $2.50
Fee per mile = $3.50
Total fare = $79.50
Let the no. of miles = m
Fee for m miles = 3.50m
Equation, 3.50m + 2.50 = 79.50.
Hence, the equation is 3.50m + 2.50 = 79.50.
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