Using linear functions, it is found that the high-performance system should be rented.
A linear function has the following format:
[tex]y = ax + b[/tex]
In which:
a is the slope, which is the variable cost.b is the y-intercept, which is the fixed cost.With the high-performance software:
Fixed cost of $3,000 per month, hence [tex]b = 3000[/tex].Cost of $200 per drawing, hence [tex]a = 200[/tex]Then, the model is:
[tex]C_{hp}(d) = 3000 + 200d[/tex]
With the standard-performance software:
Fixed cost of $2,000 per month, hence [tex]b = 2000[/tex].Cost of $240 per drawing, hence [tex]a = 240[/tex]Then, the model is:
[tex]C_{sp}(d) = 2000 + 240d[/tex]
The costs for 80 drawings, that is, [tex]d = 80[/tex] for both cases are given by:
[tex]C_{hp}(80) = 3000 + 200(80) = 19000[/tex]
[tex]C_{sp}(80) = 2000 + 240(80) = 21200[/tex]
Due to the lower cost, the high-performance system should be rented.
A similar problem is given at https://brainly.com/question/20849340
75% of the amount is 4.5 cm
Answer:
6
Step-by-step explanation:
Do Babies Understand Probability? Can babies reason probabilistically? A study1 investigates this by showing ten- to twelve-month-old infants two jars of lollipop shaped objects colored pink or black. Each infant first crawled or walked to whichever color they wanted, determining their "preferred" color. They were then given the choice between two jars that had the same number of preferred objects, but that differed in their p
Answer:
Step-by-step explanation:
Wow, that’s interesting!
Is this a question?
One non-negative number is the reciprocal of another number. The sum of the two numbers is a minimum. What are the two numbers
The two numbers are 1 and 1.
Let the non-negative number be x and its reciprocal be y = 1/x
The sum of the two numbers is f(x,y) = x + y
= x + 1/x
= f(x)
For f(x) to be minimum, we differentiate it with respect to x and equate it to zero to find the value of x at which irt is minimum.
So, df(x)/dx = d(x + 1/x)/dx
= dx/dx + d(1/x)/dx
= 1 - 1/x²
Equating it to zero, we have
1 - 1/x² = 0
1 = 1/x²
x² = 1
Taking square-root of both sides, we have
x = ±√1
x = ±1
Since x is non-negative x = + 1
We differentiate f(x) again to determine if this value gives a minimum for f(x).
So, d²f(x)/dx² = d(1 - 1/x²)/dx
= d1/dx - d(1/x²)/dx
= 0 - × (-2/x³)
= 2/x³
Substituting x = 1 into the equation,
d²f(x)/dx² = 2/x³
= 2/1³
= 2 > 0.
So x = 1 is a minimum point for f(x)
Since x = 1 and y = 1/x, y = 1/1 = 1
So, the two numbers are 1 and 1.
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Determine the solution to each system of equations given in the table. Enter your answer in the box provided
Solution
System of Equations
Sy= 2x – 10
y=-3x + 5
Answer:
x=3 and y=-4
(3,-4)
Step-by-step explanation:
I searched it up :/
Answer:
x = 3 and y = -4
Step-by-step explanation:
Solve y = 2x-10 for y:
y=2x-10
Substitute 2x-10 for y in y = -3x+5:
y=-3x+5
2x-10=-3x+5
2x-10+3x=-3x+5+3x (add 3x to both sides)
5x-10=5
5x-10+10=5+10 (add 10 to both sides)
5x=15
5x/5=15/5 (divide both sides by 5)
x = 3
Substitute 3 for x in y = 2x-10:
y=2x-10
y=(2)(3)-10
y=-4 (simplify both sides of the equation.
Therefore your answer is x = 3 and y = -4.
Given: measure 1, measure 2, measure 3, and measure 4 formed by two intersecting segments Prove: measure 1 and measure 3 are congruent. NEED HELP ASAP!!
Step-by-step explanation:
Note:The text below that are formatted in bold and underlined font are the solutions to the missing boxes in your given problem.
Explanation:Given that ∠1, ∠2, ∠3, and ∠4 are formed by two intersecting segments, and that:
∠1 and ∠2 form a linear pair
∠2 and ∠3 form a linear pair
These linear pair relationships suggest that by the Linear Pair Postulate:
∠1 and ∠2 are supplementary. ⇒ Linear Pair Postulate
∠2 and ∠3 are supplementary. ⇒ Linear Pair Postulate
m∠2 + m∠ 3 = 180° ⇒ Definition of supplementary angles.
m∠1 + m∠3 = m∠2 + m∠ 3 ⇒ Substitution Property of Equality.
m∠1 = m∠3 ⇒ Subtraction Property of Equality.
i need help with #5
Answer:
<1 = 50
<2 = 130
Step-by-step explanation:
<1 and 130 are supplementary angles
<1 + 130 = 180
<1 =180-130
<1 = 50
130 and <2 are corresponding angles and corresponding angles are equal when the lines are parallel
<2 = 130
Step-by-step explanation:
Well first we can say measure angle 2 equals 130° because they are S.s.int.ext angles, (same side interior angles and exterior). Or also corresponding
Now with measure angle 1, it is a supplementary angle
Let 1 stand for measure angle 1
[tex]130 + m1 = 180[/tex]
Subtract 130° from both sides
[tex]m1 = 50[/tex]
Have a good day :)!What is the equation of this line in slope-intercept form? (-1,5) (1,-1)
y = 3x - 2
y = -1/3x + 2
y = -3x + 2
y = 3x + 2
Can I get help please..................
Sara bought 3/4 of a pound of bananas and 3/5 of a pound of pears. How much fruit did Sara buy?
Answer:
27/20
Step-by-step explanation:
¾ + ³/5= 27/20. .......................
find the angle pls it's just 1 question
Answer:
70°
Step-by-step explanation:
isoceles so base angles are 55
55+55 is 110 so 180-110 is 70
Answer:
if the triangle is isosceles
Step-by-step explanation:
traingle angles= 180°
isosceles traingle= base angles are equal
180°-55°-55°= 70°
Juan has x quarters and y dimes, having a minimum of 16 coins worth at most $3 combined. No less than 4 of the coins are quarters. Solve this system
of inequalities graphically and determine one possible solution.
Answer:
See belowStep-by-step explanation:
Quarter - 25¢, dime - 10¢, total - $3 = 300¢
Inequalities:
x + y ≥ 1625x + 10y ≤ 300x ≥ 4See attached for graphical solution. There are many solutions.
Possible one solution:
5 quarters and 17 dimesGuys what's 1 9/15+ 1 5/15
Answer:
2 14/15. answer need to be 20
Compute the total amount accumulated if you invested $3,000 for 6 years at 3% compounded
quarterly. Round your answer to the nearest cent and include '$' in your response.
Answer:
$3,582.16
Step-by-step explanation:
How is the product of 2 and -5 shown on a number line?
-10-98235
-3 -2 -1 0 1 2 3 4 5 6 7 8 10
-10 - -
-3
-2 -1 0 1 2 3 4 5 6 7 8
10
-10 -4 -8 -7 -3
4 -3 -2 -1 0
1
2
3
4
5
6
7
9
10
-10-9-4-7-3
-4-1 -2 -1 0 1 2
3
5
6
7
10
Answer:
d
Step-by-step explanation
Step-by-step explanation:It starts at 0 and goes in the negative
17 1/3 miles in 3 1/4 hours, how many miles per hour?
Step-by-step explanation:
find the value of x in 7/8=49/x
Step-by-step explanation:
,
[tex] \frac{7}{8} = \frac{49}{x} \\ 7x = 392 \\ x = \frac{392}{7} \\ x = 56[/tex]
Answer:
x = 56
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
7/8-(49/x)=0
Step by Step solution:
Step 1:
Simplify 49/x
Equation at the end of step 1:
7/8 - 49/x = 0
Step 2:
Simplify 7/8
Equation at the end of step 2:
7/8 - 49/x = 0
Step 3:
Calculating the Least Common Multiple :
Find the Least Common Multiple
The left denominator is : 8
The right denominator is : x
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 3 0 3
Product of all
Prime Factors 8 1 8
Number of times each Algebraic Factor
appears in the factorization of:
Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
x 0 1 1
Least Common Multiple:
8x
Calculating Multipliers :
3.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = x
Right_M = L.C.M / R_Deno = 8
Making Equivalent Fractions :
3.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 7 • x
—————————————————— = —————
L.C.M 8x
R. Mult. • R. Num. 49 • 8
—————————————————— = ——————
L.C.M 8x
Adding fractions that have a common denominator :
3.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
7 • x - (49 • 8) 7x - 392
———————————————— = ————————
8x 8x
STEP
4
:
Pulling out like terms :
4.1 Pull out like factors :
7x - 392 = 7 • (x - 56)
Equation at the end of step
4
:
7 • (x - 56)
———————————— = 0
8x
STEP
5
:
When a fraction equals zero :
5.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
7•(x-56)
———————— • 8x = 0 • 8x
8x
Now, on the left hand side, the 8x cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
7 • (x-56) = 0
Equations which are never true:
5.2 Solve : 7 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
5.3 Solve : x-56 = 0
Add 56 to both sides of the equation :
x = 56
One solution was found :
x = 56
A rectangular garden to contain 3 length segments and 4 width segments. The total amount of fencing required is 24 meters. What is the maximum possible area
Answer:
12 meters sq
Step-by-step explanation:
area= length x width
area= 3x4
area=12 meters sq
brantty works 21.5 hours every week . if she earns 8.50 per hour how much does she earn in one week round part a to the nearest dollar
Step-by-step explanation:
1 hour - $8.50
21.5 hours (one week) - $8.50 × 21.5 = $182.75
One week = $183
Is this triangle not similar because it only has two proportional sides?
Answer:
The triangles are similar.
Step-by-step explanation:
They share a common angle (∠S) and the ratio of the two sides is the same, i.e. SP/SQ = SR/ST
Twice a number plus eight times a second number is 19. Five times the first number plus seven times the
second is 15. Find the numbers.
Write two linear equations to represent a system to solve this, where X represents the smaller number and
y represents the larger number. Write the equations, but do not solve them.
Answer:
Step-by-step explanation:
2x + 8y = 19
5x + 7y = 15
brief statement Bosnian Crisis.
Answer:
The Bosnian war and genocide resulted in close to 100,000 civilians killed, over 2 million people forcibly displaced, and between 20,000-50,000 women systematically raped. ... Over 7,000 Bosnian Muslim prisoners captured in the area around Srebrenica were summarily executed from 13 July to 19 July 1995.
Step-by-step explanation:
hope this helps
Select the reason why these triangles are
similar. If they are not, select "Not similar.
14
9
24
16
6
21
Answer:
SSS
Step-by-step explanation:
The triangles are similar according to SSS rule (side lengths)
You can check it by writing the following equation:
6/9 = 16/24 simplify both sides
2/3 = 2/3
7.
Find all solutions to the following triangle. (Round your answers for angles A, C, A', and to the nearest minute. Round your answers for sides a and a'to two decimal places. If either triangle is not
possible, enter NONE In each corresponding answer blank.)
B = 65° 20', b = 5.38 inches, c = 4.88 inches
First triangle (assume C greater than or equal to 90°):
A= ____ degrees ____’
C=____ degrees ____’
a= ____ in
The measures of the angles and the lengths of the sides of the triangle can
be found using sine rule.
The correct responses are;
A = 59 degrees 9'C = Nonea = 5.083 in.Reasons:
The given parameter are;
∠B = 65°20', b = 5.38 inches, c = 4.88 inches
∠C ≥ 90°
By sine rule, we have;
[tex]\dfrac{5.38}{sin(65^{\circ} 20')} = \mathbf{ \dfrac{4.88}{sin(\angle C)}}[/tex]
[tex]sin(\angle C) = \mathbf{ \dfrac{sin(65^{\circ} 20') \times 4.88}{5.38}}[/tex]
[tex]\angle C = arcsin \left(\dfrac{sin(65^{\circ} 20') \times 4.88}{5.38} \right) \approx \mathbf{ 55.517 ^{\circ}}[/tex]
∠C = 55.517° < 90°, therefore, the correct response is; None
[tex]\dfrac{sin(65^{\circ} 20')}{5.38} = \dfrac{4.88}{sin(\angle C)}[/tex]
∠A = 180° - 65°20' - 55.517° = 59.15° = 59°9'
∠A = 59°9'
Therefore;
[tex]\dfrac{5.38}{sin(65^{\circ} 20')} = \mathbf{ \dfrac{a}{sin(59.15^{})}}[/tex]
[tex]a = \dfrac{5.38 \times sin(59.15^{\circ}) }{sin(65^{\circ} 20')} \approx \mathbf{ 5.083}[/tex]
a ≈ 5.083 inches
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The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 9. If 9 fish are randomly selected, what is the probability that the mean weight will be between 17.6 and 23.6 lb
Step-by-step explanation:
mean of 20 lb and a standard deviation of 9. If 9 fish are randomly selected,
what is the probability that the mean weight will be between 17.6 and 23.6
Ib? Write your answer as a decimal rounded to 4 places
Emilia waited 11 minutes for the bus today. That is 4 minutes less than she waited yesterday. How long did Emilia wait for the bus yesterday?
11 minutes + 4 minutes more yesterday = 15 total minutes
Answer: 15 minutes
Answer:
Emilia waited 11 minutes wich was 4 minutes earlier so 11+4 because it was 4 miutes earlier so 11 minutes + 4 minutes = 15 minutes so this means Emilia wait 15 minutes for the bus yesterday
Step-by-step explanation:
Find the value of the expression 4a + 7 when a= 1/2.
plssss help quiiick
Answer:
The answer is 9
Step-by-step explanation:
1/2 of 4 is 2, so you plug that in
2+7=9
Sharon’s turtle escaped from her backyard sometime in the last few hours. According to her calculations, the farthest the turtle could have gone is 4 blocks down the road in either direction. If Sharon lives on the 112th block of town, which equation can be used to find the block numbers that represent the farthest distance that the turtle may be?
help me plz!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The answer is B. just to keep it short B.
please answer fully/////////////
Answer:
Step-by-step explanation:
Tear this apart piece by piece
15 - 8 = 7
7 * 3 = 21
11 + 21 = 32
Now so far this much is correct. The problem is the next sign. Is it add or is it divide. The only way to resolve it is to do it both ways.
Add 4
32 + 4 = 36
Divide 4
32 / 4 = 8 1/4 = 8
Answer:
8Step-by-step explanation:
Use PEMDAS:
P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)
[tex]\ [11+(15-8)\cdot3]:4=(11+7\cdot3):4=(11+21):4=32:4=8[/tex]
please help with this math
1/2 - 3/10 please help
Answer:
[tex]\huge\boxed{\dfrac{1}{5}=0.2}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{2}-\dfrac{3}{10}=\dfrac{1\cdot5}{2\cdot5}-\dfrac{3}{10}=\dfrac{5}{10}-\dfrac{3}{10}=\dfrac{5-3}{10}=\dfrac{2}{10}=\dfrac{2:2}{10:2}=\dfrac{1}{5}\\\\\\\dfrac{1}{2}=0.5;\ \dfrac{3}{10}=0.3\\\\\dfrac{1}{2}-\dfrac{3}{10}=0.5-0.3=0.2[/tex]