If f(x) = x 2 + 1 and g(x) = 3x + 1, find 2f(1) + 3g(4).
1. 45
2. 43
3. 42
Jaclyn has $120 saved and earns $40 each month in allowance. Pedro has $180 saved and earns $20 a month in allowance. If they both save their entire allowances, how long will it take before Jaclyn and Pedro have saved the same amount of money?
Answer:
3 months
Step-by-step explanation:
Let after m months they saved same amount of money.
Given,
Saving of Jaclyn = $ 120,
Amount earned by him/her per month = $ 40,
So, the total amount contained by him/her in m months = Saving + earning for m months
= 120 + 40m,
Similarly, saving of Pedro = $ 180,
Amount earned by him/her per month = $ 20,
So, the total amount contained by him/her in m months = 180 + 20m
Thus, we can write,
120 + 40m = 180 + 20m
40m = 180 + 20m - 120
40m - 20m = 60
20m = 60
⇒ m = [tex]\frac{60}{20}[/tex] = 3.
Hence, it will take 3 months before which Jaclyn and Pedro have saved the same amount of money.
Linear equations can be solved by applying arithmetic operations separately for variables and constants. If they both save their entire allowances, 3 months will it take before Jaclyn and Pedro have saved the same amount of money
Let us assumed that the saving of Jaclyn and Pedro will be the same after n months.
Now, from the given data.
Saving of Jaclyn = $ 120
Amount earned by Jaclyn per month = $ 40
Total amount in hand of Jaclyn after work for n months will be the addition of current saving and the amount earned by Jaclyn after n months.
Thus,
[tex]\rm{Amount \;after \;n \;months}= 120 + 40n[/tex],
Similarly, the saving of Pedro = $ 180
Amount earned by Pedro per month = $ 20
Total amount in hand of Pedro after work for n months will be the addition of current saving and the amount earned by Pedro after n months.
Thus,
[tex]\rm{Amount \;after \;n \;months}= 180 + 20n[/tex]
According to the question,
[tex]\begin{aligned}&120 + 40n = 180 + 20n\\&40n = 180 + 20n - 120\\&40n - 20n = 60\\&20n = 60\\&n=\dfrac{60}{20}\\&n=3\end{aligned}[/tex]
Hence, If they both save their entire allowances, 3 months will it take before Jaclyn and Pedro have saved the same amount of money.
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Jeremiah is factoring 0.64t^24 - 9 by using the rule, a^2 - b^2 = (a+B)(a-b). What will he use for the value of a? A.0.08t^12 B. 0.8t^12 C. 0.64 D. 0.8 I think it's B or C... Help please!
to factor something with an exponent you need to take the square root of it
sqrt (0.64) = 0.8, sqrt(t^24) = t^12)
Answer is B
A train leaves a train station at 1 p.m. it travels at an average rate of 60 mi/hr. a high-speed train leaves the same station an hour later. it travels at an average rate of 96 mi/hr. the second train follows the same route as the first train on a track parallel to the first. in how many hours will the second train catch up with the first train?
The second train will catch up with the first train after 5/3 hours.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a train that leaves a train station at 1 p.m. it travels at an average rate of 60 mi/hr. A high-speed train leaves the same station an hour later. it travels at an average rate of 96 mi/hr. The second train follows the same route as the first train on a track parallel to the first.
We have -
Assume that the second train catches the first in x hours. Then, we can write -
60(x + 1) = 96x
60x + 60 = 96x
96x - 60x = 60
36x = 60
x = 60/36
x = 5/3 hours
Therefore, the second train will catch up with the first train after 5/3 hours.
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Please help me whith this it is due today.
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $18,853 , and the variable costs will be $19.75 per book. With the other method, the one-time fixed costs will total $64,853 , and the variable costs will be $8.25 per book. For how many books produced will the costs from the two methods be the same?
Solve each system. Then drag each one to the column headed by a point which could be its solution. (5,y) or (x,2)
2x-2y=12
-2x-3y=-22
2x-6y=10
x+8y=5
3x-y=-5
x+4y=7
x+y=2
2x+y=13
Answer: system 2 (5,0) and system 3 (-1 2)
2x-6y=10 3x-y=-5
x+8y=5 x+4y=7
Step-by-step explanation:
Solve each system. Then drag each one to the column headed by a point which could be its solution. (5,y) or (x,2)
system 1
2x - 2y =12
-2x-3y = -22
solve simultaneous equation
2x - 2y =12
-2x-3y = -22
add the equations gives
2x +(-2x) =0
-2y+(-3y) =-5y
12+ (-22) = -10
-5y =-10
y =2
2x -2(2) =12
2x-4 =12
2x = 12+4
x= 16/2 =8 x=8 and y =2 = (8,2)
system 2
2x-6y=10 *(-1) = -2x + 6y =-10
x+8y=5 *(2) = 2x + 16y =10 add the equations
22y =0 y =0
x : 2x - 6(0) =10
x = 10/2 = 5
(5, 0)
system 3
3x-y=-5 *(-1) = -3x + y =5
x+4y=7 * (3) = 3x + 12y = 21
add the equations = 13y = 26 y = 2
3x -2 =-5 = 3x = -3 =x =-1
(-1 2) answer
system 4
x+y=2 *(-2) = -2x -2y = -4
2x+y=13 *(1) = 2x +y = 13
add the two equations = -y =9
y = -9
substitute 2x-9= 13= 2x =22 x =11
(11 -9)
What is the product? (7.1×10 ^4)⋅(4.8×10 ^3)
3.408×10^7
3.408×10^8
3.408×10^12
3.408×10^13
The length of the hypotenuse of a right triangle is 13 cm. the length of one leg is 5 cm. find the length of the other leg. (1 point) 14 cm 144 cm 8 cm 12 cm
Answer: 12
Step-by-step explanation:
Which graph represents the solution set for the system 6x + y > -3 and 2x + y ≤ 4?
A. graph A
B. graph B
C. graph C
D. graph D
Answer:
Option B. Graph B
Step-by-step explanation:
The given system of the inequalities are 6x + y > -3 and 2x + y ≤ 4
If we take the first inequality which represents the area below the line 6x + y = -3 or y = -6x - 3 (Slope of the line -6 and y-intercept is -3)
Second graph is represented by 2x + y ≤ 4 which represents the area below the line y = 4 - 2x ( slope = -2 and y intercept = 4)
Option B shows the shaded area which the common area representing the solution set of these systems.
Al drives from Boston to Washington D.C. and then returns. On his trip to Washington, he travels 60 miles per hour. On his return trip, he travels 50 miles per hour. His trip to Boston takes an hour and a half longer than his trip to Washington. How far apart are Washington and Boston? Make a equation
The distance apart from Washington and Boston is 450 miles.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
Trip from Boston to Washington:
Speed (2) = 60 miles per hour
Trip from Washington to Boston:
Speed (1) = 50 miles per hour
Speed = Distance / Time
Time = Distance / Speed
Distance is the same for both trips.
Time taken for the trip from Washington to Boston = t(1)
Time taken for the trip from Boston to Washington = t(2)
His trip to Boston takes an hour and a half longer than his trip to Washington.
This can be written as,
t(1) - t(2) = 1.5 hours
Distance ( 1/50 - 1/60) = 1.5
Distance ( (6 - 5)/300 ) = 1.5
Distance (1 / 300) = 1.5
Distance = 1.5 x 300
Distance = 450 miles
Thus,
The distance apart from Washington and Boston is 450 miles.
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What os a comparison of two quantities and can be written as a fraction when the two quantities have two different units?
Suppose Raj receives a raise for his hard work and now earns $6.25 per hour how many hours would he need to work to earn $132?
-3(w-3)≥9-3w
If all real numbers can solve please tell me why
Answer: " w = (all real numbers) " —as explained below.
_________
Step-by-step explanation:
_________
Given the following "inequality":
_________
" -3(w – 3) ≥ 9 – 3w " ; Solve for "w" ;
and see if the answer ["value for "w"]; is:
"all real numbers."
_________
→ " -3(w – 3) ≥ 9 – 3w " ;
_________
Method 1):
_________
On the "right-hand side" of the "inequality";
Factor out a "(-3)" ;
_________
" -3(w – 3) ≥ ( -3 * ? = 9?) – (-3 * ? = 3w? ) " ;
_________
1) " -3 * (what value?) = 9 "?
Let "x" be the 'unknown value' :
→ " -3x = 9 " ;
Divide each side of the equation by "(-3)" ;
to isolate "x" on one of the equation;
& to solve for "x" ;
-3x / -3 = 9 / -3 ;
to get: " x = -3 " ;
_________
2) " -3 * (what value?) = 3w " ?
Let "x" be the 'unknown value' :
→ " -3x = 3w " ? ;
→ Divide each side or the equation by ("-3").
→ to isolate "x" on one side of the equation;
→ & to solve for "x" ;
-3x / 3 = 3w / -3 ;
to get: x = -1w ;
_________
So: " -3(w – 3) ≥ -3* (? = 9?) – (-3 * ? = 3w?) " ;
_________
Rewrite as:
" -3(w – 3) ≥ -3* [(-3 – (-1w)] " ;
_________
Now, let us consider the Following Portion of the "right-hand side" of the inequality:;
" (-3 – (-1w)] = " (-3 + 1w) " ;
→ {since: "subtracting a "negative value is the equivalent of adding that particular value's positive value"} ;
and bring down the "(-3)" on the "right-hand side" of the inequality; and rewrite the inequality as:
_________
" -3(w – 3) ≥ -3(-3 + 1w) " ;
→ Now, divide EACH SIDE of the inequality by "(-3)" :
{Note: Each time when one multiplies or divides an inequality by a "negative value"—the inequality sign flips to the other direction.}.
→ [ -3(w – 3)] / -3 ≥ [-3(-3 + 1w ] / -3 ;
to get:
→ " (w – 3) ≤ (-3 + 1w) " ;
_________
Note: " (-3 + 1w) " ; ↔ " [(1w + (-3)] = " 1w – 3 " = "w – 3 " ;
_________
Rewrite the inequality:
_________
→ " (w – 3) ≤ (w – 3 ) " ;
↔ " w – 3 ≤ w – 3 " ;
The same value is equal to each other: not less than or equal to each other: For instance:
→ " w – 3 ≤ w – 3 " ;
If we add "3" to each side of the equation:
→ " w – 3 + 3 ≤ w – 3 + 3 " ;
We get: " w ≤ w " . "w = w". "w is not "less than" itself. So all real numbers apply!
_________
Method 2)
_________
Given the following "inequality":
_________
" -3(w – 3) ≥ 9 – 3w " ; Solve for "w" ;
and see if the answer ["value for "w"]; is:
"all real numbers."
_________
On the "left-hand side of the inequality;
we have:
_________
" -3(w – 3) " ;
_________
Take note of the "distributive property of multiplication" :
→ " a(b + c) = ab + ac " ;
_________
As such:
_________
We can expand:
" -3(w – 3) = (-3*w) + (-3*-3) " ;
= -3w + (9) ;
_________
Now, we can rewrite the original inequality:
_________
" -3w + 9 ≥ 9 – 3w " ;
_________
Note: " -3w + 9 = 9 + (-3w) = 9 – 3w " ;
→ {since: adding a "negative value" gets the same value as subtracting that value's "positive equivalent"};
And we can rewrite our inequality as:
_________
" 9 – 3w ≥ 9 – 3w " ;
_________
Note: We have the same value on each side.
"(9 – 3w)" is not greater than itself; it is "equal to itself".
Any and all real numbers as values for "w" will result in the same value for any particular expression's Exact Same Expression!
_________
So: "w = (all real numbers)" .
_________
Hope this is helpful to you!
Best wishes!
_________
Help me please thanks
Marcus and three of his friends are guessing the radius of a circular pond. They read that the circumference is 157 ft, so they can use the equation 3.14*2r=157 to determine which of these guesses which form the replacement set {20,25,30,35} is correct?.
What is the radius of the pond?
A. 20ft
B. 25ft
C. 30ft
D. 35ft
Answer:
Option B. 25 ft
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=157\ ft[/tex]
assume
[tex]\pi =3.14[/tex]
substitute in the formula
[tex]157=2(3.14)r[/tex]
Solve for r
Divide by 2(3.14) both sides
[tex]r=157\(2(3.14))[/tex]
[tex]r=25\ ft[/tex]
One-eleventh of all sales at Joe's Diner are for cash. If cash sales for the week were $380, what were Joe's total sales?
To find Joe's total sales when one-eleventh are cash sales amounting to $380, multiply the cash sales by 11, which results in a total of $4180.
To find Joe's total sales, one would apply the concept of proportions in mathematics. Here is a step-by-step breakdown of the problem:
Identify the fraction of total sales that are cash, which is one-eleventh.
Understand that $380 equals this fraction of the total sales.
To find the total sales, divide the cash sales by the fraction that represents cash sales 1/11
Calculate the total sales by using the following equation: Total Sales = Cash Sales / (1/11) = $380 / (1/11).
Perform the division: Total Sales = $380 * 11 = $4180.
Hence, Joe's total sales for the week were $4180.
what is the measure of each interior angle in a regular hexagon?
HELP?
Two people start from the same point and move in opposite directions. The
first person jogs west traveling 5 mph, and the second person walks east
traveling 3 mph. In how many hours will the two people be 48 miles apart?
Chrissy walked 550 meters in 7 minutes and 20 seconds. If each lap is 25 meters, which is Chrissy’s MOST LIKELY time per lap in seconds? *A) 20 seconds b. 22 seconds c 42 seconds d. 64 seconds
Martin drives to work at a speed of 45 miles per hour. It takes him about 2 hours and 15 minutes to get to work. If gas costs $2.75 per gallon and Marin’s car gets 25 gallons of gas per mile, about how much does Martin spend on gas to get to work? a. 3.87 b. 4.05 c. 10.64 d. 11.14
Sammy has a 10-foot ladder, which he needs to climb to reach the roof of his house. the roof is 12 feet above the ground.
What are the solutions of the inequality? -2(3x + 2) greater than or equal to -6x - 4
Which is the line shown in the figure?
line XY
line XZ
line WX
line WZ
Option B is the correct answer.
We need to check which is the line shown in the figure.
What is a line?In geometry, a line is an infinitely long object with no width, depth, or curvature. Thus, lines are one-dimensional objects, though they may exist in two, three, or higher-dimension spaces. The word line may also refer to a line segment in everyday life, which have two points to denote its ends.
Now, from the given figure we can see XZ is a line.
Therefore, option B is the correct answer.
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the correlation coefficient (r) between the number of hours worked x and the amount of money earned y is 0.456 what percent of the variation in the amount of money earned can be explained by differences in the number of hours worked
A :79.2%
B:54.4%
C:45.6%
D:20.8%
What value of n would make point A the circumcenter?
1. 2
2. 3
3. 4
4. 5
Answer:
The correct option is 2. The value of n is 3.
Step-by-step explanation:
Circumcenter is the point, where the perpendicular bisectors of a triangle intersect each other.
Circumcenter is also known as the center of the triangle. The distance from circumcenter to each vertex are same.
In triangle DEF, if A is the circumcenter.
[tex]AE=AD[/tex]
[tex]10=2n+4[/tex]
Subtract 4 from both sides.
[tex]10-4=2n[/tex]
[tex]6=2n[/tex]
Divide both sides by 2.
[tex]3=n[/tex]
Therefore the value of n is 3 and option 2 is correct.
Answer:
Option 2 is true
Step-by-step explanation:
We have to find the value of n for which point A becomes circumcenter.
Circumcenter: It is that point where perpendicular bisectors of triangle intersects.
The circumcenter is also knows as center of triangle.
Circumcenter is at equal distance from each vertex of triangle.
If point A is circumcenter then
AE=AD
We have AE=10 units
AD=2n+4
Substitute the value
10=2n+4
[tex]2n=10-4[/tex]
By subtraction property of equality
[tex]2n=6[/tex]
[tex]n=\frac{6}{2}=3[/tex]
Hence, the value of n is 3 would make point A the circumcenter.
A drama club wants to raise at least $500 in tickets sales for its annual show. The members of the club sold 50 tickets at a special $5 rate. The usual ticket price the day of the show is $7.50. At least how many tickets do they have to sell the day of the show to meet the goal. Let t=tickets
To meet their fundraising goal, the drama club needs to sell 34 tickets at $7.50 each.
Answer:
The drama club wants to raise at least $500 in ticket sales. They already sold 50 tickets at $5 each. Let the number of tickets they need to sell at $7.50 be represented by 't'.
Revenue from $5 tickets: $5 × 50 = $250To find the number of $7.50 tickets needed: $500 - $250 = $250Number of $7.50 tickets needed: $250 / $7.50 = 33.33Therefore, the drama club needs to sell at least 34 tickets at $7.50 each to meet their goal.
The function BN equals 6n represents the number of light bulbs BN that are needed for n chandeliers how many light bulbs are needed for 15 chandeliers
BN =6n
n = chandeliers
you have 15 chandeliers so n = 15
so BN = 6(15)
BN = 90
you will need 90 light bulbs
Simplify.
(4a^5b^6)^4
^ means exponent
256a^20 b^24
256a^9 b^10
16a^9 b^10
16a^20 b^24
[tex]\text{Use}\\\\(ab)^n=a^nb^n\\\\(a^m)^n=a^{n\cdot m}\\---------------------\\\\\left(4a^5b^6\right)^4=4^4(a^5)^4(b^6)^4=256a^{5\cdot4}b^{6\cdot4}=256a^{20}b^{24}[/tex]
Find the distance between the points (-2, 4) and (4, -6).
2√2
2√(10)
2√(34)
Answer: The correct option is (C) 2√34.
Step-by-step explanation: We are given to find the distance between the points (-2, 4) and (4, -6).
We have the distance formula as follows :
DISTANCE FORMULA :
The distance between the points (a, b) and (c, d) is given as
[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]
Therefore, the distance between the points (-2, 4) and (4, -6) is given by
[tex]D\\\\=\sqrt{(4-(-2))^2+(-6-4)^2}\\\\=\sqrt{6^2+10^2}\\\\=\sqrt{36+100}\\\\=\sqrt{136}\\\\=\sqrt{4\times34}\\\\=2\sqrt{34}.[/tex]
Thus, the required distance between the given points is 2√34 units.
Option (C) is CORRECT.
a bookstore rents books to students for $2 per book. the cost of running bookstore is $300 per hour. using a for coin flip distribution how many students would the store need to rent to break even?
Answer:
75
Step-by-step explanation:
300/4=75.