Answers
Hello,
First, you must understand that
(f-g)(x) means f(x)-g(x) it is the difference of two functions :
f(x)=2x+4 and g(x)=3x-7
f(5)=2*5+4=10+4=14
g(5)=3*5-7=15-7=8
So, (f-g)(5)= f(5)-g(5)=14-8=6
Answer A: none of the choices are correct.
An other way to do it:
(f-g)(x)=f(x)-g(x)=2x+4-(3x-7)= 2x-3x+4+7=-x+11
if x= 5 then (f-g)(5)=-5+11=6
Related Questions
Pipe A can fill 3 tanks in 8 minutes. Pipe B can fill 5 tanks in 10 minutes. How long will it take for them to fill a single tank if they work together?
Answers
Answer:
8/7 min = [tex]1 \frac{1}{7} minutes[/tex]
Step-by-step explanation:
A rate 2 2/3 = 8/3 min per tank
B rate 2 min per tank
thus:
A rate = 3/8 tank per min
B rate = 1/2 tank per min
A+ B = 3/8 + 4/8 = 7/8 tank per min
7/8 x = 1
x = 8/7 min
please someone help I know the answer but I don't know how to place it on the scales below. (15 Points)
Answers
Given:
a. 35% of 150 g
b. 113% of $55
To find:
The correct values for the given blanks.
Solution:
a. 35% of 150 g
Here, the percent part is 35% and percent whole is 100%.
35% of 150 g is:
[tex]\dfrac{35}{100}\times 150=52.5[/tex]
So, the number part is 52.5 g and the whole number is 150 g.
Therefore, the percent part is 35%, number part is 52.5 g and the whole number is 150 g.
b. 113% of $55 g
Here, the percent part is 113% and percent whole is 100%.
113% of $55 is:
[tex]\dfrac{113}{100}\times 55=62.15[/tex]
So, the number part is $62.15 and the whole number is $55.
Therefore, the percent part is 113%, number part is $62.15 and the whole number is $55.
3. Una forma de dividir facilmente entre 4 es dividiendo dos veces entre 2.Observa el ejemplo y aplica el procedimiento utilizado
Ejemplo: 568÷4=(568÷2)÷2
= 284 ÷2
= 142
a) 936÷4= c)2 812÷4=
b) 2 084÷4= d)3 720÷4=
Answers
Which congruence theorem can be used to prove BDAS DBC?
Answers
Answer:
We know that the hypotenuse-leg theorem states that if the hypotenuse and one leg of a right triangle are congruent to hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. hypotenuse(AB) of △BDA equals to hypotenuse (CD) of △DBC.
Answer:
A. HL
Step-by-step explanation:
Write a recursive rule for the sequence.
x, x, 2x, 3x, 5x, 8x, ...
I know that it adds its last term but I don't know the rule/formula to show that.
Answers
Answer:
f(n)=f(n-1)+f(n-2)
f(1)=1x
f(2)=1x
Step-by-step explanation:
This is the fibonacci sequence with each term times x.
Notice, you are adding the previous two terms to get the third term per consecutive triples of the sequence.
That is:
1x+1x=2x
1x+2x=3x
2x+3x=5x
3x+5x=8x
So since we need the two terms before the third per each consecutive triple in the sequence, our recursive definition must include two terms of the sequence. People normally go with the first two.
f(1)=1x since first term of f is 1x
f(2)=1x since second term of f is 1x
Yes, I'm naming the sequence f.
So I said a third term in a consecutive triple of the sequence is equal to the sum of it's two prior terms. Example, f(3)=f(2)+f(1) and f(4)=f(3)+f(2) and so on...
Note, the term before the nth term is the (n-1)th term and the term before the (n-1)th term is the (n-2)th term. Just like before the 15th term you have the (15-1)th term and before that one you have the (15-2)th term. That example simplified means before the 15th term you have the 14th and then the 13th.
So in general f(n)=f(n-1)+f(n-2).
So the full recursive definition is:
f(n)=f(n-1)+f(n-2)
f(1)=1x
f(2)=1x
The width of a rectangle is (2x – 7)inches and its width is (x^2 – 5) inches. Find an expression for the perimeter of the rectangle.
a. 2x^3 + 35
b. x^2 - 2x + 2
c. x^2 + 2x – 12
d. 2x^2 + 4x – 24
Answers
Answer:
(2x²+4x-24) in.
Step-by-step explanation:
.
Maths assignment
9p^2-16q^2
Answers
Answer:
[tex]9p^2-16q^2[/tex]
[tex](3p)^{2} -(4p)^{2}[/tex]
[tex]\underline{x^2-y^2=\left(x+y\right)\left(x-y\right)}[/tex]
[tex]\left(3p\right)^2-\left(4q\right)^2=\left(3p+4q\right)\left(3p-4q\right)[/tex]
[tex]=\left(3p+4q\right)\left(3p-4q\right)[/tex]
------------------------
hope it helps....
have a great day!!
The students in a school can be arranged in 12, 15 and 18 equal rows and also into a solid square. What is the lowest number of students that can be in the school?
Answers
Hello,
Let's x then number of students.
x is divisible by 12,15,18 thus by 180 (lcm)
x=180*k is a square
2²*3²*5*k= a square ==> k=5
x=180*5=900
Proof:
900/12=75
900/15=60
900/18=50
900=30²
What is the result of converting 60 ounces to punds remember there are 16 ounces in a pound pleasdnsjjsjs
Answers
Answer:
A. 3.75 pounds
Step-by-step explanation:
16 ounces = 1 pound
converting 60 ounces to pounds
Let x = number of pounds
60 ounces = x pounds
Find the proportion
16 / 1 = 60 / x
Cross product
16 * x = 1 * 60
16x = 60
Divide both sides by 16
x = 60/16
x = 3.75
Therefore,
60 ounces = 3.75 pounds
Solve the system of equations.
5x – 4y = -10
y = 2 x – 5
x =
y =
Answers
Answer:
6x2+3y2=12,x+y=2,2x-y=-1x+y=4,x-y=2
Step-by-step explanation:
I just know.
Answer:
Step-by-step explanation:
5x – 4y = -10
y = 2 x – 5
Rearrage the equation:
5x – 4y = -10 (1)
-2 x +y = 5. (2)
pluging variable y equation2 in 1
5x - 4•(2x-5) = -10
-3x = -30
Solve equation [1] for the variable x
3x = 30
x = 10
x = 10
y = 2x-5
Use the x value to solve for y
y = 2(10)-5 = 15
x= 10
y= 15
yall rockin w yung kayo
Answers
Answer:
YALLLLLLLLL
Step-by-step explanation:heheh okie thats funnie
if tanA=12/16,find sin 2A
Answers
First, we need to draw a right triangle to represent the given trigonometric ratio. (Kindly refer to the attached photo for the figure.)
Second, we need to determine the length of the unknown side.
In this case, the unknown side is the hypotenuse. Since the length of the opposite side is 12 and the length of the adjacent side is 16, then the length of the hypotenuse is
[tex]c = \sqrt{16^{2} + 12^{2}}[/tex]
[tex]c = 20[/tex]
After this, we need to know the trigonometric identity of sin 2A in order to solve for its value.
We know that,
sin 2A = 2 sin A cos A
Then, we need to determine the values of sin A and cos A.
Based on the figure (attached photo), the values of sin A and cos A are
sin A = opposite side / hypotenuse
sin A = 12/20
sin A = 3/5
cos A = adjacent side / hypotenuse
cos A = 16/20
cos A = 4/5
Finally, we can now solve for the value of sin 2A by substituting the values of sin A and cos A to the trigonometric identity of sin 2A.
Therefore, the the value of sin 2A is
sin 2A = 2 sin A cos A
sin 2A = 2(3/5)(4/5)
sin 2A = 24/25
the line segment AB is rotated through 90° clockwise about the point C. the coordinates of A', the image of A, are
Answers
Answer:
B
Step-by-step explanation:
We dont know rules about rotating a point. We only know rules about rotating about the orgin.
We can translate this line segment so point c is on the orgin because
A translation is a rigid transformationWe also know rotation rules about the orgin.Point C is at (1,3) so let move this all points 1 to the left and 3 down. Why All Points?
A translation is parallel from it original image to its second or new image so this means Point B and Point A will both move as well. Let just focus on Point A. The new coordinates are:
Point A prime is (1,0).Let apply the 90 degree clockwise rule. Point C doesnt move since it is at the orgin and it at the center of rotation.
(x,y) goes to (y,-x).
So Point A prime is now at
(0,-1).
Now let translate the figure back to Point C (1,3). by going 1 to the right and 3 up so our new point of Point A prime is at
(1,2).
The value of -9 is __ than the value of -12 because -9 is to the __of -12 on the number line.
Less
Or
Greater
Answers
Answer:
Step-by-step explanation:
-9 is greater than the value of -12 because -9 is to the right of -12 on the number line.
Solve for x. Round to the nearest tenth, if necessary.
Answers
Answer:
25.5
Step-by-step explanation:
first find angle E.
remember, all angles in a triangle always add up to 180 degrees.
E = 180 - 90 - 20 = 70 degrees
now we use the law of sines.
ED/sin(20) = DC/sin(70) = EC/sin(D)
EC = x
sin(D) = sin(90) = 1
24/sin(70) = x/1 = x
x = 25.5
Help plsssssss ,it would mean a lot thankyou
Answers
Answer:
Part 1;
(0, 0)
Part 2;
(0, 2.5)
Step-by-step explanation:
Part 1
The given system of inequalities is presented as follows;
f(x) < x + 4; f(x) > -x - 3; and f(x) < 5
We check each of the points as follows;
The point (0, 0) in the inequality f(x) < x + 4, gives;
f(0) < 0 + 4
f(0) = 0 < (is less than) 0 + 4 = 4
Therefore, (0, 0) is a solution of the inequality f(x) < x + 4
The point (0, 0) in the inequality f(x) > -x - 3, gives;
f(0) < -0 - 3
f(0) = 0 > (is larger than) -0 - 3 = -3
Therefore, (0, 0) is a solution of the inequality f(x) > -x - 3
The point (0, 0) in the inequality f(x) < 5, gives;
f(0) < 5
f(0) = 0 < (is less than) 5
Therefore, (0, 0) is a solution of the inequality f(x) < 5
The point (-6, 0) in the inequality f(x) > -x - 3, gives;
f(-6) = -6 - 3 = 3
The point (-6, 0) with y = 0 < (is less than) f(-6) = 3, therefore (-6, 0) is not a solution to (not included in the graph of) the inequality f(x) > -x - 3 and therefore to the system of inequalities because at x = -6, the values of f(x) > -x - 3 are larger than 3
The point (-3, 4) in the inequality f(x) < x + 4, gives;
f(-3) = -3 + 4 = 1
The point (-3, 4) with y = 4 < (is larger than) f(-2) = 1, therefore (-3, 4) is not a solution to (not included in the graph of) the inequality f(x) < x + 4 and therefore to the system of inequalities because at x = -3, the values of f(x) < x + 4 are less than 1
The point (4, 6) is not a solution to (not included in the graph of) the inequality f(x) < 5 and therefore to the system of inequalities because f(x) is larger than 5 for all x
Therefore, the point which is part of the solution set of the system of inequalities is (0, 0)
Part 2
The given system of inequalities are, f(x) ≥ 2·x + 2; f(x) ≤ -4·x + 3; and f(x) ≤ 6·x + 5
Plotting the given system of inequalities on MS Excel the point which is part of the solution is given by points which are within the triangular intersection area of the three inequalities, with coordinates, (1/6, 7/3), (-3/4, 1/2), and (-1/5, 19/5)
Therefore, the points, (0, 0), (-2.5, 0) are not solutions because, the y-value of the solution area are all higher than the line y = 0
The point (0. 6.5) is not a solution because the points in the triangular solution area all have x-values lesser than x = 6.5
The point which is part of the solution by examination is the point (0, 2.5) which is a point between the lines y = 19/5 = 3.8, y = 1/2, x = -3/4, and x = 1/6.
Help me out plz bbbhbbhh
Answers
hopefully that’s the answer you needed
the solution is in the picture ☝️
ANSWER: 240 hours
this is for n.12
What should you substitute for y in the bottom equation to solve the system by the substitution method?
A. y=3x+15
B. y =-x-5
C. y=x+5
D. y=-3-15
Answers
Step 1: Determine which equation to change
Since we will be using the substitution method, we will need to substitute y from the bottom equation with information from the top equation. This will be the equation we change.
Step 2: Change the equation
Let’s rewrite the equation we will be working with.
3x+3y= -15
Our goal will be to get y alone on the left side. To start, let’s subtract 3x from both sides, leaving only 3y on the left side.
3x+3y= -15
3y= -3x-15
Now we need to get y completely alone by eliminating the coefficient of 3. Let’s do this by dividing each term by 3.
3y= -3x-15
y= -x-5
This is your answer. Hope this helps! Comment below for more questions.
A farmer builds a fence to enclose a rectangular pasture. He uses 155 feet of fence. Find the total area of the pasture if it is 45.5 feet long. The length is 6 and the height is 5 what is the width?
Answers
Answer: [tex]1456\ ft^2[/tex]
Step-by-step explanation:
Given
Length of whole fence is 155 feet
If the length of rectangle is 45.5 ft
Suppose width is w
Length of whole fence is perimeter which is given by
[tex]\Rightarrow 155=2(45.5+w)\\\Rightarrow 77.5=45.5+w\\\Rightarrow w=32\ ft[/tex]
Area of the rectangle is given by the product of length and width
[tex]\Rightarrow A=lw\\\Rightarrow A=45.5\times 32\\\Rightarrow A=1456\ ft^2[/tex]
Thus, total area of pasture is [tex]1456\ ft^2[/tex]
product of (6x+8us^2)(x-us^2)
Answers
Answer:
−8s4u2+2s2ux+6x2
Step-by-step explanation:
=(6x+8us2)(x+−s2u)
=(6x)(x)+(6x)(−s2u)+(8us2)(x)+(8us2)(−s2u)
=6x2−6s2ux+8s2ux−8s4u2
=−8s4u2+2s2ux+6x2
Answer:
6x² + 2xus² - 8u²s^4
Step-by-step explanation:
(6x+8us²)(x-us²)
6x² - 6xus² + 8xus² - 8u²s^4
6x² + 2xus² - 8u²s^4
The width of this rectangle is measured as 19.4 correct to 1 decimal place. What is the lower bound for the area of the rectangle
Answers
Answer:
:D
Step-by-step explanation:
19.35 = 7062.75 mm²
What is the slope of the line represented by the equation y-6 = 5(x-2)?
O A. 6
O B. 5
O C. -5
O D. 2
Answers
Answer:
B
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 6 = 5(x - 2) ← is in point- slope form
with slope m = 5 → B
Sofia has 25 coins in nickels and dimes in her pocket for a total of $1.65 how many of each type of coin does she have?
Answers
Answer:
She has 23 nickels and 5 dimes.
Step-by-step explanation:
Let n = the number of nickles and d = the number of dimes.
The number of each = 28. Set up the equation:
n + d = 28
Solve for n:
n = 28 - d
The total amount is $1.65 or 165 cents:
5n + 10d = 165
Substitute:
5(28 - d) + 10d = 165
140 - 5d + 10d = 165
140 + 5d = 165
5d = 165 - 140
5d = 25
d = 5, the number of dimes.
Solve for n:
n = 28 - d
n = 28 - 5 = 23, the number of nickles.
Proof:
5n + 10d = 165
5(23) + 10(5) = 165
115 + 50 = 165
165 = 165
Hope this Helps! Have an Awesome Day!!! <3
Step-by-step explanation:
Answer:
Sofia has 23 nickles & 5 dimes
Step-by-step explanation:
The number of each is 28
Form an equation:
[tex]n+d=28[/tex]
Solve for n:
[tex]n=28-d[/tex]
The total amount is $1.65 for 165 cents:
[tex]5n+10d=165[/tex]
Substitute:
[tex]5(28-d)+10d=165[/tex]
[tex]140-5d+10d=165[/tex]
[tex]140+5d=165[/tex]
[tex]5d=165-140[/tex]
[tex]5d=25[/tex]
[tex]d=25/5[/tex]
[tex]d=5[/tex]
Solve for n:
[tex]n=28-d[/tex]
[tex]n=28-5=23[/tex] ⇒ the number of nickles
CHECK:
[tex]5n+10d=165[/tex]
[tex]5(23)+10(5)=165[/tex]
[tex]115+50=165[/tex]
[tex]165=165[/tex]
hope this helps....
What is
4
7
as a decimal rounded to 3 decimal places?
Answers
Answer:
4/7 as a decimal is 0.57142857142857.
Circle W has a radius of 20 in and right central angle, ZVWX. Find the length of vx. Leave your answer in terms of pi.
5
10
15
20
Answers
Answer:
The length of the arc is 10 pi
Step-by-step explanation:
Mathematically, the length of an arc is calculated as;
theta/360 * 2 * pi * r
theta represents the central angle subtended by the arc which is a right angle according to the question (a right angle is 90 degrees)
r is the circle radius which is 20 inches
so we have the length of the arc as;
90/360 * 2 * pi * 20 = 40 pi/4 = 10 pi
The two
triangles are similar.
What is the value of x?
Enter your answer in the box
Answers
Answer:
13
Step-by-step explanation:
the scale factor is 4:1 so just divide 52 by 4.
A cable 45 m long runs from the top of a utility pole to a point on the ground 40 m from the base of the pole. How tall is the utility pole, to the nearest tenth?
20.6 m
85 m
5 m
60.2 m
Answers
Answer:
20.6 m
Step-by-step explanation:
Hi there!
Assuming that the utility pole makes a 90-degree angle with the ground, this scenario creates a right triangle.
The 45 m-long cable is the hypotenuse and the 40 m between the base of the pole and the cable is one of the legs.
We must solve for the height of the utility pole, which is essentially the other leg of the right triangle.
We can use the Pythagorean theorem: [tex]a^2+b^2=c^2[/tex] where a and b are the legs and c is the hypotenuse
Plug in the known information (leg=40, hyp=45)
[tex]40^2+b^2=45^2\\1600+b^2=2025\\b^2=2025-1600\\b^2=425\\b=20.6[/tex]
Therefore, when rounded to the nearest tenth, the height of the utility pole is 20.6 m.
I hope this helps!
Plz help. How to convert this standard notation to scientific notation 549,755,813,888.
Answers
Answer:
To change a number from scientific notation to standard form, move the decimal point to the left (if the exponent of ten is a negative number), or to the right (if the exponent is positive). You should move the point as many times as the exponent indicates. Do not write the power of ten anymore
Find the equation of the line.
Use exact numbers.
Answers
Answer:
Y = 2x + 5
Step-by-step explanation:
2x is your slope and 5 is your y intercept.
The formula for this is: y = mx + b
The question is in the image
Answers
Answer:
$9Step-by-step explanation:
f(x) = - 25 ( x - 9 )² + 200when x = 5 ,
f(5) = - 25 ( 5 - 9 )² + 200 = - 200
when x = 9 ,
f(9) = - 25 ( 9 - 9 )² + 200 = 200
when x = 10 ,
f(10) = - 25 ( 10 - 9 )² + 200 = 175
when x = 15 ,
f(15) = - 25 ( 15 - 9 )² + 200 = -700
∴ when price = $9
the company receive the maximum profit
Answer:
9$
Step-by-step explanation:
