The factored form of given expression is:
[tex]40x + 24y - 56 = 8(5x + 3y-7)[/tex]
Solution:
Given that we have to factor the given expression
Given expression is:
40x + 24y - 56
We can factor the expression by taking the greatest common factor out
When we find all the factors of two or more numbers, and some factors are the same , then the largest of those common factors is the Greatest Common Factor.
Find G.C.F of 40, 24 and 56
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40
The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56
Then the greatest common factor is 8
Thus factor out 8 from given expression
[tex]40x + 24y - 56 = 8(5x + 3y-7)[/tex]
Thus the given expression is factored
In rectangle LMNP LN=7x-8 and MP=4x+1 find the length of LN
Answer:
LN = 13 units.
Step-by-step explanation:
If LMNP is a rectangle, then LN and MP are the two diagonals of the rectangle and they are equal.
Now, given that LN = 7x - 8 and MP = 4x + 1
So, 7x - 8 = 4x + 1
⇒ 3x = 9
⇒ x = 3
Therefore, LN = 7x - 8 = 7(3) - 8 = 13 units. (Answer)
in the standard equation for a line,what does the variable b stands for .
y=mx+b
Answer: y-intercept
Explanation The "b" or the constant term represents the y-intercept which is the point where the line crosses the y-axis.
Write an equation from the following points (plug in the numbers you would use for "m" and "b"):
(3, 9) and (6, 13)
Answer:
[tex]y =\fracc{4}{3}x+5[/tex]
m=4/3 and b=5
Step-by-step explanation:
We want to find the equation of the line passing through (3,9) and (6,13).
We determine the slope using:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
Let:
[tex](x_1=3,y_1=9), (x_2=6,y_2=13)[/tex]
We substitute the points to get:
[tex]m = \frac{13 - 9}{6 - 3} = \frac{4}{3} [/tex]
We now use the formula:
[tex]y-y_1=m(x-x_1)[/tex]
We substitute to get:
[tex]y - 9 = \frac{4}{3} (x - 3)[/tex]
Multiply through by 3 to get;
[tex]3y - 27 = 4(x - 3)[/tex]
We expand further to get:
[tex]3y - 27 = 4x - 12[/tex]
This implies that:
[tex]4x - 3y = - 15[/tex]
We solve for y to get:
[tex]y =\fracc{4}{3}x+5[/tex]
Therefore m=4/3 and b=5
Twelve decreased by twice a number is the same as 8 times the sum of the number and 4. What is the number.
Answer: -2
Step-by-step explanation:
Let the number be x , then twice the number is 2x.
Twelve decreased by twice the number = 12 - ( 2x )
8 times the sum of the number and 4 = 8 ( x + 4 )
combining the two , we have
12 - 2x = 8 ( x + 4 )
12 - 2x = 8x + 32
12 - 32 = 8x + 2x
-20 = 10x
x = -20/10
x = -2
Which system of equations could be graphed to solve the equation below?
log (2 x + 1) = 3 x minus 2
(Image Attached Below)
Answer:
[tex]\left\{\begin{array}{l}y_1=\log (2x+1)\\ \\y_2=3x-2\end{array}\right.[/tex]
Step-by-step explanation:
Given the equation
[tex]\log (2x+1)=3x-2[/tex]
This equation consists of two parts. In the left part, there is a logarithmic function [tex]y=log (2x+1)[/tex]
In the right part, there is a linear function [tex]y=3x-2[/tex]
To solve the equation graphically, you have to plot the graphs of these two functions and find the point of intersection of these graphs.
Hence, appropriate system is
[tex]\left\{\begin{array}{l}y_1=\log (2x+1)\\ \\y_2=3x-2\end{array}\right.[/tex]
A new car is purchased for 24000 dollars. The value of the car depreciates at 6.75% per year. To the nearest year, how long will it be until the value of the car is 15500 dollars?
Final answer:
To the nearest year, it will take about 6 years for the value of the car to reach $15,500.
Explanation:
To find how long it will take for the value of a car to depreciate to $15,500, we can set up an equation using the formula for exponential decay: V = P[tex](1 - r)^t[/tex], where V is the final value, P is the initial value, r is the depreciation rate, and t is the time in years.
Plugging in the given values, we have 15500 = 24000[tex](1 - 0.0675)^t[/tex]. To solve for t, we can take the logarithm of both sides:
log(15500) = log(24000[tex](1 - 0.0675)^t)[/tex]
t * log(1 - 0.0675) = log(15500/24000)
t = log(15500/24000) / log(1 - 0.0675)
Using a calculator, we find that t is approximately 5.54 years. Rounding to the nearest year, it will take about 6 years for the value of the car to reach $15,500.
-5(-× -6) =31
Solve the equation
Answer: I believe the answer to this question is: X= 1/5.
if k is a constant, what is the value of k such that the polynomial k^2x^3 - 6kz+9 is
divisible by x-1?
The value of k that makes the polynomial k^2x^3 - 6kz + 9 divisible by x-1 is 3. This is found using the Remainder Theorem and substituting x=1 into the polynomial and solving the resulting equation.
Explanation:The question asks for the value of k such that the polynomial k2x3 - 6kz + 9 is divisible by x-1. To find the value of k, we use the Remainder Theorem, which states: if a polynomial f(x) is divisible by x-c, then f(c) = 0.
Applying this theorem, we set x=1 and solve for k:
Therefore, the value of k that makes the polynomial divisible by x-1 is 3.
Nate scored 5 more than twice the number of points as jake scored. write an expression that represents the relationship of the number of points Nate scored in terms of the number of points jake scored,p. help pls
Answer:
2p+5=n
(p = Jake's points) (n = Nate's points)
The relationship between Nate's and Jake's scores can be expressed by the expression N = 2p + 5.
Explanation:The relationship between the number of points Nate scored (represented by N) and the number of points Jake scored (represented by p) can be expressed as:
N = 2p + 5
This expression represents that Nate's score is equal to twice the number of points Jake scored, plus 5.
Suppose your parents invest $20,000 in an account paying 5% interest compounded annually. What will the balance be after 10 yr?
Answer:
$32,577.89
Step-by-step explanation:
Use the formula for amount after compound interest. A = P(1 + i)ⁿ
'P' is the principal, meaning starting amount. P = $20,000
'i' is the interest per compounding period in decimal form. Since the compounding period is annual, just like the interest rate is given as, i = 0.05. If the compounding period was not annual: then i = r/c (annual interest rate divided by number of compounding periods in a year).
'n' is the number of compounding periods, or the number of times the interest increases. n = 10. Calculate 'n' using n = tc (number of years times number of compounding periods in a year). Since c=1, n = t. ('t' is the number of years).
'A' is the amount after 'n' years. We need to find A.
Use all of the numbers that we know for the variables, replace the variables with the numbers in the formula. Solve for 'A'.
A = P(1 + i)ⁿ
A = $20,000(1 + 0.05)¹⁰ Add inside brackets first
A = $20,000(1.05)¹⁰ Do (1.05)¹⁰ then multiply by 20,000
A = $32,577.89 Answer
Therefore the balance will be $32,577.89 after 10 years.
Evaluate the expression if b = 3.
12 (63 -1)
6=3
2
1/2(3^3-1)
1/2(27-1)
1/2(26)
13
Answer:
13
Step-by-step explanation:
Replace b with 3, then multiply 3^3 get the answer then subtract by 1, last multiply what u got from the paranthesis by 1/2
Wu make and fill out the table using equation
Y = 4x - 2
Answer:
[tex]x = \frac{1}{4} y + \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]y = 4x - 2[/tex]
first flip
[tex]4x - 2 = y[/tex]
now add 2 to each side
[tex]4x + 2 = y + 2[/tex]
now
[tex]4x = y + 2[/tex]
divide by 4
[tex]4x \div 4 = 4 + 2 \div 4[/tex]
so
[tex]x = \frac{1}{4} y + \frac{1}{2} [/tex]
Find the two missing terms of the sequence and determine if the sequence is arithmetic, geometric, or neither.
3, 1, -1, -3, __, __
If f(x) = 2x^2+1 and g(x) =x^2-7 find (f+g)(x)
Answer:f=−
7
x
2
+1−2g−x
Step-by-step explanation:
1 Subtract {x}^{2}x
2
from both sides.
2{x}^{2}+1-g-x-{x}^{2}=-7f+g2x
2
+1−g−x−x
2
=−7f+g
2 Simplify 2{x}^{2}+1-g-x-{x}^{2}2x
2
+1−g−x−x
2
to {x}^{2}+1-g-xx
2
+1−g−x.
{x}^{2}+1-g-x=-7f+gx
2
+1−g−x=−7f+g
3 Subtract gg from both sides.
{x}^{2}+1-g-x-g=-7fx
2
+1−g−x−g=−7f
4 Simplify {x}^{2}+1-g-x-gx
2
+1−g−x−g to {x}^{2}+1-2g-xx
2
+1−2g−x.
{x}^{2}+1-2g-x=-7fx
2
+1−2g−x=−7f
5 Divide both sides by -7−7.
-\frac{{x}^{2}+1-2g-x}{7}=f−
7
x
2
+1−2g−x
=f
6 Switch sides.
f=-\frac{{x}^{2}+1-2g-x}{7}f=−
7
x
2
+1−2g−x
Identify the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola. x^2 + 2y^2 = 2
This is an equation representing the ellipse
Explanation:
The general equation for an ellipse is [tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1[/tex] so, when you simplify it according to the characteristics of a and b, you would end up in the similar form of the equation givenwhere a represents half the length of the major axis and b represents half the length of the minor axis. The easiest method to identify, look at whether both the variables are squared, and also the coefficient of x and y should be positive but different.Anita's mother hosted a party. The table shows the costs. Use associative property to write two equivalent expressions that could be used to find the total amount spent. TABLE ITEM:cake COST: $12 ITEM: hot dogs and hamburgers COST:$24 ITEM:drinks COST: $6
Using the associative property of addition, two equivalent expressions to find the total cost are: (1) ($12 + $24) + $6 and (2) $12 + ($24 + $6). Both expressions will yield the same result due to the associative property.
The question involves using the associative property of addition to find equivalent expressions for the total cost of items bought for Anita's mother's party. The total costs given are for three items: cake ($12), hot dogs and hamburgers ($24), and drinks ($6). To demonstrate the associative property, we can group the costs in different ways before adding them.
The first expression could group the cost of the cake and hot dogs and hamburgers together, then add the cost of drinks: ($12 + $24) + $6.The second expression could group the cost of hot dogs and hamburgers and drinks together, then add the cost of the cake: $12 + ($24 + $6).Both expressions will yield the same total cost when calculated, which shows the associative property of addition in action.
10
2
5
2
6
7
9
2
3
Calculate the mean,
median and mode of the
following set of numbers.
Answer:
Step-by-step explanation:
Mean= 10+2+5+2+6+7+9+2+3/9
=46/9 = 5.11
Arrange in Ascending order:
2,2,2,3,5,6,7,9,10
Mode = 2 ( that occurs most number of times)
Median = 5 ( median is the middle term)
If b equals 8 and h equals 6 what does bh/2 equal
Answer:
if b = 8
and h = 6
and if im understanding correctly it is asking B*H/2 that would be 8*6 which is 48 then divided by 2 would be 24
Step-by-step explanation:
Final answer:
Using the formula A = bh/2 for the area of a triangle, with b as 8 and h as 6, we find that the area A equals 24 square units.
Explanation:
To solve the given problem, we need to apply the formula for the area of a triangle, which is A = bh/2, where 'b' is the base of the triangle and 'h' is the height. Given that b equals 8 and h equals 6, we can substitute these values into the formula to find the area.
A = bh/2
A = (8)(6)/2
A = 48/2
A = 24
Therefore, the area of the triangle when b is 8 and h is 6 is 24 square units.
Which equation represents the line that passes through points (0,6) and (2,0)?
A) y= -1/3x + 2
B) y= -1/3x + 6
C) y= -3x +2
D) y= -3x + 6
( yes, im that dumb, sorry )
Answer:
D) y= -3x + 6
Step-by-step explanation:
y = mx + p
m = slope = (0-6)/(2-0) = -6/2 = -3
p = y-intercept = 6 ,because the line passes through points (0,6)
Answer:
D) y= -3x + 6
Julia is allowed to watch no more than 5 hours of television a week. So far this week, she has watched 1.5 hours. Write and solve an inequality to show how many hours of television Julia can still watch this week.
Answer:
The inequality to show how many hours of television Julia can still watch this week can be given as:
⇒ [tex]x+1.5\leq 5[/tex]
where [tex]x[/tex] represents he number of hours of television that Julia can still watch this week
On solving for [tex]x[/tex], we get
[tex]x\leq3.5[/tex]
Thus, Julia can still watch no more than 3.5 hours of television this week.
Step-by-step explanation:
Given:
Julia is allowed to watch television no more than 5 hours a week.
She has already watched 1.5 hours
To write and solve an inequality to show how many hours of television Julia can still watch this week.
Solution:
Let the number of hours of television that Julia can still watch this week be = [tex]x[/tex]
Number of hours already watched = 1.5
Total number of hours of watching television this week would be given as:
⇒ [tex]x+1.5[/tex]
It is given that Julia is allowed to watch no more than 5 hours of television in a week.
Thus, the inequality can be given as:
⇒ [tex]x+1.5\leq 5[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by 1.5
[tex]x+1.5-1.5\leq 5-1.5[/tex]
[tex]x\leq3.5[/tex]
Thus, Julia can still watch no more than 3.5 hours of television this week.
The equation v=-2000+20000 describes the value in dollars of a certain model of car after it is t years old. If a car is worth $10,000, substitute 10,000 into the equation to find the age of the car.
I'm assuming the equation is:
v = -2000t + 20,000 because the value of a car decreases with time
v = worth of the car
t = number of years
Since you know the value of v = 10,000, substitute or plug in 10,000 for v in order to find t
v = -2000t + 20,000 Substitute 10,000 into v [To find t, you need to get the variable by itself to one side of the equation.]
10,000 = -2000t + 20,000 Subtract 20,000 on both sides
-10,000 = -2000t Divide -2000 on both sides to get t by itself [negative divided by a negative results in a positive]
5 = t
A rectangular yard measuring 35ft and 45ft is bordered (and surrounded) by a fence. Inside, a walk that is 4ft wide goes all the way along the fence find the area of this walk
First, calculate the area of the rectangular yard.
A = L x W where A equals area, L equals length, and W equals width.
According to your stated problem:
A = 31 x 49
A = 1519 square feet <-------Area of Rectangular yard.
An outfielder throws a ball vertically upward with a velocity of 30 meters per second. Its distance from the ground after t seconds is approximately equal to 30t - 5t² meters. How many seconds will it take the ball to reach its maximum distance from the ground?
15
6
1.5
3
Answer:
12
Step-by-step explanation:
I calbvkjy
The answer is 3 :)
Have a nice day!
A fraction f multiplied by 4 equals 1/2
Answer:
f = 1/8
Step-by-step explanation:
f x 4 = 1/2
f = 1/8 ( multiplying both sides by 1/4 )
The fraction f that gives 1/2 when multiplied by 4 is 1/8.
That is, f = 1/8
A fraction f multiplied by 4 equals 1/2
This can be written mathematically as:
[tex]f \times 4 = \frac{1}{2}[/tex]
This can be re-written as:
[tex]4f=\frac{1}{2}[/tex]
Divide both sides by 4
[tex]\frac{4f}{4} =\frac{1}{2} \div 4\\\\f= \frac{1}{2} \times \frac{1}{4}\\\\f=\frac{1}{8}[/tex]
The fraction f that gives 1/2 when multiplied by 4 is 1/8.
That is, f = 1/8
Learn more here: https://brainly.com/question/14513877
What is the value of x?
Enter your answer in the box.
°
Answer:
x = 111
Step-by-step explanation:
Sum of interior angles= (n-2)*180= (7-2)*180 = 5*180 = 900
x + 139 + 121 + 125 + 126 + 158 + 120 = 900
x + 789 = 900
x = 900 - 789 = 111
x = 111
Fast forward a few years...and suppose you need to get your car repaired. You see the ads above. Your father, who knows a bit about cars, says it will probably take 3 hours to fix your car. How do you determine where you should take your car to get it repaired?1. Write an equation for each repair shop to represent the total cost of the car repair as a function of the number of hours worked.Let x = number of hours worked Let y = total cost to you
Mikes repair shop $100 service charge plus $65 per hour Amys auto repair $40 service charge plus $80 per hour write an equation for each repair shop to represent the total cost of a car repair as a function of the number of hours worked let C = total cost to you let h = number of hours worked. Suppose you need to get the dent in your car repaired you see the ads above in the newspaper your father who knows a bit about cars said it would take no more than 3 hours for the repair person to fix your car how do you determine where you should take your car to get it repaired
-Mike Cost:: M(3) = 100 +65*3 = $295
-Amy Cost:: A(3) = 40 + 80*3 = $280
------------------------------------------------------------
-Mike charges 100 dollars service charge plus 65 dollars per hour.
-Amy charges 40 dollars service charge plus 80 dollars per hour.
-The cost to repair from mike is 100 + 65 * x.
-The cost to repair from amy is 40 + 80 * x.
------------------------------------------------------------
Let x = 3 and you get:
The cost to repair from mike is 100 + 65 * 3 = 295 dollars.
The cost to repaid from amy is 40 + 80 * 3 = 280 dollars.
As long as the time to repair is 3 hours or less, the cost to repair will be cheaper from Amy.
Pls help me x+4=__+24 I don’t know the answer pls I really need this 200 points I give you
Answer:
x-20
Step-by-step explanation:
x+4=y+24
x=y+24-4
x=y+20
y=x-20
please help!! Kurt's car gets 23 miles to a gallon of gasoline. He filled up his car's gas tank with g gallons. Write an expression that shows how far Kurt can drive on a tank of gasoline.
Expression that shows distance Kurt can drive on a tank of gasoline is 23g miles
Solution:
Given that, Kurt's car gets 23 miles to a gallon of gasoline
He filled up his car's gas tank with g gallons
To find: Expression that shows distance Kurt can drive on a tank of gasoline
From given,
1 gallon of gasoline = 23 miles
Kurt fills up his car with "g" gallons
Therefore, for "g" gallons,
[tex]1 \times g \text{ gallons of gasoline } = 23 \times g \text{ miles }\\\\g \text{ gallons of gasoline } = 23g \text{ miles }[/tex]
Thus the distance Kurt can cover with "g" gallons is:
[tex]distance = 23g\ miles[/tex]
Thus with "g" gallons of gasoline, Kurt can drive 23g miles
how do u compare rate of change and slope help plz
Step-by-step explanation:
The slope is described by the the initial and final value of one quantity over the difference between the initial and final of the other
Rate: for points on a Cartesian plane,(x1, y1) and (x2, y2)
the slope, m= (y2 - y1)/(x2 - x1)
The rate of change on the other hand is mostly refers to how much a quantity is changing with time i.e the rate of change of y from y1 to y2 can be expressed as
rate = (y2 - y1)/(t2 - t1)...where t1 and t2 are the various time in y1 and y2 respectively...
J. Reexamine the sequence 20, 14, 8, 2, ... from the problem
term of the sequence.
-- from the problem above. Write an equation for the nth
Answer:
The n th of the given sequence is [tex]t_{n} = 26-6 n[/tex]
Step-by-step explanation:
Step 1 :-
Given sequence is 20,14,8,2,.......this sequence in arithmetic progression but this sequence is decreasing sequence.
given first term is 20 and difference is[tex]d = second term- first term = 14-20=-6[/tex]
now the nth term of given sequence is
by using formula [tex]t_{n}=a+(n-1)d[/tex]
[tex]t_{n}= 20+(n-1)(-6)[/tex]
[tex]t_{n}= 20-6 n+6[/tex]
final answer:-
[tex]t_{n} = 26-6 n[/tex]
verification:-
[tex]t_{n} = 26-6 n[/tex]
put n=1 we get first term is 20
put n=2 we get second term is 14
put n=3 we get third term is 8
put n=4 we get fourth term is 2
so the n th term of sequence is
[tex]t_{n} = 26-6 n[/tex]