Answer: (x−3)(x+7)
=(x+−3)(x+7)
=(x)(x)+(x)(7)+(−3)(x)+(−3)(7)
=x^2+7x−3x−21
=x^2+4x−21
The product of (x-3) and (x+7) is x² + 4x - 21
The product of (x - 3) and (x + 7) can be found as follows:
(x - 3)(x + 7)
open the bracket by multiplying
Therefore,
x(x) +x(7) - 3(x) - 3(7)
x² + 7x - 3x - 21
combine like terms
x² + 4x - 21
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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]
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
Find the value of x. Round your answer to the nearest tenth.
A.) 52.6
B.) 52.9
C.) 6.2
D.) 6.5
Answer:
Option A: 12.5
Step-by-step explanation:
We use trigonometric ratios on this right angled triangle.
[tex]$ cos \hspace{1mm} \theta = \frac{adj}{hyp} $[/tex]
we get:
[tex]$ cos \hspace{1mm} 28^{\circ} = \frac{11}{x} $[/tex]
Also cos 28° = 0.88
Therefore, x = [tex]$ \frac{11}{0.88} $[/tex]
[tex]$ = \frac{100}{8} =\textbf{12.5} $[/tex]
OPTION A is the answer.
What’s the slope of y=-7x+5
Answer:
m=-7
Step-by-step explanation:
The slope intercept form is y=mx+b.
So, the variable that represents slope is x.
If your plug your equation in, -7 would be the slope.
Find the two missing terms of the sequence and determine if the sequence is arithmetic, geometric, or neither.
3, 1, -1, -3, __, __
A video game system costs $185 and one video game costs $14.95. You can spend no more than $280 on the system and games. set up and solve an inequality to calculate the maximum number of games you can purchase
Answer:
Therefore the maximum number of video games that we can purchase
is 6.
Step-by-step explanation:
i) Let us say the number of video game system we can buy that costs $185
is x and the number of video games of cost $14.95 is y.
ii) The total amount we can spend on the purchase of the video game
system is $280.
iii) Now with the amount of $280 mentioned in ii) we can see that the
number of game systems that can be bought is 1.
Therefore x = 1.
Therefore the equation we can write to equate the number of video
games and video game system is given by $185 + $14.95 × y ≤ 280
Therefore 14.95 × y ≤ 280 - 185 = 95
Therefore y ≤ 95 ÷ 14.95 = 6.355
Therefore the maximum number of video games that we can purchase
is 6.
what is n/8=11/5 solve for n
Answer:
n = 17.6
Step-by-step explanation:
Cross-multiply and you have:
5 * n = 11 * 8
5n = 88
n = 88/5 = 17.6
M - 2 3/4 = 6 1/2 what does the m equal
Answer:
Step-by-step explanation:
6 1/2 + 2 3/4=M
M=9 1/4
What is the values of x and y?
(5x) + (9y)
Answer:
x=5 y=9
Step-by-step explanation:
hope this helps :) have a nice day :) :) :)
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.
the graph of f(x)=|x| is reflected across the x-axis, moved 2 units to the right and 7 units down. What is the function?
The transformed function after reflecting f(x)=|x| across the x-axis, moving it 2 units to the right, and 7 units down is f(x)=-|x-2|-7.
Explanation:The original function is f(x)=|x|.
When the graph of the function is reflected across the x-axis, it changes the sign of the output or y-coordinate.
Thus, the absolute value function becomes f(x)=-|x|.
When this function is moved 2 units to the right, it results in a shift in the coordinate of x within the function, thus becoming f(x)=-|x-2|.
Lastly, when the function is moved 7 units down, 7 is subtracted from the function, resulting in the final equation of f(x)=-|x-2|-7.
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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
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
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.
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.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
What is the length of the radius, r?
Answer:
18 cm
Step-by-step explanation:
The circumference (C) of a circle is calculated as
C = 2πr ← r is the radius
Given
C = 36π, then
2πr = 36π ( divide both sides by 2π )
r = [tex]\frac{36\pi }{2\pi }[/tex] = 18
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...
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.
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)
Solve by factoring:
4x² - 8x=0
Answer:
Step-by-step explanation:
4x² - 8x= 0
4x(x -2) = 0
: 4x = 0 or x - 2 = 0
4x = 0
Dividing by 4
x = 0/4
x = 0
And
x - 2 = 0
x = 2
PLEASEEE HELPPP ASAPP! THANK YOU LOTS!! <3 (7TH GRADE MATH)
btw January: -5/8 and July: 6 5/8
Answer:
Therefore the change in water level over the course of 9 months is a drop in level of 3.4 cm (= -3.4 cm)
Step-by-step explanation:
i) change in water level over the course of 9 months =
[tex]- \frac{5}{8} - 0.4 - 0.4 - 6 - 2.9 + 3.2 + 6\frac{5}{8} - 3.2 + 0.3[/tex]
= [tex]-0.625 - 0.4 - 0.4 - 6 - 2.9 + 3.2 + 6.625 - 3.2 + 0.3[/tex]
= -3.4
Therefore the change in water level over the course of 9 months is a drop in level of 3.4 cm (= - 3.4 cm)
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]
What is an equation of the line that passes through the points (7,-6)(3,-6)
Answer:
Step-by-step explanation:
Since both points have their y coordinate as -6, and this is a line,
Then your answer would be y = -6
what is the slope of (1,2) and (4,11)
Answer:
slope = 3
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (4, 11)
m = [tex]\frac{11-2}{4-1}[/tex] = [tex]\frac{9}{3}[/tex] = 3
Answer:
3
Step-by-step explanation:
y2 - y1/ X2 - X1
11 - 2/ 4-1
9/3
= 3
Five times a number , subtracted from ten , is triple the number . Find the number.
The value of the variable number x will be 1.25.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Let x be the number. Then the Five times a number is written as 5x. Then the expression will be
⇒ 10 - 5x
The triple number is written as 3x. Then the equation is given below.
10 - 5x = 3x
Simplify the equation, then we have
10 = 3x + 5x
10 = 8x
x = 10 / 8
x = 1.25
The value of the variable number x will be 1.25.
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Final answer:
The algebraic equation set up from the problem 10 - 5x = 3x leads us to find that x = 1.25. Thus, the number in question is 1.25.
Explanation:
The question describes an algebraic problem where we are trying to find a particular number. According to the problem, five times this number, when subtracted from ten, equals three times the number. To find the number, we set up the equation based on the given information:
10 - 5x = 3x
Where x is the number we are trying to find. Now, we will solve for x:
Add 5x to both sides of the equation to get all x terms on one side:
10 = 3x + 5x
Combine like terms on the right side:
10 = 8x
Divide both sides by 8 to solve for x:
x = 10/8
Simplify the fraction:
x = 1.25
So, the number we were seeking is 1.25.
F(x)=2x+6
G(x)=-5x-9
Find the product of f and g.
A.-10x^2-54
B.-10x^2-48x-54
C.-10x^2-12x-54
D.-10x^2+48x-54
Answer:
Step-by-step explanation:
F(x) = 2x + 6
G(x) = - 5x - 9
product of F and G .....the product is the result of multiplication
(2x + 6)(-5x - 9) =
-10x^2 - 18x - 30x - 54 =
-10x^2 - 48x - 54 <====
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!
Hank has eight action figures this is 12 less than the quotient of 60 and the number figures palo has
Answer:
6
Step-by-step explanation:
hold up hold up so you are saying 60 less than what quotient I'm guessing 68 divided by 12 so the answer would be 6