Answer:
The value of x is equal to 1, written as x = 1.
General Formulas and Concepts:
Algebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTerms/Coefficients
Functions
Function NotationStep-by-step explanation:
Step 1: Define
g(x) = 5x + 4
g(x) = 9
Step 2: Solve for x
Substitute in function value: 9 = 5x + 4[Subtraction Property of Equality] Subtract 4 on both sides: 5 = 5x[Division Property of Equality] Divide 5 on both sides: 1 = xRewrite: x = 1∴ when the function g(x) equals 9, the value of x that makes the function true would be x = 1.
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Topic: Algebra I
In 1992 the average family income was about 42000, and in 2002 it was about 56256. Let x = 0 represent 1992, x = 1 represent 1993, and so on. Find values for a and b (rounded to one decimal place if necessary) so that f ( x ) = a x + b models the data a = b = What was the average family income in 1997? $
Step-by-step explanation:
Given the function that models the income of a family as g(X) = ax+b
at x = 0, g(x) = 42000, the function becomes;
g(X) = ax+b
42000 = a(0)+b
42000 = 0+b
b = 42000
at x = 1, g(x) = 56256
56256 = a(1) + b
56256 = a+b
a = 56256 -b
a = 56256 - 42000
a = 14,256
To get the average family income in 1997, wee need to calculate g(x) at when x = 5, since the number of years between 1992 and 1997 is 5years.
g(x) = ax+b
g(5) = 14256(5) + 42000
g(5) = 71,280+42000
g(5) = 113,280
Hence the average family income in 1997 is 113,280
Make d the subject of the formula h = d/3 + 2
Sabrina’s schedule is listed below. Each of her teachers only teaches one subject. Is this an example of a function? Why or Why not?
Period
Class
1st
Band
2nd
PE
3rd
Math
4th
SS
5th
ELA
6th
Science
The equation of a circle in general form is x2+y2+20x+12y+15=0 .
What is the equation of the circle in standard form?
(x+10)2+(y+6)2=121
(x+10)2+(y+6)2=225
(x+20)2+(y+12)2=121
(x+20)2+(y+12)2=225
Answer:
[tex](x+10)^2+(y+6)^2=121[/tex]
Step-by-step explanation:
The standard form of a circle's equation is
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Where (h,k) is the center and r is the radius of the circle.
The equation is given in general form, we need to convert it to the standard form. This can be done by completing squares.
The equation is:
[tex]x^2+y^2+20x+12y+15=0[/tex]
Rearrange x's and y's separate:
[tex]x^2+20x+y^2+12y=-15[/tex]
We have also subtracted 15. Now to complete squares, recall the formula:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
The first two terms are equivalent to the first two terms of the above formula. It's clear that the second term is 2ab=20x. Solving for b:
b=10. Thus, to complete the square, we add 100 to the equation.
The third and fourth terms can also be used to complete the squares for y, knowing that 2ab=12y. In this case:
b=6. To complete this square, we add 36. The equation is now:
[tex](x^2+20x+100)+(y^2+12y+36)=-15+100+36=121[/tex]
Operating and simplifying, knowing that 121=11^2:
[tex]\boxed{\mathbf{(x+10)^2+(y+6)^2=121}}[/tex]
This corresponds to the first choice
Evaluate -18 + x(-6)
When x = -9
The answer to your question is 36
-18 + x(-6)
Substitute x with -9
-18 + (-9) (-6)
Then you get 36
Hey there!
-18 + x(-6)
= -18 + (-9)(-6)
= -18 - 9(-6)
= -18 - (-54)
= -18 + 54
= 36
Therefore, your answer is: 36
REMEMBER!
• Negative & negative = positive
• Positive & positive = positive
• Negative & positive = negative
• Positive & negative = negative
• Negatives are smaller than 0
• Positives are bigger than 0
• Negatives are to the LEFT of 0
• Positives are to the RIGHT of 0
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Solve the following system of equations:
2x + 4y = 18
-3x + 2 = y
A.(-1, 4)
B.(1, 4)
C.(-1, 5)
D.(1, -1)
Answer:
Option C
Step-by-step explanation:
Given the following question:
[tex]2x+4y=18[/tex]
[tex]-3x+2=y[/tex]
To find the answer we need to find the values of each of the variables by solving one equation at a time, and then substitute those answers into each equation in till we have our answers.
[tex]2x+4y=18[/tex]
[tex]-3x+2=y[/tex]
[tex]y-y=0[/tex]
[tex]-3x+2+ -y=0[/tex]
[tex]2-2=0[/tex]
[tex]-3x+-y=0+-2[/tex]
[tex]-3x+3x=0[/tex]
[tex]-y=3x-2[/tex]
[tex]-y\div-1=y[/tex]
[tex]3x+2\div-1=-3x+2[/tex]
[tex]y=-3x+2[/tex]
Substitute y for -3x + 2:
[tex]2x+4y=18[/tex]
[tex]y=-3x+2[/tex]
[tex]2x+4(-3x+2)=18[/tex]
[tex]2x+4(-3x+2)=18=-10x+8=18[/tex]
[tex]-10x+8=18[/tex]
[tex]8-8=0[/tex]
[tex]18-8=10[/tex]
[tex]-10x=10[/tex]
[tex]-10x\div10=x[/tex]
[tex]10\div-10=-1[/tex]
[tex]x=-1[/tex]
Substitute x for -1:
[tex]y=-3x+2[/tex]
[tex]x=-1[/tex]
[tex]y=-3(-1)+2[/tex]
[tex]-3\times-1=3[/tex]
[tex]y=3+2[/tex]
[tex]3+2=5[/tex]
[tex]y=5[/tex]
[tex]x=-1[/tex]
[tex]y=5[/tex]
Your answer is "(-1, 5)" or option C.
Hope this helps.
Please help me
Jjsjs
Answer:
1-70mm
2-77m
Step-by-step explanation:
so to do this, take the first one as an exmple, to find the unknown line on the ground I added 15+8 to find the total on the bottom
still on the first question, to find the unknown number on the side, I subtracted 12-7
I hope this makes any sense, but I dont know
whats important is that you have the answers.
Mr. Chen purchased a board game for $14 and 6 puzzles. Each puzzle cost the same amount. The total cost was $86. How much did each puzzle cost?
Answer:
$12
Step-by-step explanation:
$86-$14 = $72 that you have left for the 6 puzzles
72÷6 = 12
(7, -1) 2. What is the slope of a line that is perpendicular to the line joining point A (9, 9)? and point B
Answer:
-1/5Step-by-step explanation:
Given the point A (9, 9) and B(7, -1)
The slope of the line AB is expressed as:
slope = Δy/Δx
slope = y2-y1/x2-x1
slope = -1-9/7-9
slope = -10/-2
slope = 5
For two lines to be perpendicular, the product of their slope must be -1
mM = -1
M is the slope of the line perpendicular to AB
Substitute m = 5 into the equation
5M = -1
M = -1/5
Hence the slope of a line that is perpendicular to the line joining point A and B is -1/5
Can you please answer this question I need to submit in 30 min please HURRY ASAP PLEASE NEED HELP PLEASE !!!!!!!!!!!
Answer:
The answer is "21"
Step-by-step explanation:
mn + 3r
m = 5
n = 4
r = 1/3
Now just substitute the values given in the question into the equation
5(4) + 3(1/3)
Multiply 5 and 4 to get 20
20 + 3(1/3)
3(1/3) cancels out and becomes 1
20 + 1
Add 20 and 1
21
So "21" is your answer
. choose the model that represents the division sentence . a rectangle divided into six parts with one part shaded.becomesa rectangle divided into twelve parts with six part shaded. a rectangle divided into six parts with one part shaded.becomesa rectangle divided into twelve parts with two part shaded. a rectangle divided into six parts with one part shaded.becomesa rectangle divided into twelve parts with four part shaded. a rectangle divided into six parts with one part shaded.becomesa rectangle divided into twelve parts with one part shaded.
Answer:
B
Step-by-step explanation:
How many solutions does 23y+50+27y=50y+50 have
23y + 50 + 27y = 50y + 50 original equation
50y + 50 = 50y + 50 combine like terms
Because both sides of the equation are the same, meaning they are equal, the equation has INFINITELY MANY SOLUTIONS (y can be any number) .
find the LCM of 3 and 12
Answer:
12
Step-by-step explanation:
Seats in a movie theater are numbered 1-500, and the manager is handing out snacks during the movie. Every person whose seat is a multiple of 4 gets Twizzlers. Every person whose seat is a multiple of 7 gets nachos, and every person in a seat that is a multiple of 10 gets popcorn. The person in which seat number is the first to get all 3 treats?
Answer:
Seat number 140 gets all three treats
Step-by-step explanation:
Given
[tex]Twizzlers = Multiples\ of\ 4[/tex]
[tex]Nachos = Multiples\ of\ 7[/tex]
[tex]Popcorn = Multiples\ of\ 10[/tex]
Required
Determine first person to get all kinds of treats
To do this, we simply need to determine the LCM of the given multiples:
[tex]4 = 1 * 2 * 2[/tex]
[tex]7 = 1 * 7[/tex]
[tex]10 = 1 * 2 * 5[/tex]
[tex]L.C.M = 1 * 2 * 2 * 7 * 5[/tex]
[tex]L.C.M = 140[/tex]
Seat number 140 gets all three treats
Can someone help me with this question
Answer:
∠ CDE = 134°
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 6 , then
sum = 180° × 4 = 720°
let ∠ BCD = x then ∠ CDE = 2x
sum the angles and equate to 720
121 + 144 + 129 + 125 + x + 2x = 720 , that is
519 + 3x = 720 ( subtract 519 from both sides )
3x = 201 ( divide both sides by 3 )
x = 67
Then
∠ CDE = 2x = 2 × 67 = 134°
want money. answer this.
Susan pushes a box up an inclined plane doing 50 Joules of work. The output work was calculated to be 25 loules. Find the efficiency of this inclined plane
A) 25%
B) 50%
C)100%
D) 200%
the height of a cone shaped building is 50 ft, and the radius of its base is 20 ft. find the buildings slant height
Answer:
1,000
Step-by-step explanation:
hello people ~
factorise: x² + 4x - 77
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer}}[/tex]
Let's solve ~ ☂
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 4x - 77[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 11x - 7x - 77[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{} (x + 11) -7(x + 11)[/tex]
[tex]\qquad \sf \dashrightarrow \: {}^{} (x + 11)(x - 7)[/tex]
Answer:
x = 7
x = -11
Step-by-step explanation:
x² + 4x = 77
Complete the square to make it a square of a binomial
x² + 4x + 4 = 77 + 4
(x+2)² = 81
Square root both sides (two solutions)
x + 2 = 9
x = 7
x + 2 = -9
x = -11
Hope this helps :)
Have a nice day!
Which value is NOT equivalent to the other values?
Answer:
1.5
Step-by-step explanation:
All the other values are .15, 1.5 does not equal .15, so it is not equivalent.
Hopefully this helps- let me know if you have any questions!
Answer:
1.5
Step-by-step explanation:
3/20 =15% =0.15
1.5 is not equivalent to the other values
The value of y is _ more than the value of x
Answer:
The answer is x = y - 30
Step-by-step explanation:
y=31 and x=1, therefore y-30=x
what is the possible solution to the quadratic equation 2x^2+10=28
Answer:
x=3
Step-by-step explanation:
plug it into the equation and see if it's correct
7 of 10
Sara was thinking of a number. Sara doubles it, then adds 7 to get an answer of 92.9. What
was the original number?
Answer:
42.95
Step-by-step explanation:
We just reverse the steps. So we take 92.9 and subtract by 7 to get 85.9. Then we divide that number by 2. So we get 42.95. To check our work, we can use this number and follow the steps Sara did. So 42.95*2=85.9+7=92.9
The original number that Sara was thinking of is 42.95.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
Let's represent the original number "x".
According to the question, we know that:
x × 2 + 7 = 92.9
To determine the original number, we'll want to undo the operations that were done to it.
First, we'll subtract 7 from both sides to undo the addition:
x × 2 = 92.9 - 7
x × 2 = 85.9
Then, we'll divide both sides by 2 to undo the doubling:
x = 85.9 / 2
x = 42.95
Therefore, the original number that she was thinking of is 42.95.
Learn more about the number system here:
https://brainly.com/question/21751836
#SPJ2
Which expression is equivalent to -4.6 + (-0.4) + (-7.2)?
A. – 4.6 - (0.4 + 7.2)
B. (4.6 + 0.4 + 7.2)
C. – (4.6 – 0.4) + ( -7.2)
D. (4.6 + 0.4) + (-7.2)
Please help!!!
- Jimmy is 440 miles from home, but he is driving back at a speed of 60 mph. Which equation
represents this scenario where d represents the distance from home and t represents the time in
hours?
440d=60t it would take jimmy 7.33 hours to get home if he drove at a constant rate of 60 Miles Per Hour
MEKS is a rectangle. Find mEKM if mEMK =30
Which expression is equivalent to 6-(8)
-6+8
-6+(8)
6+(8)
6+8
Answer:
-6+8
Step-by-step explanation:
-6+8=6-(8)
-2=-2
Hoped it helped :)
5 40/60 simpified no decimals
Answer:
5 2/3
Hope this helps! Please mark Brainliest!
Answer:
17/3
Hope this helps!!! :)
Hey guys please help
Please help me 50 points and brainliest for all questions