A and B are postive integers such that 1/a + 1/b +1/ab = 1. Find ab
Answer: ab =6
have:
[tex]\frac{1}{a}+\frac{1}{b}+\frac{1}{ab}=1\\\\=>\frac{b}{ab}+\frac{a}{ab}+\frac{1}{ab}=1\\\\<=>\frac{a+b+1}{ab}=1[/tex]
=> a + b + 1 = ab
⇔ a + b + 1 - ab = 0
⇔ b - 1 - a(b - 1) + 2 = 0
⇔ (b - 1)(1 - a) = -2
because a and b are postive integers => (b - 1) and (1 - a) also are integers
=> (b - 1) ∈ {-1; 1; 2; -2;}
(1 -a) ∈ {-1; 1; 2; -2;}
because (b -1).(1-a) = -2 => we have the table:
b - 1 -1 1 2 -2
1 - a 2 -2 -1 1
a -1 3 2 0
b 0 2 3 -1
a.b 0 6 6 0
because a and b are postive integers
=> (a;b) = (3;2) or (a;b) = (2;3)
=> ab = 6
Step-by-step explanation:
HELP ASAP! Relations and Functions!!! Giving brainliest!!!
Answer:
Step-by-step explanation:
Neither are a function because they do not pass the vertical line test.
Please answer correctly !!!!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!
Answer:
106°
Step-by-step explanation:
they are parallel to each other
Answer: 106
Step-by-step explanation:
What is the solution set of the following equation?
-8x + x + 15 = -7x + 12
Answer:
-3 is the solution set of the following equation
N-(-7)= 12 how do you rewrite
Answer:
N + 7 = 12
Step-by-step explanation:
When you have a number minus a negative number, it's the same as addition.
Answer:
N=4
Step-by-step explanation:
or N- x -7=12 because
( ) means multiplication
please solve this math problem look at the screenshot
Answer:
D
Step-by-step explanation:
A graph represents a function of x when it passes the vertical line test. That is, no x values map out to more than 1 y value.
Therefore, D is the only function of x.
What is the slope of a line that is perpendicular to the graph of y = 4/5x+9?
Answer:
m = -5/4
General Formulas and Concepts:
Algebra I
The slope of the perpendicular line is the negative reciprocal of the original slope.
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Slope-Intercept Form (Original): y = 4/5x + 9
Step 2: Break Original Function
Slope m = 4/5
y-intercept b = 9
Step 3: Find slope of perpendicular line
Take the negative reciprocal.
Perpendicular Slope m = -5/4
Which expression is equivalent to (5x - 4)2?
Answer:
Step-by-step explanation:
the answer is 25x^2-40x+16
25x^2-40x+16 is equivalent to (5x - 4)^2.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
(5x - 4)^2
we know,
(a-b)^2= a^2-2ab+b^2
by using this, we get,
(5x - 4)^2
=5x*5x-2*5x*4+4*4
=25x^2-40x+16.
Hence, 25x^2-40x+16 is equivalent to (5x - 4)^2.
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Molly is getting an early start on holiday shopping! She has $55.00 to spend on gifts. She first buys her mom a sweater for 17.50. She then found matching bracelets for her friends that cost $7.50 each. How many bracelets did she buy?
a) Write a let statement below to define your variable(s): *
b) Set up an equation using the variable you defined in (a): *
c) Solve your equation & Check. How many bracelets did Molly buy? JUST TYPE THE NUMBER. EXAMPLE: IF she bough 17 bracelets JUST TYPE "17" *
d) Upload a picture of your SOLUTION & CHECK. *
Plz help me anyone oi need help
Answer:
5
Step-by-step explanation:
55$-17.50=37.5
37.5/7.5=5
The radio hot 97 plays despacito ft Justin beiber every 5 minutes. Another station Z 100 plays despacito every 7 minutes. Both stations at 3:00 pm and time will it be when despacito at the same time
Answer:
The next time they would play despacito on both stations is after 35 minutes.
Hence, 3:00pm + 35
= 3:35 pm
Step-by-step explanation:
The radio hot 97 plays despacito ft Justin beiber every 5 minutes. Another station Z 100 plays despacito every 7 minutes. Both stations at start 3:00 pm and what time will it be when despacito at the same time ?
Find and list multiples of time that despacito plays Radio hot 97 and Station Z 100.
Hence, we find the Multiples of 5 minutes and 7 minutes until the first common multiple is found. This is the lowest common multiple.
Multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40, 45
Multiples of 7:
7, 14, 21, 28, 35, 42, 49
Therefore, the first common multiple is found which is the lowest common multiple is 35
LCM(5, 7) = 35
The next time they would play despacito on both stations is after 35 minutes.
Hence, 3:00pm + 35
= 3:35 pm
Answer:
of course they play despacito that much lol
Step-by-step explanation:
Find the zero of the function f(x) = 5x-3
I need help with #18 & 20
Please explain so I understand
1) Which of the following is NOT a property of reflection?
A)distance between points is preserved (stays the same)
B)angle measure is preserved (stays the same)
C)pre-image and image are congruent
D)orientation is preserved (stays the same)
Answer:
orientation is preserved (stays the same)
Step-by-step explanation:
Could an angle be complementary to itself? If so, what would its measure be
Answer:
I think it would be 45 degrees
Answer:
A complementary angle would be two different angles that add up to 90 degrees. If you have an angle of 60 degrees, the other side would have to be 30 to be complementary.
Maliah goes to an electronics store. Let y represent the price of a laptop and let z represent the price of a television. The equation
y=32 + 12 relates the prices.
Answer:
hi
Step-by-step explanation:
Please help asap
25m^2+30m-30m-36
Answer:
(5m+6) (5m-6)
Step-by-step explanation:
That's how you factor it since +30 and -30 cancel out
Vicky records the low temperature for three consecutive days. Between the first and second days the temperature increased 6 degrees. Between the second and third days the temperature decreased 3 degrees. On the third day the low temperature was –6º. What was the low temperature on the first day?
Answer:
3
Step-by-step explanation:
-6+6=0
Plus the 3
Your answer is 3
Answer:
-3 or 3
Step-by-step explanation:
3(7 - 2x) - 19 - 5(4- x) = 3(8 - 6x) - 9x + 5(4- x)
Answer:
x=2
Step-by-step explanation:
3(7-2x)-19-5(4-x) = 3(8-6x)-9x+5(4-x)
or, 21-6x-19-20+5x = 24-18x-9x+20-5x
or, 21-19-20-6x+5x = 24+20-18x-9x-5x
or, -18-x = 44-32x
or, -x+32x = 44+18
or, 31x = 62
or, x = 62/31
or, x = 2
Answer:
Step-by-step explanation:
21-6x-19-20+5x=24-18x-9x+20-5x distribution property
-x-18=44-32x common factors
31x-18=44 add 32x to both sides
31x=62 add 18 to both sides
x=2 divide 31 to both sides(equals 2) so x equals 2
Solve for x: x+ 1/6 = 5/12
Answer:
x=3/12 or 1/4
Step-by-step explanation:
x + 1/6 = 5/12
x + 2/12 = 5/12
x = 3/12
converts to 1/4
Answer:
x= 1/4
Step-by-step explanation:
5/12- 1/6 = 1/4
Jack has $65 to spend on art supplies. He needs to buy an easel that costs $18. He also wants to buy some canvases that cost $11 each
Which of the following inequalities represents the amount of money Jack can spend if he buys n canvases?
A:65 >(line underneath sign)18 + 11n
B:65 > 18 + 11n
С:65 < (line underneath sign) 18 + 11n
D:65 < 18 + 11n
Answer:
C
Step-by-step explanation:
Jack can spend less than or equal to. So C is correct.
The inequality represents the given situation is 65 ≥ 18 + 11n will be correct thus, option (A) is correct.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
As per the given,
Total budget = 65
Total spent = 18 + 11n where n is the number of canvases.
Total spent ≤ total budget
18 + 11n ≤ 65
Hence "The inequality represents the given situation is 65 ≥ 18 + 11n will be correct".
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HELP ME PLEASE, ASAP I JUST NEED X !!
Answer:
x = 6 deg
Step-by-step explanation:
14x + 11 = 16x - 1 (corresponding angles, // lines)
-2x = -12
x = 6
Answer:
C
Step-by-step explanation:
16x - 1 and 4x + 11 are corresponding angles and are congruent, thus
16x - 1 = 14x + 11 ( subtract 14x from both sides )
2x - 1 = 11 ( add 1 to both sides )
2x = 12 ( divide both sides by 2 )
x = 6
Substitute x = 6 into either of the 2 equal angles
Substituting into 14x + 11 , then
14x + 11 = 14(6) + 11 = 84 + 11 = 95° → C
HELP ILL GIVE BRAINLIEST
Answer:
i think its is 1.x 2.x4 3.x9 4.1x-2Step-by-step explanation:
i tride but it will be helpful if you give me brainlits
The Jefferson band is selling baked goods to raise money for their trip. Their goa; is to profit at least $500. Each baked good sells for 2 dollars but costs $0.50 to make. How many baked goods will they have to sell to reach the goal?
Answer:
Break-even point in units= 334
Step-by-step explanation:
Giving the following information:
Desired profit= $500
Selling price= $2
Unitary variable cost= $0.5
To calculate the number of units to be sold, we need to use the following formula:
Break-even point in units= (fixed costs + desired profit) / contribution margin per unit
Break-even point in units= (0 + 500) / (2 - 0.5)
Break-even point in units= 334
What does the graph of the function represent
Use the given information to write the equation of the parabola.
Vertex: [tex](0,0)[/tex]
Focus: [tex](0,-\dfrac{1}{2})[/tex]
Answer:
x² = -2y
Step-by-step explanation:
The focus is p away from the vertex, and so is the directrix.
To find the equation of the parabola, we must first determine if the parabola is horizontal or vertical.
Horizontal parabola [Standard form]: (y – k)² = 4p(x – h)Vertical parabola [Standard form]: (x – h)² = 4p(y – k)If the parabola is vertical, the directrix, and focus will have the same x value but different y value compared to the vertex (h, k). You can also tell if the directrix in in the form y = k – p, and if the focus is in the form (h, k + p).
Likewise, if the parabola is horizontal, the directrix, and focus will have the same y value but different x value compared to the vertex (h,k) . You can also tell if the directrix is in the form x = h – p, and if the focus is in the form (h + p, k).
For this problem, given that the vertex is at the origin (0,0), and that the focus is at the point (0, -½).
You can tell that the x value is the same for the vertex, and focus so this must be a vertical parabola. Because this is a vertical parabola, we can use the form mentioned as earlier (x – h)² = 4p(y – k).
If h = 0, and k = 0, the p value must be the difference between the k of the vertex, and the k of the focus: -½ - 0 → -½.
Now we can just plug in our known information to derive the equation!
h = 0, k = 0, p = -½ → (x - h)² = 4p(y - k) →
(x - 0)² = 4(-½)(y - 0) → x² = -2(y - 0) →
x² = -2y.
Also p = 1/4a, if you are wondering.
So because this is a vertical parabola, x² = -2y is generally the same as y = -1/2x² in standard quadratic form. I just like to think of the horizontal parabola as an inverse quadratic because it is like reflecting over the line y = x.
Answer:
[tex]\boxed {\boxed {\sf x^2=-2y}}[/tex]
Step-by-step explanation:
First, plot the two points. We can see the focus is below the vertex. The result will be a vertical parabola. Since the parabola must contain the focus, it will have to open downward.
From this information, we know that the following equation must be used:
[tex](x-h)^2=-4p(y-k)[/tex]
where (h,k) is the vertex and p is the distance from the focus to the vertex.
Next, find p, the distance between the focus and vertex. We can use the distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The vertex is (0,0) and the focus is (0, -1/2). Therefore:
[tex]x_1=0\\y_1=0\\x_2=0\\y_2= -1/2[/tex]
[tex]d=\sqrt{(0-0)^2+(0--1/2)^2}[/tex]
[tex]d=\sqrt{(0)^2+(0+1/2)^2}[/tex]
[tex]d=\sqrt{0+(1/2)^2}[/tex]
[tex]d=\sqrt{0+1/4}[/tex]
[tex]d=\sqrt{1/4}[/tex]
[tex]d=1/2[/tex]
Now we know the distance and vertex. We can plug the values into the equation.
d=1/2 and (h,k)= (0,0)
[tex](x-0)^2=-4(1/2)(y-0)[/tex]
[tex](x)^2=-2(y)[/tex]
[tex]x^2=-2y[/tex]
The equation of the parabola is x²= -2y
Please help me before I fail... I really need some help <3 please ;-;
Answer:
sin( 61) = x/55
55(sin(61)) = x
48.1 = x
Hope this helps!
Please help!!!
3(x + 8) − 1 = 3x + 4
Answer:No value
Step-by-step explanation:there are no value solutions that make x a solution
Answer:
19
Step-by-step explanation:
3(x+8)-1=3x+3 3x+24-1=3x+4 3x+23=3x+4 3x+19=3x -3x+3x=19
x=19
He Martins have a solar energy system. The system produces 9.1 Kilowatts of energy each hour. The system produces electricity for 5 hours each day. How much energey, in KWh, will the system produce in 100 day?
Answer:
4550 kilowatt
Step-by-step explanation:
Given that :
Amount of energy produced per hour by solar energy system = 9.1 kw per hour
Number of hours for which electricity is produced per day = 5 hours
How much energy will be produced in 100 days
Number of kilowatt of energy produced per day:
Energy produced per hour * number of hours
9.1 kw per hour * 5 hours = 45.5 Kilowatt per day
In 100 days :
Daily energy produced * number of days
45.5 kilowatt * 100 days
4550 kilowatt
Solve for t: t - 2 = 10
Question 3 options:
t = 2
t = 8
t = 10
t = 12
Answer: t=12
Step-by-step explanation:
t-2=10
add 2 to both sides of the equation
t=12
Muriel says she has written a system of two linear equations that has an infinite number of solutions. One of the equations of the system is 3y = 2x – 9. Which could be the other equation?
2y = x – 4.5
y = x – 3
6y = 6x – 27
y = x – 4.5
Answer: B
Step-by-step explanation: If you divide the 3 Y to get Y by itself, you will divide 3 on both sides. So 2X/3=2X/3 and -9/3=-3
So it will be Y=2X/3-3