Answer: The sum is 127
Step-by-step explanation:
A 2-digit number N = ab can be written as (where a and b are single-digit numbers)
a*10 + b.
Now, we want that:
(a + 2)*(b + 2) = a*10 + b.
So we must find all the solutions to that equation such that a can not be zero (if a = 0, then the number is not a 2-digit number)
We have:
(a + 2)*(b + 2) = a*b + 2*a + 2*b + 4 = a*10 + b
a*b + 2*b - b + 4 = a*10 - a*2
a*b + 4 + b = a*8
a*b + 4 + b - a*8 = 0.
Now we can give one of the variables different values, and see if the equation has solutions:
>a = 1:
1*b + 4 + b - 8 = 0
2*b - 4 = 0
b = 4/2 = 2
Then the number 12 has the property.
> if a = 2:
2*b + 4 + b -16 = 0
3b -12 = 0
b = 12/3 = 4
The number 24 has the property.
>a = 3 is already known, here the solution is 35.
>a = 4.
4*b + 4 + b - 8*4 = 0
5*b + 4 - 32 = 0
5*b = 28
b = 28/5
this is not an integer, so here we do not have a solution.
>if a = 5.
5*b + 4 + b - 8*5 = 0
6b + 4 - 40 = 0
6b - 36 = 0
b = 36/6 = 6
So the number 56 also has the property.
>if a = 6
6*b + 4 + b - 8*6 = 0
7b + 4 - 48 = 0
7b - 44 = 0
b = 44/7 this is not an integer, so here we do not have any solution.
>if a = 7
7*b + 4 + b -8*7 = 0
8b -52 = 0
b = 52/8 = 6.5 this is not an integer, so we here do not have a solution.
>if a = 8
8*b + 4 + b -8*8 = 0
9*b + 4 - 64 = 0
9*b = 60
b = 60/9 this is not an integer, so we here do not have any solution:
>if a = 9
9*b + 4 + b - 8*9 = 0
10b + 4 - 72 = 0
10b -68 = 0
b = 68/10 again, this is not an integer.
So the numbers with the property are:
12, 24, 35 and 56
And the sum is:
12 + 24 + 35 + 56 = 127
The sum of five consecutive numbers is 360. What is the smallest of these numbers? *
Answer:
70
Step-by-step explanation:
An easy way to do this is to simply take 360(the sum) and divide it by 5(the number of numbers) to get 72. Thus, 72 is the middle number and the numbers are:
72
72,72,73
70,71,72,73,74
The smallest of these numbers is 70
Hope it helps <3
Hello!
Answer:
70 is the smallest number.
Step-by-step explanation:
If the sum of 5 consecutive numbers is 360, we can solve for the smallest number algebraically:
Let 'x' represent the smallest number:
and (x + 1), (x + 2), (x + 3), and (x+4) represent the other consecutive numbers:
x + (x + 1) + (x + 2) + (x + 3) + (x+ 4) = 360
Combine like terms:
5x + 10 = 360
Subtract 10 from both sides:
5x = 350
Divide both sides by 5:
x = 70. This is the smallest of the consecutive numbers.
We can check our work:
70 + 71 + 72 + 73 + 74 = 360.
Hope this helped!
The path of a cannon firing a cannonball can be modeled by the function h(x) = –x2 + 4x + 12, where x is time in seconds and h(x) is the height of the cannonball in feet. At what time does the cannonball reach its maximum height? seconds
Answer:
after 2 seconds
Step-by-step explanation:
Given
h(x) = - x² + 4x + 12
The ball will reach its maximum at the vertex of the parabola
Find the zeros by letting h(x) = 0, that is
- x² + 4x + 12 = 0 ← multiply through by - 1
x² - 4x - 12 = 0 ← in standard form
(x - 6)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 2 = 0 ⇒ x = - 2
The x- coordinate of the vertex is at the midpoint of the zeros, thus
[tex]x_{vertex}[/tex] = [tex]\frac{-2+6}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2
Substitute x = 2 into h(x)
h(2) = - 2² + 4(2) + 12 = - 4 + 8 + 12 = 16
The cannonball reaches its maximum height of 16 ft after 2 seconds
Answer:
2 seconds
Step-by-step explanation:
I just did it just trust me. This isn't reated to the answer but I had spagehtti for lunch
(25 points) The range of [tex]y=\frac{1}{x-10}[/tex] is All Real Numbers. TRUE or FALSE, and why?
Answer:
True
Step-by-step explanation:
Real Numbers are just numbers like:
1 12.38 −0.8625 34 π (pi) 198
In fact:
Nearly any number you can think of is a Real Number
Real Numbers include:
yes Whole Numbers (like 0, 1, 2, 3, 4, etc)
yes Rational Numbers (like 3/4, 0.125, 0.333..., 1.1, etc )
yes Irrational Numbers (like π, √2, etc )
Real Numbers can also be positive, negative or zero.
So ... what is NOT a Real Number?
not Imaginary Numbers like √−1 (the square root of minus 1)
are not Real Numbers
not Infinity is not a Real Number
Mathematicians also play with some special numbers that aren't Real Numbers.
Real numbers can be represented on a number line.
how to do this question plz
Answer:
Step-by-step explanation:
9-5=4
8*4*10=320
5*10*3=150
320+150=470
470 cm³
Can someone give me some help??
Answer:
OPtion B)
Step-by-step explanation:
Answer: Choice C)
y < (-1/5)x + 1
The boundary line is y = (-1/5)x+1 as it goes through the points shown. The boundary line is dashed or dotted, meaning that points on this boundary line are not in the solution set. So we will not have an "or equal to" as part of the inequality sign. More specifically, the inequality sign is "less than" because we shade below the boundary line. So that's how we end up with y < (-1/5)x+1.
If tan(theta+alpha)/tan(theta+bita) =a/b then show that a+b/a-b sin²(alpha-bita)=sin²(theta+alpha)-sin²(theta+bita)
Answer:
son
Step-by-step explanation:
son-sin
The average student loan debt is reported to be $25,235. A student belives that the student loan debt is higher in her area. She takes a random sample of 100 college students in her area and determines the mean to be $27,524 and the standard devition to be $6000. Is there sufficient evidence to support the student' claim at a 5% significance level?
Answer:
We reject the students claim because the P-value is less than the significance level.
Step-by-step explanation:
First of all let's define the hypothesis;
Null hypothesis;H0; μ = 25,235
Alternative hypothesis;Ha; μ > 25,235
Now, let's find the test statistic. Formula is;
t = (x' - μ)/(σ/√n)
We are given;
x' = 27,524
μ = 25,235
σ = 6000
n = 100
Thus;
t = (27524 - 25235)/(6000/√100)
t = 2289/600
t = 3.815
So from online p-value calculator as attached, using t=3.815, DF = 100-1 = 99 and significance level of 0.05, the P-value is gotten as p = 0.000237.
The p-value is less than the significance level of 0.05. Thus,we reject the students claim.
What is the center of the circle with the equation (x-1)^2 + (y+3)^2= 9? a (1,3) b (-1,3) c (-1,-3) d (1,-3)
Answer:
The center is ( 1,-3) and the radius is 3
Step-by-step explanation:
The equation of a circle can be written in the form
( x-h)^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
(x-1)^2 + (y+3)^2= 9
(x-1)^2 + (- -3)^2= 3^2
The center is ( 1,-3) and the radius is 3
If alpha and beta are the angles in the first quadrant tan alpha = 1/7 and sin beta =1/ root 10 then usind the formula sin (A +B) = sin A. CosB + sina. CosB find the value of alpha + 2beta
Answer:
[tex]$\arcsin\left(\frac{129\sqrt{2}}{250}\right)\approx 0.8179$[/tex]
Step-by-step explanation:
[tex]\alpha \text{ and } \beta \text{ in Quadrant I}[/tex]
[tex]$\tan(\alpha)=\frac{1}{7} \text{ and } \sin(\beta)=\frac{1}{\sqrt{10}}=\frac{\sqrt{10} }{10} $[/tex]
Using Pythagorean Identities:
[tex]\boxed{\sin^2(\theta)+\cos^2(\theta)=1} \text{ and } \boxed{1+\tan^2(\theta)=\sec^2(\theta)}[/tex]
[tex]$\left(\frac{\sqrt{10} }{10} \right)^2+\cos^2(\beta)=1 \Longrightarrow \cos(\beta)=\sqrt{1-\frac{10}{100}} =\sqrt{\frac{90}{100}}=\frac{3\sqrt{10}}{10}$[/tex]
[tex]\text{Note: } \cos(\beta) \text{ is positive because the angle is in the first qudrant}[/tex]
[tex]$1+\left(\frac{1 }{7} \right)^2=\frac{1}{\cos^2(\alpha)} \Longrightarrow 1+\frac{1}{49}=\frac{1}{\cos^2(\alpha)} \Longrightarrow \frac{50}{49} =\frac{1}{\cos^2(\alpha)} $[/tex]
[tex]$\Longrightarrow \frac{49}{50}=\cos^2(\alpha) \Longrightarrow \cos(\alpha)=\sqrt{\frac{49}{50} } =\frac{7\sqrt{2}}{10}$[/tex]
[tex]\text{Now let's find }\sin(\alpha)[/tex]
[tex]$\sin^2(\alpha)+\left(\frac{7\sqrt{2} }{10}\right)^2=1 \Longrightarrow \sin^2(\alpha) +\frac{49}{50}=1 \Longrightarrow \sin(\alpha)=\sqrt{1-\frac{49}{50}} = \frac{\sqrt{2}}{10}$[/tex]
The sum Identity is:
[tex]\sin(\alpha + \beta)=\sin(\alpha)\cos(\beta)+\sin(\beta)\cos(\alpha)[/tex]
I will just follow what the question asks.
[tex]\text{Find the value of }\alpha+2\beta[/tex]
[tex]\sin(\alpha + 2\beta)=\sin(\alpha)\cos(2\beta)+\sin(2\beta)\cos(\alpha)[/tex]
[tex]\text{I will first calculate }\cos(2\beta)[/tex]
[tex]$\cos(2\beta)=\frac{1-\tan^2(\beta)}{1+\tan^2(\beta)} =\frac{1-(\frac{1}{7})^2 }{1+(\frac{1}{7})^2}=\frac{24}{25}$[/tex]
[tex]\text{Now }\sin(2\beta)[/tex]
[tex]$\sin(2\beta)=2\sin(\beta)\cos(\beta)=2 \cdot \frac{\sqrt{10} }{10}\cdot \frac{3\sqrt{10} }{10} = \frac{3}{5} $[/tex]
Now we can perform the sum identity:
[tex]\sin(\alpha + 2\beta)=\sin(\alpha)\cos(2\beta)+\sin(2\beta)\cos(\alpha)[/tex]
[tex]$\sin(\alpha + 2\beta)=\frac{\sqrt{2}}{10}\cdot \frac{24}{25} +\frac{3}{5} \cdot \frac{7\sqrt{2} }{10} = \frac{129\sqrt{2}}{250}$[/tex]
But we are not done yet! You want
[tex]\alpha + 2\beta[/tex] and not [tex]\sin(\alpha + 2\beta)[/tex]
You actually want the
[tex]$\arcsin\left(\frac{129\sqrt{2}}{250}\right)\approx 0.8179$[/tex]
Answer:
ok bye guy................
25 POINTS + BRAINLIEST !!!! A fruit bowl contains apples and bananas in the ration 4 : 5. Two apples are removed changing the ratio to 2 : 3. Work out the total number of fruit that remain in the bowl.
Answer:
Total number of fruits remaining = 25
Step-by-step explanation:
Let the number of
apples = 4x
bananas = 5x
Therefore
4x-2 / 5x = 2 / 3
Solve for x, cross multiply
3(4x-2) = 2(5x)
12x - 6 = 10 x
2x = 6
x = 3
Apples = 4*3 = 12
Bananas = 5*3 = 15
Apples remaining = 12-2 = 10
Total number of fruits remaining = 10+15 = 25
Answer:
[tex]\boxed{25 \ fruits}[/tex]
Step-by-step explanation:
Let apples be 4x and Bananas be 5x
So, the given condition is:
[tex]\frac{4x-2}{5x} = \frac{2}{3}[/tex]
Cross Multiplying
5x*2 = 3(4x-2)
10x = 12x - 6
Adding 6 to both sides
10x+6 = 12x
12x - 10x = 6
2x = 6
x = 3
Now, Fruits remaining in the bowl are:
=> 4x-2 + 5x
=> 12 - 2 + 15
=> 10+15
=> 25
A study of the annual population of toads in a county park shows the population, S(t), can be represented by the function S(t)=152(1.045)t, where the t represents the number of years since the study started. Based on the function, what is the growth rate?
Answer:
Based on the function, the growth rate is 4.5%
Step-by-step explanation:
In this question, we are given the exponential equation and we are told to deduce the growth rate.
Mathematically, we can rewrite the exponential equation as follows;
S(t) = 152(1.045)^t = 152(1 + 0.045)^t
What we see here is that we have successfully split the 1.045 to 1 + 0.045
Now, that value of 0.045 represents the growth rate.
This growth rate can be properly expressed if we make the fraction given as a percentage.
Thus the issue here is converting 0.045 to percentage
Mathematically, that would be;
0.045 = 4.5/100
This makes is 4.5%
So the growth rate we are looking for is 4.5%
Angle measures and segment lengths. Two tangents. PLEASE HELP ASAP! LIKE IN 2 MINS PLZ!!! :)
Answer:
x=60 degrees
Step-by-step explanation:
Formula for angle at x=1/2(240-120)
x=60
PLEASE help me with this question!! I really need help!
Answer:
324π in²
Step-by-step explanation:
The surface area of a sphere = 4πr² ( r is the radius )
Calculate r using the volume (V) formula
V = [tex]\frac{4}{3}[/tex]πr³
Here V = 972π , thus
[tex]\frac{4}{3}[/tex]πr³ = 972π ( divide both sides by π )
[tex]\frac{4}{3}[/tex]r³ = 972 ( multiply both sides by 3 to clear the fraction )
4r³ = 2916 ( divide both sides by 4 )
r³ = 729 ( take the cube root of both sides )
r = [tex]\sqrt[3]{729}[/tex] = 9
Thus
surface area = 4π × 9² = 4π × 81 = 324π in²
The floor of a rectangular swimming pool has an area of 350 sq.meters, and every point on the floor is of equal depth. If 4,200
cubic meters of water is poured into the pool, how deep will the water level be?
Answer: The depth is 12m
Step-by-step explanation:
The area is 350m^2
And the depth in each point of the base is at the same depth D.
Then we have a cuboid.
Now, the volume of a cuboid is equal to:
V= L*W*D
L = lenght, W = width and D = depth.
Such that L*W = area = 350m^2
then we have:
V = D*350m^2
Now we want V = 4200m^3
4200m^3 = D*350m^2
D = (4200/350) m = 12m
The depth is 12m
Please answer it now in two minutes
Answer:
[tex]2\sqrt{33}[/tex].
Step-by-step explanation:
This triangle is a 30-60-90 triangle. That means that the hypotenuse is double the length of the smaller side.
Since the smaller side measures [tex]\sqrt{33}[/tex], the hypotenuse is [tex]2\sqrt{33}[/tex].
Hope this helps!
What are the coordinates of the image of point B, after the segment has been dilated by a scale factor of 3 with a center of dilation at the origin? On a coordinate plane, line segment A B has points (negative 6, 8) and (negative 3, 3). (–9, 9) (9, –9) (–1, 1) (1, –1)
Answer: (–9, 9)
Step-by-step explanation:
if the original point (x,y) gets dilated by a scale factor 'k' with a center of dilation at the origin, then
The coordinates of the image point are (kx, ky).
Given: The coordinates of line segment A B are A(-6,8) and B(-3,3).
then , the coordinates of B after dilation by scale factor of 3 with a center of dilation at the origin,
[tex](-3,3)\to(3(-3),3(3))\\\\\Rightarrow\ (-3,3)\to(-9,9)[/tex]
Hence, the coordinates of the image of point B, after the segment has been dilated by a scale factor of 3 with a center of dilation at the origin = (–9, 9).
Answer:option A.
Step-by-step explanation: because the point B is dialated and that’s where you will find you answer and edge cumulitive exam 2020.
If a and b are rational numbers and 5 +2 root 3/7+4 root3=a-b root 3;then a and b=
Answer:
[tex]\bold{a=5\,,\quad b=-4\frac27}[/tex]
Step-by-step explanation:
[tex]5+\frac{2\sqrt3}7+4\sqrt3=5+\frac27\sqrt3+4\sqrt3=5+4\frac27\sqrt3=5-(-4\frac27)\sqrt3[/tex]
How to do this question plz answer
Answer:
126 cm³
Step-by-step explanation:
The volume (V) of the prism is calculated as
V = Al ( A is the cross sectional area and l the length ), thus
V = 21 × 6
= 126 cm³
A circle has a radius of sqrt 45 units and is centered at -2.4, -4.8 write the equation of the circle
Answer:
(x+2.4)^2+(y+4.8)^2=2025
If you'd like additional help with math or another subject, check out growthinyouth.org!
Step-by-step explanation:
If 3, x, y, -9 are in A.P, find the values of x and y.
Answer:
x = -1y = -5Step-by-step explanation:
The common difference (d) can be found using the first and 4th terms:
a1 = 3
a4 = a1 +d(4 -1)
-9 = 3 +3d . . . . . simplify
-3 = 1 + d . . . . . . divide by 3
-4 = d . . . . . . . . . subtract 1
Then ...
x = a1 + d = 3 -4 = -1
y = x + d = -1 -4 = -5
The values of x and y are -1 and -5, respectively.
PLEASEEEEE HELP MEEE
Answer:
4.16% is the hourly growth rate
Step-by-step explanation:
What we can do here is to first set up an exponential relationship that relates the present number of bacteria, the initial number of bacteria, the growth rate of the bacteria and the number of hours.
What we want to establish here has a resemblance with the compound interest formula in finance.
Let’s see the initial number of bacteria as the amount deposited, the present number of bacteria as the amount after some months, the growth rate as the monthly percentage while the number of hours works like the number of months.
Mathematically, what we have will be;
P = I(1 + r)^h
where P is the present bacteria number, I is the initial, r is the growth rate while h is the number of hours.
Thus, we have the following values from the question;
P = 1530
I = 1,300
r = ?
h = 4
Substituting these values, we have;
1530 = 1300(1 + r)^4
divide both sides by 1,300
1.177 = (1+r)^4
Find the fourth root of both sides
(1.177)^(1/4) = 1+ r
1.0416 = 1 + r
r = 1.0416-1
r = 0.0416
This in percentage is 4.16%
Which of the following segments is a radius of 0?
Answer:
D. RO
Step-by-step explanation:
A paper cup is dropped and its landing position is recorded. The cup can land on the side, on the open end, or on the closed end. The results of 20 trials are shown in the table below: Based on the table, which of the following best compares the experimental probability of the cup landing on its open end with the experimental probability of the cup landing on its closed end?
The probabilities are equal.
The probability of landing on the open end is greater.
The probability of landing on the closed end is greater.
No conclusion can be made.
Answer:
"The probabilities are equal."
Step-by-step explanation:
Since the amount of times the paper cup landed on its open, and closed end is equal, then the answer is "The probabilities are equal."
Answer: the probability’s are equal
Step-by-step explanation:
Plane A is descending toward the local airport, and plane B is ascending from the same airport. Plane A is descending at a rate of 2,500 feet per minute. Plane B is ascending at a rate of 4,000 feet per minute. If plane A is currently at an altitude of 14,000 feet and plane B is at an altitude of 1,000 feet, how long will it take them to be at the same altitude? The equation representing plane A’s descent is y = -2,500x + 14,000. The equation representing plane B’s ascent is y = 4,000x + 1,000. In both equations, y represents altitude and x represents time in minutes.
Answer: 2 minutes
Step-by-step explanation:
Given the following :
Plane A's descent :
y = -2,500x + 14,000
Plane B's Ascent :
y = 4,000x + 1,000
where y = altitude x = minute
Time to be at the same altitude :
Being at the same altitude means ;
Plane A's descent = Plane B's Ascent
-2,500x + 14,000 = 4,000x + 1,000
-2500x - 4000x = 1000 - 14000
-6500x = - 13000
x = 13000 / 6500
x = 2
x = 2minutes.
Do you know the adjustments for the graph to show the intersecting lines.
SHOW ME HOW TO SOLVE THIS PLSS>>> The price of a tennis racquet is inversely proportional to its weight. If a 20 oz. racquet cost $30.00, what would a 25 oz. racquet cost?
Answer:
$24
Step-by-step explanation:
Inversely proportional means that the two variables (price and weight in this case) will always have the same product. Therefore, we can write the following equation:
25 * x = 20 * 30 (where x is the price of a 25 oz. racquet)
25x = 600
x = $24
What is the equation of the line that passes through (1, 3) and (-2, -3)? y = -2x + 1 y = 2x + 1 y = x - 1 y = -x + 1
Answer: y = 2x+1
Step-by-step explanation:
It is the only line with (1,3) as a solution. A slower algebraic way to solve this would be to plug in 1 for x and 3 for y, then, out of the equations in which it works, plug in -2 for x and -3 for y. The equation that remains true for both points is the answer.
Hope it helps <3
Answer:
[tex]\boxed{y = 2x + 1}[/tex]
Step-by-step explanation:
The line passes through (1, 3).
The solution of the line is the points it crosses.
x = 1
y = 3
Plug x as 1 and y as 3 in the equation.
y = -2x + 1
3 = -2(1) + 1
3 = -2 + 1
3 = -1 False
Plug x as 1 and y as 3 in the equation.
y = 2x + 1
3 = 2(1) + 1
3 = 2 + 1
3 = 3 True
Plug x as 1 and y as 3 in the equation.
y = x - 1
3 = 1 - 1
3 = 0 False
Plug x as 1 and y as 3 in the equation.
y = -x + 1
3 = -(1) + 1
3 = -1 + 1
3 = 0 False
Which set of ordered pairs does not represent a function?
A{(-8,0),(4,0),(5,-2), (7,-9)}
B{(-6,0), (-4,2), (4,0), (-1,-9)}
C{(6,-9),(-3,6),(-3,-7),(-9, -2)}
D{(5,-6), (0,5), (-4, -8), (1, -8)}
Answer:
C
Step-by-step explanation:
In a function, each domain has one range. But a range can have many domains.
Think about it like this:
Patty is eating dinner
Patty is swimming
Both can't happen at the same time.
But:
Patty is eating dinner
Leo is eating dinner
C has two domains of -3, each having different ranges.
Hope that helps, tell me if you need further info. =)
Answer:
C. C{(6,-9),(-3,6),(-3,-7),(-9, -2)}
Step-by-step explanation:
If you see the same x-coordinate used more than once, it is not a function.
Here, you only see this in choice C, where x = -3 for two points. That makes this relation not a function.
Answers:
3x-2y=-12
2x-3y=-12
3x+2y=12
3x+3y=-12
Answer:
3x + 2y = 12.
Step-by-step explanation:
Two conspicuous points on the graph are at (0, 6), and (4, 0).
That means the slope of the line is (6 - 0) / (0 - 4) = 6 / -4 = -3 / 2.
The intercept of the line is at (0, 6).
This means that the equation of the line is y = -3/2x + 6.
y = -3/2x + 6
Add 3/2x to both sides
3/2x + y = 6
Multiply all terms by 2
3x + 2y = 12
Hope this helps!
2. Ravi purchased an old house for Rs. 76.5000 and
spent Rs. 115000 on its. Then he sold it at a
gain of 5%. How many
much did he get.
Answer:
Rs. 924000.
Step-by-step explanation:
Cost of house = 765000
Additional money spent on it = 115000
Total cost incurred by Ravi = 765000 + 115000 = 880000
Gain = 5% of total cost
gain in Rs = 5/100 * 880000 = Rs. 44000
Total selling price of house = total cost incurred + profit = 880000+ 44000
Total selling price of house = Rs. 924000
Thus, Ravi got Rs. 924000.
4) John's sister is 8 years less than twice his age. If John is 39, what age is his sister?
Answer:
Sister is 70
Step-by-step explanation:
John is 39.
8 less than twice his age is
39*2-8 = 70
Answer:
70 years old.
Step-by-step explanation:
Since John's sister is 8 years younger than TWICE his age, we just need to multiply 39*2 which equals 78. Now we just need to subtract 8 which equals 70.
Hope this helps!! <3