Answer:
5
Step-by-step explanation:
Fifteen years from now Ravi's age will be four times his present age. What is Ravi's present age? So, Ravi′s present age is 5 years.
4x-8/x^2+3x-10 = 4(x-2)/x^2+3x-10 factor the quadratic expression in the denominator of the expression.
Answer:
(x + 5)(x - 2)
Step-by-step explanation:
Given
x² + 3x - 10 ← expression on the denominator
Consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)
The factors are + 5 and - 2, since
5 × - 2 = - 10 and 5 - 2 = + 3, thus
x² + 3x - 10 = (x + 5)(x - 2)
Help.me!!!!!!!!!!!!!!!!!
Answer:
∠U = 40°
Step-by-step explanation:
in order to find the missing angle of U we need to know the two other angles.
We know that ∠T is 65° and we know that ∠TSF is 105°. Because ∠TSF is an exterior angle, we can subtract 180 to get the interior angle. This would mean that ∠S is 75°.
Using this we can add 65 to 75 then subtract the total from 180 to get ∠U.
This would mean that ∠U is 40°
PLS HELP WRITE EACH EXPRESSION AS A SINGLE POWER DO NOT EVALUATE
Answer:
1. 3³
2. (-5)⁴
3. 3¹⁰
4. 4⁰
Step-by-step explanation:
When multiplying exponents with the same base, you add the exponents. When dividing exponents with the same base, you subtract the exponents. When raising a number with an exponent to another power, multiply the exponents.
1. [tex]\frac{3^4*3^6}{3^2*3^5} =\frac{3^{10}}{3^7}=3^3[/tex]
2. [tex]\frac{(-5)^{12}}{(-5)^3*(-5)^5} =\frac{(-5)^{12}}{(-5)^8}=(-5)^4[/tex]
3. [tex](3^2)^5=3^{10}[/tex]
4. [tex]\frac{4^0*4^4}{4^1 * 4^3} =\frac{4^4}{4^4}=4^0[/tex]
Find the total surface area of this cylinder. Give your answer to one decimal place first correct answer will get brainliest and 5 stars!!!
Answer:
The surface area formula is 2πr (h + r) where r and h are the radius and height respectively. Since π = 3.14, r = 7, h = 15 the answer is:
2 * 3.14 * 7 * (15 + 7) = 43.96 * 22 = 967.6
what is the 8th term of the geometric sequence with this explicit formula
Answer: 640 (B)
Step-by-step explanation:
The explicit formula
an = -5 × ( -2 )(n - 1) bearing in mind that n = 8
Therefore, putting n = 8 - 1, = 7
-5 × -2(7) raised to the power of 7
an = -5 × -128
= 640
Identify any outlier(s) in the data. {76, 78, 63, 70, 64, 90, 65, 28, 66, 83, 74}
Step-by-step explanation:
In my opinion 28
Is an outlier
4. Use a tree diagram to display the possible outcomes when a coin is tossed three times
and use it to find the probability of tossing exactly 2 tails.
Answer:
i. {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
ii. The probability of tossing exactly 2 tails is [tex]\frac{3}{8}[/tex] (or 0.375)
Step-by-step explanation:
when a coin is tossed, the outcomes can either be a head or a tail. The tree diagram attached to this answer shows the display of the possible outcomes when a coin is tossed three times.
The possible outcomes when a coin is tossed three times are:
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
where; H represents the head and T represents the tail.
Pr(tossing exactly 2 tails) = [tex]\frac{number of outcome of 2 tails}{total number of outcome}[/tex]
= [tex]\frac{3}{8}[/tex]
= 0.375
The probability of tossing exactly 2 tails is [tex]\frac{3}{8}[/tex] (or 0.375).
What are the first four terms of the sequence a1=−9 and an+1=an+n. I really need help with this im struggling
[tex]a_{n+1}=a_n+n[/tex]
The formatting was a bit confusing, so please do let me know if this isn't the correct equation for the sequence.
The first term is given, which is
[tex]a_1=-9[/tex]
Now, use the equation for the next terms:
[tex]a_{1+1}=a_2=-9+1=-8[/tex]
[tex]a_{2+1}=a_3=-8+2=-6[/tex]
[tex]a_{3+1}=a_4=-6+3=-3[/tex]
Thus, the first 4 terms are -9, -8, -6, and -3. Let me know if you need any clarifications, thanks!
In 9 minutes, Ivanna can type 36 words. What is her rate in words per minute?
Answer:
4
Step-by-step explanation:
9 divided by 36
Answer:
4 words/minute
Step-by-step explanation:
Since we need words per minute, we divide the number of words by the number of minutes.
words/minute = (36 words)/(9 minutes) = 4 words/minute
What is the explicit formula of -1,-3,-9,-27
Answer:
(-1)* (3)^(n-1)
Step-by-step explanation:
common ratio is 3 and the first term is -1
the explicit formula is a * r^ ( n-1)
i.e., (-1) * 3^(n-1)
help can you also show how you do it too
Answer:
m the slope of function=-3
Step-by-step explanation:
to find the slope take two points from the graph:
(0,4), (1,1)
m= y2-y1/x2-x1
m=1-4/1-0
m=-3/1=-3
the equation : y=mx+b find b
when x=0, y=b=4
y=-3x+4
2 rectangles have the same area. rectangle A is 6cm by 4cm, B is 3cm by Xcm. what is the value of X?
Answer:
x=8
Step-by-step explanation:
If the two rectangles have the same area, then you have to first find the area to solve the problem. To find the area, do 6(Length)x4(Width)=24. So now that we know that the area is 24, now all you have to do is divide 24 by 3 to find the missing dimension. 24÷3=8. Therefore, x=8.
the range of y=x^3 is all real numbers, y>0, or y>_0
Answer:
All real numbers
Step-by-step explanation:
When you graph f(x) = x³, you should be able to see that within the range of y-values, you get infinite outputs because the domain has infinite inputs.
Solve for x. 2000=500e^4x
Answer:
A. x = (ln(4))/4
Step-by-step explanation:
2000 = 500e⁴ˣ
(2000)/500 = (500e⁴ˣ)/500
4 = e⁴ˣ
ln(4) = ln(e⁴ˣ)
ln(4) = 4x
(ln(4))/4 = (4x)/4
(ln(4))/4 = x
x = (ln(4))/4
Answer:
A. x = ln(4)/4
Step-by-step explanation:
The amount of money in Joe’s savings account is increased by 8% each year. Given that he has £500 in 2016. Work out how much Joe will have in 2021.
Answer:
£700
Step-by-step explanation:
First we find the interest on this money.
Interest = Principal * Rate * Time
=[tex]\frac{500 * 8 * 5}{100}[/tex]
=5 * 8 * 5
=£200
Interest = £200
Now you add his actual money to the interest you just found to give you the total amount.
Amount = £500 + £200
= £700
5x4 – 7x3 – 5x2 + 5x + 1 = 0
Simplify
Note ; In this case, ^ means to power
p^2 - 2pq + q ^2
over
p^3 - p{q^2} + {p^2}q - q^2
Answer:
Step-by-step explanation:
(p-1)(p-1)
p(p^2-q^2) +q(p^2-q^2)
[tex]\frac{(p-q)(p-q)}{(p+q)(p-q)(p+q) }[/tex]
[tex]\frac{(p-q)}{(p+q)^{2} }[/tex]
Han and Clare are stuffing envelopes. Han can stuff 20 envelopes in one minute, and Clare can stuff 10 envelopes in one minute. They start working together on a pile of 1,000 envelopes. How long does it take them to finish the pile?
Answer:
it will take them 33 minutes and 20 seconds
Step-by-step explanation:
What we have here is that Han can stuff 20 envelopes in a minute while Clare can do 10 in a minute
So in a minute, they can jointly stuff 30 envelopes.
Mathematically we know that the number of time it will take to finish stuffing would be number of envelopes/ joint rate = 1000/30 envelopes per minute
So it will take 33 1/3 minutes
1/3 of a minute is same as 1/3 * 60 seconds = 20 seconds
So it will take them 33 minutes and 20 seconds
To prove that objects of different weights fall at the same
rate, Galileo dropped two objects with different weights
from the Leaning Tower of Pisa in Italy. The objects hit the
ground at the same time. When an object is dropped from
a tall building, it falls about 16 feet in the first second, 48
feet in the second second, and 80 feet in the third second,
regardless of its weight. How many feet would an object
fall in the tenth second?
Answer:
y = 1609 ft
Step-by-step explanation:
g is equal to 9,8 m/s² or 32,18 ft/s²
According to g = 32,18 ft/s²
In the first second as y = -1/2 g*t²
y = 1/2 32,18*(1)² ⇒ y = 16,9 ft we dismiss the sign we know the object is falling down. Is enough for the purpose of this question
The second one
y = 1/2* (32,18)* (2)²
y = 32,18*2 ⇒ y = 64,36 ft
third second
y = 1/2*32,18*(3)² ⇒ y = 144,81 ft
And in the tenth second
y =( 1/2)* 32,18 * (10)² ⇒ y = 1609 ft
A consumer is considering two different purchasing options for the car of their choice. The first option, which is leasing, is described by the equation 250x - y + 4000 = 0 where x represents the number of months of ownership and y represents the total paid for the car after ‘x' months. The second option, which is the financing option, will cost $400 for 0 months of ownership, (0,400), and $4400 for 10 months of ownership, (10, 4400). Part A: Find the equations, in slope/y-intercept form, for each of the purchasing options. Explain the significance of the slope and y-intercept for each purchasing option. Part B: Graph each equation on the same set of axes and compare. Under what conditions is each purchasing option the best choice? Be sure to provide a thorough answer. Use detailed information from your graph to back up your choices.
Answer:
Part A:
First option leasing:
[tex]y = 250x + 4000[/tex]
Second option financing:
[tex]y = 400x + 400[/tex]
The slope of the second option is greater than the first option meaning that monthly payments are greater for the second option as compared to the first option.
The y-intercept of the first option is greater than the second option meaning that the initial payment of the first option is much greater than the second option.
Part B:
As you can see in the graph, the second option is better when x is less than 24 months and the first option is better when x is greater than 24 months.
The second option has less initial payment but greater monthly payment that is why it is better for the short term (for less number of months)
On the other hand, the first option has a greater initial payment but less monthly payment that is why it is better for the long term (for greater number of months)
Step-by-step explanation:
Part A:
First option leasing:
The standard slope-intercept form is given by
[tex]y = mx + b[/tex]
Convert the given equation into slope-intercept form.
[tex]250x - y + 4000 = 0 \\\\y = 250x + 4000[/tex]
where x represents the number of months of ownership and y represents the total paid for the car after ‘x' months and 250 is the slope that indicates the rate of change of y with respect to x.
Second option financing:
We are given two points,
[tex](x_1,y_1) = (0,400)[/tex]
[tex](x_2,y_2) = (10,4400)[/tex]
The slope m is given by
[tex]$ m = \frac{y_2 - y_1}{x_2 - x_1} $[/tex]
[tex]$ m = \frac{4400 - 400}{10 - 0} $[/tex]
[tex]m = 400[/tex]
To find the value of the y-intercept (b),
substitute [tex](x_1,y_1) = (0,400)[/tex]
[tex]y = 400x + b \\\\400 = 400(0) + b \\\\b = 400[/tex]
So the equation of the second option is
[tex]y = 400x + 400[/tex]
Comparison:
The slope of the second option is greater than the first option meaning that monthly payments are greater for the second option as compared to the first option.
The y-intercept of the first option is greater than the second option meaning that the initial payment of the first option is much greater than the second option.
Part B:
Refer to the attached graph,
The point of intersection is obtained when we equate both equations,
[tex]250x + 4000 = 400x + 400 \\\\4000 - 400 = 400x - 250x \\\\3600 = 150x \\\\x = 3600/150 \\\\x = 24[/tex]
x = 24 months is the break-even point meaning that at this point both options are equally good.
As you can see in the graph, the second option is better when x is less than 24 months and the first option is better when x is greater than 24 months.
The second option has less initial payment but greater monthly payment that is why it is better for the short term (for less number of months)
On the other hand, the first option has a greater initial payment but less monthly payment that is why it is better for the long term (for greater number of months)
NEED MATH HELP NOW. Please solve for the x-intercept. Please show work.
Answer:
x = 1 and x = 3.
Step-by-step explanation:
y = 2[tex]x^{2}[/tex] - 8x + 6
y = 2([tex]x^{2}[/tex] - 4x + 3)
y = 2(x - 3)(x - 1)
So, the x-intercepts would be at...
x-3 = 0
x = 3
and
x - 1 = 0
x = 1
Hope this helps!
Yoko flew on a plane from Tokyo to Sydney. The plane flew a distance of 7800 km. The flight time was 9 hours 45 minutes. Work out the average speed of the plane in kilometres per hour.
Answer:
The average speed is 800 km/h
Step-by-step explanation:
The first thing to do here is to completely write the speed in hours.
We have 9 hours 45 minutes
45 minutes in hours is 45/60 = 3/4 = 0.75
So 9 hours 45 minutes = 9.75 hours
The average speed mathematically = Total distance/ Total time
That would be;
7800/9.75 = 800 km/h
what is productivity?
a. quantity of input per unit of output
b. quantity of output per unit of input
c. quality of output per unit of input
d. quality of input per unit of output
Answer:
This is the quantity of output per unit of input.
Step-by-step explanation:
I'm very sure.
PLZ HELP, AND PLZ EXPLAIN!
Answer: 20 units
Step-by-step explanation: The diagonal forms a Right Triangle with the side opposite the 30° angle, and the hypotenuse is the base. In a 30, 60, 90 triangle, the hypotenuse is always twice the length of the short side, given as 4. So the base is 8.
The upper triangle is iscosceles, and the trapezoid is iscosceles, so the other sides are all 4 units in length.
3×4=12
8+12=20 units
A grocery store employs 15 cashiers, 25 stock clerks, and 10 delivery personnel. Among them, 10 cashiers, 10 stock clerks, and 5 delivery personnel are married. If an employee is selected at random, find the probability that the employee is not married.
Answer:
0.5 or 50%
Step-by-step explanation:
The number of total employees is:
[tex]T=15+25+10 =50\ Employees[/tex]
The number of married employees is:
[tex]M=10+10+5 =25\ Employees[/tex]
The probability that a randomly selected employee is not married is given by:
[tex]P=1-\frac{M}{T}\\P=1-\frac{25}{50}\\P=0.5\ or\ 50\%[/tex]
The probability is 0.5 or 50%.
Someone please help!!
Answer:
A) V + 6 B = 372
B) 4V + 12B = 780
We'll divide B) by -4
B) -V -3B = -195 Then we add A)
A) V + 6 B = 372 which equals
3B = 177
1 Bus carries 59 Students
For the Van let's use equation A)
V + 6 * 59 = 372
Van = 372 -354
Each Van Carries 18 Students
Step-by-step explanation:
What expression is equivalent to rm÷rn?
A) rm-n
B) rm+n
C)m×n
D)rm÷n
Answer:
A) rm - n is the answer.
hope this helps
Answer:
D
Step-by-step explanation:
rm/rn can be factored into r(m/n) which is what is seen in answer D
Which property best describes the conditional statement below?
If triangle ABC= triangleDEF, then ADEF= triangleABC
Answer:
symmetric property
Step-by-step explanation:
because if we say
a=b and b=a
we referred to symmetric property
Keith is the leading goal scorer for a team in an ice hockey league . Last season , he scored 42 goals in 82 games . Assuming he scores goals at at a constant rate , what is the slope of the line that represents this relashonships if the number of games is is along the x-axis and the number of goals is along the y-axis
Answer: The slope is 21/41.
Step-by-step explanation:
IF the goals he scores is at a constant rate the we know if you would have to graph it, it will go through the origin.
To find the slope of a constant relationship,you will divide the y value by the x value.Now it indicates to us that x is the number of games while y is the number of goals.
so 42/82 which reduces to 21/41 has to be the slope .
Answer:
it’s 21/41 or A (I got a 100% on the test)
Need help with #11 please
Answer: The graph is a linear graph or linear function in the form y= mx + b where m is the slope and b is the y-intercept. You could plot the points (0,5) (1,4) (2,3) (4,1) and draw a straight line through them.
Step-by-step explanation:
The equation y= 5-x can be rewrite as y = -1x + 5 and it can be identify as a linear equation in slope intercept form. Now you could plot in any value of x and solve for y.
x y (x,y)
0 5 (0,5) If you put in 0 for x y will be 5
1 4 (1,4) if you put in 1 for x, y will be 4
2 3 (2,3) if you put in 2 for x, y will be 3
4 1 (4,1) if you put in 4 for x, y will be 1
5 0 (5,0) if you put in 5 for x y will be 0.