Answer:
x = 16
y = 11
Step-by-step explanation:
Let the larger number = x
Let the smaller number = y
x - y = 5
x = 2*y - 6
Put the second equation into the first. Substitute for x
2y - 6 - y = 5
combine
y - 6 = 5
and 6 to both sides.
y - 6 + 6 = 5 + 6
Combine
y = 11
=======================
Find x
x - y = 5 Substitute for y
x - 11 = 5 Add 11 to both sides.
x - 11+11=5+11
x = 16
a maple tree is 4.2 meters tall. A pine tree is 1.02 shorter that the maple tree. An oak tree is 1.89 taller than the pine tree . How tall is the oak tree?
Answer:
7.782352941
Step-by-step explanation:
4.2 divided by 1.02 the multiply the out come of that by 1.89 to get 7.782352941
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 The length of a rectangle is 6 inches, and the width is 5 inches. When each dimension is increased by x inches, the area triples. Which equation models this situation?
A)(6x)(5x) = 60B)(6x)(5x) = 90C)(x + 6)(x + 5) = 60D)(x + 6)(x + 5) = 90
Answer:
D
Step-by-step explanation:
Before the increase, the length is 6 and the width is 5, so the area is 5×6 = 30.
After the increase, the length is x+6, the width is x+5, and the area is tripled: 30×3 = 90.
Therefore:
(x+6) (x+5) = 90
what is the relationship between turning points of a graph and its derivative function
Answer:
see explanation
Step-by-step explanation:
Given a function f(x)
Then at the turning points the derivative of f(x) equals zero, that is
f'(x) = 0 at the turning points
let f(x) =2x and g(x)= x - 2 the graph of (f.g )(x) is shown below
What is the domain of ?
x >0
all real numbers except x =0
x <0
all real numbers
Answer:
The domain of the graph is all real number ⇒ the last answer
Step-by-step explanation:
* Remember that our original exponential formula was y = ab^x
- The b value is the growth factor
* Lets revise how to find the domain of this function
- The domain is all values of x that make the function defined
* Lets revise the composite function
- A composite function is a function that depends on another function.
- A composite function is created when one function is substituted
into another function.
- For example, f(g(x)) is the composite function that is formed when
g(x) is substituted for x in f(x).
∵ f(x) = 2^x
∵ g(x) = x - 2
∴ (f · g)(x) = f(x - 2)
∵ f(x) = 2^x
∴ (f · g)(x) = f(x - 2) = 2^(x - 2)
- For this function there is no values of x make the function undefined
∴ The Domain is all real numbers
- Look to the graph, the values of x go from -∞ to ∞
* The domain of the graph is all real number
I need help on NS part b plz help me!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Any number between 0.390 and 0.400 will work. For example, 0.391, 0.392, and 0.393.
Find the range and interquartile range of the
data. Round to the nearest tenth.
259, 125, 158, 168, 187,334, 198
Answer: the range is 209
Step-by-step explanation: the biggest number minus the smallest will give you the range
The answer is 209. Hope this helps
What is the distance of the segment formed by joining the following two points on a coordinate plane? (8,4) and (-7,-4)
Answer:
17
Step-by-step explanation:
Use the distance equation.
d² = (x₁−x₂)² + (y₁−y₂)²
The order doesn't matter. If I choose (x₁, y₁) to be (8, 4) and (x₂, y₂) to be (-7, -4), then:
d² = (8−(-7))² + (4−(-4))²
d² = 15² + 8²
d² = 289
d = 17
Final answer:
The distance between the points (8,4) and (-7,-4) on a coordinate plane is 17 units.
Explanation:
In order to find the distance between two points on a coordinate plane, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the points (8,4) and (-7,-4), we can substitute the x and y values into the formula:
d = √((-7 - 8)^2 + (-4 - 4)^2)
d = √(225 + 64)
d = √289
d = 17
Therefore, the distance of the segment formed by joining the two given points is 17 units.
Determine the vertex of the function f(x) = 2(x − 5)2 + 8.
(8, −5)
(8, 5)
(−5, 8)
(5, 8)
Answer:
Vertex ( 5 ,8) .
Step-by-step explanation:
Given : f(x) = 2(x − 5)² + 8.
To find : Determine the vertex of the function .
Solution : We have given
f(x) = 2(x − 5)² + 8.
Vertex form of parabola : f (x) = a(x - h)² + k, where (h, k) is the vertex.
On comparing f(x) = 2(x − 5)² + 8. with vertex form of parabola.
a = 2 , h = 5 , k = 8 .
Vertex ( 5 ,8) .
Therefore, Vertex ( 5 ,8) .
Answer: (5,8)
Step-by-step explanation:
The given function :[tex]f(x) = 2(x - 5)^2 + 8.[/tex]
We know that the vertex form of a quadratic equation is given by :
[tex]f (x) = m(x - a)^2+ b[/tex] (1)
, where (a,b)= Vertex of the function f(x).
When we compare the given function [tex]f(x) = 2(x - 5)^2 + 8.[/tex] to equation (1) , we conclude that the given function is already in its vertex form.
with a= 5 and b= 8
Therefore , the vertex of the function [tex]f(x) = 2(x - 5)^2 + 8.[/tex] = (5,8)
I need both really bad please and thank you
Answer:
15. Option A is correct
16. Option B is correct.
Step-by-step explanation:
Question 5:
sin2Ф = 2sinФcosФ
We are given sinФ = 9/13
and we need to find cosФ in order to find sin2Ф
We know that sin^2Ф + cos^2Ф= 1
so, cos^2Ф = 1- sin^2Ф
cos^2Ф = 1- (9/13)^2
cos^2Ф = 88/169
taking √ on both sides:
√cos^2Ф = √88/169
cosФ = (2√22)/13
Now
sin2Ф = 2sinФcosФ
= 2 (9/13) (( 2√22)/13)
sin 2Ф = 36√22 / 169
Now we find cos2Ф
The formula for cos2Ф = cos^2Ф - sin^2Ф
cos2Ф = ((2√22)/13)^2 - (9/13)^2
cos2Ф = 4*22 /169 - 81/169
cos2Ф = 7/169
So, Option A is correct
Question No 6
We need to find sin2Ф and cos2Ф where cosФ = 6/13
We are given cosФ = 6/13
and we need to find sinФ in order to find sin2Ф and cos2Ф
We know that sin^2Ф + cos^2Ф= 1
so, sin^2Ф = 1- cos^2Ф
sin^2Ф = 1- (6/13)^2
sin^2Ф = 133/169
taking √ on both sides:
√sin^2Ф = √133/169
sinФ = √133/13
Now
sin2Ф = 2sinФcosФ
= 2 (√133/13) (6/13)
sin2Ф = 12√133 / 169
Now we find cos2Ф
The formula for cos2Ф = cos^2Ф - sin^2Ф
cos2Ф = (6/13)^2 - (√133/13)^2
cos2Ф = 36/169 - (133/169)
cos2Ф = -97/169
Since the quadrant is 1st so, cos2Ф will be Positive i.e. 97/169
cos2Ф = 97/169
So, Option B is correct.
The president of a certain University receives a salary that is three times the salary of one of the department heads the total of the two salaries is 190000 what is the salary of the president of the University
Answer:
$142500
Step-by-step explanation:
We are given that the resident of a certain University receives a salary that is three times the salary of one of the department heads.
Assuming [tex]x[/tex] to be the salary of the department head, if the total of the two salaries is $190000, we are to find the salary of the president of the University.
We can write an equation in terms of [tex]x[/tex]:
[tex]3x+x=190000[/tex]
[tex]4x=190000[/tex]
[tex]x=47500[/tex]
Salary of the president of the University = [tex]3(47500)[/tex] = $142500
A sports store had a 60% off sale. Justin bought a pair of sneakers that were on sale for $22.40. What was the original price ?
Hello wendywagor!
Let x = the original price of the sneakers
x - .60x = 22.40
.40x = 22.40
x = $56
Thanks For Using Brainly.com
Have A Great rest of Your Day!
Help help help math image:
Answer:
13. 90
14. 43
15. 146
DUDE washed 5 windows in 35 minutes. At this rate, how long
will it take DUDE to wash 12 windows?
Answer:
35/5 = 7 Minutes per Window thus: 12*7 = 84 Minutes
Step-by-step explanation:
Answer:
84 minutes or 1 hour and 24minutes
Step-by-step explanation:
12*35=420
420/5=84
This Data set represents the number
of children in 8 families
4,2,1,2,4,2,6,3
The mean of this data set is 3. what is the mean absolute deviation
A. 1.25
B. 3
C. 3.3
D. 8
Answer:
The answer would be A. 1.25
(HELP ASAP PLEASE)
Band students are tested on, and required to pass, a certain number of scales during the year. As of today, Nick has passed 5 scales, whereas his friend Mary has passed 12 of them. Going forward, Nick has committed to passing 4 scales per week, and Mary has committed to passing 3 per week. At some point soon, the two friends will have passed the same number of scales. How many scales will that be? How long will that take?
The friends will each have passed ___ scales in ___ weeks.
Answer:
The friends will each have passed _33_ scales in _7_ weeks.
Step-by-step explanation:
We must write an equation for the number of scales that Nick approves and an equation for the number of scales that Mary approves.
For Nick we have:
5 initial scales
Nick has committed to approve 4 scales per week. Let's call x the number of weeks.
So the number of scales and for Nick is:
[tex]y = 5 + 4x[/tex]
For Mary we have:
12 initial scales
Mary has committed to approve 3 scales per week. Let's call x the number of weeks.
So the number of scales and for Mary is:
[tex]y = 12 + 3x[/tex]
To know when the two friends have passed the same number of scales we must equal both equations and solve for x:
[tex]12 + 3x = 5 + 4x[/tex]
[tex]12-5= 4x-3x[/tex]
[tex]x= 7\ weeks[/tex]
And
[tex]y=12+3*7\\\\y=33\ scales[/tex]
Final answer:
Nick and Mary will both have passed 33 scales in 7 weeks. This is determined by setting the equation for the number of scales Nick will pass equal to the number for Mary and solving for the number of weeks.
Explanation:
To determine when Nick and Mary will have passed the same number of scales, we can set up an equation based on the given information. Nick has currently passed 5 scales and will pass 4 scales each week. Mary has passed 12 scales and will pass 3 scales each week. The point at which they will have passed the same number of scales is when their total passed scales are equal.
Let's denote the number of weeks it will take to reach this point as w. For Nick, the total number of scales passed after w weeks will be 5 + 4w (his current count plus 4 times the number of weeks). For Mary, it will be 12 + 3w (her current count plus 3 times the number of weeks). Setting these two expressions equal to each other:
5 + 4w = 12 + 3w
Subtract 3w from both sides:
5 + w = 12
Subtract 5 from both sides:
w = 7
So, it will take 7 weeks for Nick and Mary to have passed the same number of scales. At that point, to find the total number of scales:
Nick: 5 + 4 x 7 = 33 scales
Mary: 12 + 3 x 7 = 33 scales
The friends will each have passed 33 scales in 7 weeks.
17) There are 15 boys and 18 girls in seventh grade. Find the ratio of boys to girls in seventh grade.
18) Janet bought 12 guavas and 16 apples. What is the ratio of guavas to apples?
19) Sandy has 8 candies and Tabitha has 10 candies. Find the ratio of Sandy’s candies to Tabitha’s candies.
20) For a birthday party, Evelyn orders 10 chicken pizzas and 15 vegetable pizzas. Find the ratio
of chicken pizzas to the vegetable pizzas.
21) In a local animal sanctuary, there are 48 deer and 64 monkeys. Find the ratio of deer to monkeys.
22) Gerry scored 56 in Math and 84 in Science. Find the ratio of his scores in Math to Science.
23) A fruit seller bought 75 mangoes and 125 apples from vendor. Find the ratio mangoes to apples bought.
24) Yulee primary school maintains a library with 81 English books to every 90 Math books. Find the ratio of English books to the Math books.
17) 5:6
18) 3:4
19) 4:5
20) 2:3
21) 3:4
22) 2:3
23) 3:5
24) 9:10
These answers are all simplified ratios
Final answer:
The questions involve finding the ratio of two quantities and simplifying them by dividing both numbers by their greatest common divisor. Each ratio gives a comparative relationship between two different counts of items or scores in different subjects.
Explanation:
The questions provided all relate to finding the ratio of two quantities.
The ratio of boys to girls in seventh grade is 15:18, which can also be simplified to 5:6 by dividing both numbers by 3.The ratio of guavas to apples Janet bought is 12:16, which simplifies to 3:4 after dividing both numbers by 4.For Sandy and Tabitha's candies, the ratio is 8:10, which simplifies to 4:5 once both numbers are divided by 2.Evelyn orders chicken and vegetable pizzas at a ratio of 10:15, which is equal to 2:3 after dividing both numbers by 5.In the animal sanctuary, the ratio of deer to monkeys is 48:64, simplifying to 3:4 after dividing by 16.Gerry's scores in Math to Science are at a ratio of 56:84, which can be reduced to 2:3 by dividing by 28.The ratio of mangoes to apples the fruit seller bought is 75:125, simplified to 3:5 after dividing both by 25.Lastly, the ratio of English books to Math books in Yulee primary school's library is 81:90, which simplifies to 9:10 upon division by 9.In each case, the ratio is found by comparing two quantities and simplifying by dividing both numbers by their greatest common divisor (GCD).
The center of Circle D is (0,0). The circumference of the circle passes through Point E (-7,-4).
Find the length of the radius of Circle D.
Answer:
[tex]\boxed{\sqrt{65}}[/tex]
Step-by-step explanation:
The radius of circle D is the distance from the origin to (-4, -7).
In math, the distance formula gives us the distance between two points, (x₁, y₁) and x₂, y₂):
[tex]d = \sqrt{(x _{2}-x_{1})^{2} +(y _{2}-y_{1})^{2}}[/tex]
You are really using Pythagoras' Theorem to find the distance. You are building a right triangle whose hypotenuse connects two given points.
For example, in the blue triangle below, the distance between the points (0,0) and (-4, -7) is
[tex]d = \sqrt{(0 - (-4))^{2} +(0 -(- 7))^{2}}\\\\ = \sqrt{4^{2} +7^{2}}\\ = \sqrt{16 + 49}\\=\sqrt{65}[/tex]
[tex]\text{The radius of the circle is }\boxed{\mathbf{\sqrt{65}}}[/tex]
factor the expression below x^2 + 12x + 36
Answer:
(x + 6)²
Step-by-step explanation:
This is a perfect square of the form
(x + a)² = x² + 2ax + a²
here a² = 36 ⇒ a = 6 and 2ax = 2 × 6x = 12x
Hence
x² + 12x + 36 = (x + 6)²
Answer:
(x+6)(x+6)
Step-by-step explanation:
Given that (-8,-8) is on the graph of f(x), find the corresponding for the function f(x)+5.
ANSWER
[tex](-8, - 3)[/tex]
EXPLANATION
Given that: (-8,-8) is on f(x).
Then we can write (-8,f(-8)) is on f(x).
The corresponding point on
[tex]f(x) + 5[/tex]
will be
[tex](-8,f(-8)+5)[/tex]
We substitute f(-8)=-8 to obtain;
[tex](-8, - 8+5)[/tex]
This simplifies to
[tex](-8, - 3)[/tex]
Therefore the corresponding point on f(x)+5 is (-8,-3).
Josh simplified 4x - 8x ÷ 2 and said the answer was -2x. What was josh's error? What should his answer have been?
Answer:
see explanation
Step-by-step explanation:
Given
4x - 8x ÷ 2
Under the rules of PEMDAS , division must be performed before subtraction.
Hence
4x - 8x ÷ 2 = 4x - 4x ← dividing - 8x by 2, then
4x - 4x = 0 ← correct answer
Can someone help me with this I’ll give brain
Answer:
-65/2
Step-by-step explanation:
I am just a natural genius ;)
Answer:
see explanation
Step-by-step explanation:
Evaluate the parenthesis before multiplication
4² = 4 × 4 = 16 and
( [tex]\frac{1}{2}[/tex] )² = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{4}[/tex]
Thus 16 + [tex]\frac{1}{4}[/tex] = 16 [tex]\frac{1}{4}[/tex] = [tex]\frac{65}{4}[/tex]
Hence
- 2 × [tex]\frac{65}{4}[/tex] = [tex]\frac{-2(65)}{4}[/tex] = - [tex]\frac{65}{2}[/tex] = - 32 [tex]\frac{1}{2}[/tex]
help me with this too and god bless :3 o,o
Answer:
For the first pic its mode interval and median for the second pic its frequency table.
Step-by-step explanation:
HELP!!!!!! READ BELOWW
Answer:
The missing words
# x ⇒ # y ⇒ # 4 ⇒ # 0
Step-by-step explanation:
* Lets revise how to find the inverse function
- At first write the function as y = f(x)
- Then switch x and y
- Then solve for y
- The domain of f(x) will be the range of f^-1(x)
- The range of f(x) will be the domain of f^-1(x)
* Now lets solve the problem
∵ f(x) = √(x - 4)
∴ y = √(x - 4) ⇒ switch x and y
∴ x = √(y - 4) ⇒ square the two sides
∴ x² = [√(y - 4)]² ⇒ cancel the root by squaring
∴ x² = y - 4 ⇒ add 4 to the both sides
∴ y = x² + 4
∴ f^-1(x) = x² + 4
* To find the domain of the inverse, find the range of the function
∵ The domain of f(x) is ⇒ x - 4 ≥ 0 (no negative value under√)
∴ the domain is x ≥ 4
- Substitute this value in the function to find the range
∵ x = 4
∴ y = √(4 - 4) = 0
∴ y ≥ 0
- The range of f(x) is y ≥ 0
∴ The domain of the inverse f^-1(x) is x ≥ 0
- The missing words
# x
# y
# 4
# 0
Without calculating, which has a bigger volume. A cube that has a length, width, and height of 18 m. Or a sphere with a radius of 9 m? Explain.
Weird. A period appears above this... huh.
Answer:
[Th]e cube has a greater value.
Step-by-step explanation:
What the word problem really wants us to get [is ]the question of 'Which is greater, A=6a^2 when 'a' [is] 18 or A=4[tex]\pi[/tex]r^2 when r = 9? And here's how to solve that.
Starting with the[ c]ube we have A=6a^2. A bit t[o]o simple, right?
A=6(18)^2 Substitute numbers.
A=6(324) Solve ex[p]onents.
A=1944 Mult[i]ply.
So w[e] know that the cube is 1944 meters cube[d ] in area. But what about the more [f]ormidable sphere? Fo[r] it we need a slightly m[o]re co[m]plicated formula, A=4[tex]\pi[/tex]r^2. However, instead of using the real pi I will be rounding to 3.14, since we have no calculator so anything more would take way too long and fry your[ bra]in.
A=4(3.14)(9)^2 Subst[i]tute numbers.
A=4(3.14)(81) Solve expone[n]ts.
A=12.56(81) Multip[ly].
A=1017.36 Multiply again[.]
Now, since I'm sure all of us can count, we know that 1944 is greater than 1017.36. Or in other words, the cube is bigger than the sphere.
And PLEASE don't copy this guys. Make your own iteration. Change it up!
you have 13 coins in your wallet some are nickels and some are dimes altogether you have 0.85. how many nickels do you have
Answer:
4 Dimes
9 Nickels
Step-by-step explanation:
I did guess and check (if you have an equation leave a comment or answer!)
So I did kept playing with the numbers making them go down until I could subtract the number of coins and divide to get the rest:
85-40 (4 dimes)=45
45/5=9 nickels
4+9=13
I hope this helps!
To solve for the number of nickels and dimes amounting to $0.85 in 13 coins, we set up and solve a system of equations. We found that there are 9 nickels and 4 dimes in the wallet.
To find out how many nickels you have when you have 13 coins composed of nickels and dimes amounting to $0.85, we can set up a system of equations where the number of nickels is represented by n and the number of dimes by d.
The first equation comes from the total number of coins: n + d = 13.
The second is derived from the total amount of money: 0.05n + 0.10d = 0.85.
We have two equations:
n + d = 13
0.05n + 0.10d = 0.85
Now, let's multiply the second equation by 20 to get rid of the decimals:
n + 2d = 17
By subtracting the first equation from this new equation:
d = 4
Substitute d back into the first equation:
n + 4 = 13
Thus:
n = 9
So you have 9 nickels and 4 dimes.
A fish tank has a length of 14cm, a width of 25cm, and a height of 15cm. It is only filled with water up to a height of 7 centimeters. How much more water is needed to fill the tank to the brim?
Answer:
2800 cm^3, or 2.8 liters
Step-by-step explanation:
The base of the tank remains 14 cm × 25 cm. The remaining height is 15 -7 = 8 cm, so the remaining volume is ...
(14 cm)(25 cm)(8 cm) = 2800 cm^3 = 2.8 liters
_____
1 liter = 1000 cm^3
z + mx = yx , for x can you pls give me the answer I need it fast
To solve the equation Z + mx = yx for x, we first move 'mx' to the right side to get 'yx - mx = Z'. We then factor out 'x' to get 'x(y - m) = Z'. Finally, we divide by '(y - m)' to get 'x = Z / (y - m)'. This solution holds as long as y ≠ m.
Explanation:Here, we're going to solve the equation for x: Z + mx = yx.
We can start by grouping the terms with 'x' together. This gives us: yx - mx = Z. Now, we can factor x out of the left side of the equation. This results in: x(y - m) = Z. Finally, to solve for x, we divide both sides of the equation by (y - m). This gives us the solution: x = Z / (y - m).
Note: This solution is under the assumption that y ≠ m because division by zero is undefined.
Learn more about algebra here:https://brainly.com/question/24875240
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on monday, carly walked 3 miles and ran 2 miles for a total of 78 minites on a treadmill. on thursday she walked 2 miles and ran 3 miles for atotal of 72 minutes using the same speed setting for the treadmill as she did on Monday. let wand r represent the rates, in minutes per mile , that carly walked a d ran on the treadmill, respectivelsy
Answer:
w=18 minutes per mile, r=12 minutes per mile
Step-by-step explanation:
Let w and r represent the rates, in minutes per mile, that Carly walked and ran on the treadmill, respectively.
1. On Monday, Carly walked 3 miles and spent 3w minutes, ran 2 miles and spent 2r minutes. In total Carly spent 78 minutes, so
3w+2r=78
2. On Thursday, Carly walked 2 miles and spent 2w minutes, ran 3 miles and spent 3r minutes. In total Carly spent 72 minutes, so
2w+3r=72
Solve the system of two equations:
[tex]\left \{ {{3w+2r=78} \atop {2w+3r=72}} \right.[/tex]
Multiply the first equation by 2, the second equation by 3 and subtract them:
[tex]2(3w+2r)-3(2w+3r)=2\cdot 78-3\cdot 72\\ \\6w+4r-6w-9r=156-216\\ \\-5r=-60\\ \\r=12[/tex]
Substitute it into the first equation:
[tex]3w+2\cdot 12=78\\ \\3w=78-24\\ \\3w=54\\ \\w=18[/tex]
Find f(-3) for f(x) = 4(2)^x
Hey there! :D
f(-3)= 4(2)^x
Just plug in -3 as x and solve.
4(2)^-3
First do the exponent, and then multiply the four on the outside.
4(1/8)
=1/2
I hope this helps!
~kaikers
Final answer:
To calculate f(-3) for the function f(x) = 4(2)ˣ, substitute -3 into the function, yielding f(-3) = 1/2 after simplifying 4 times 2 raised to the power of -3.
Explanation:
To find f(-3) for the function f(x) = 4(2)ˣ, simply substitute -3 for x in the equation. Here's How:
Start with the original function f(x) = 4(2)ˣ.
Replace every x with -3 to get f(-3) = 4(2)⁻³.
Calculate 2⁻³, which equals 1/8 because negative exponents represent the reciprocal of the base raised to the positive exponent.
Now, multiply 4 by 1/8 to get f(-3) = 4 * 1/8 = 1/2.
Therefore, f(3) for the given function equals 1/2.
Which answer shows 0.00897 written in scientific notation?
Answer:
8.97*10^-3Step-by-step explanation:
just did the question and got it right.