Answer:
One-half
Step-by-step explanation:
Given
Exponential function
Required
The initial value that shrinks the function by [tex]50\%[/tex]
An exponential function is represented as:
[tex]y = ab^x[/tex]
Where the growth function is:
[tex]r = b^x[/tex]
[tex]a \to[/tex] initial value
For the growth function to shrink by x%, then:
[tex]a =1 - x\%[/tex]
In this case; x = 50. So, we have:
[tex]a =1 - 50\%[/tex]
Express as fraction
[tex]a =1 - \frac{50}{100}[/tex]
Take LCM
[tex]a =\frac{100 -50}{100}[/tex]
[tex]a =\frac{50}{100}[/tex]
Reduce fraction
[tex]a =\frac{1}{2}[/tex]
Answer:
It's D on edge :D
Step-by-step explanation:
please me in the math
Find the H.C.F
[tex] {x}^{2} - 4 \\ {x}^{3} + 8 \\ {x}^{2} + 5x + 6[/tex]
it so simple
Step-by-step explanation:
Solution
First equation x ² - 4
= (x+2) (x-2)
Second equation = x ³ +8 + = x³+2^3
= (x-2) (x² + x₁2 +2²) = (x-2) (x² + 2x+4)
3 Third equation = x ² + 5x + 6
= x² + 6x= x +6 = x(x+6)-1(x+6)
(x-1) (x+6)
H.C. F= x-2
state the dimensions of the matrix. identify the indicated element
Answer:
D; 2 * 3; -4
Step-by-step explanation:
The dimension of the matrix refers to the number of elements in a row multiplied by the number of elements is a column
In a row, we have 2 elements, in a column , we have 3 elements
So the matrix is of 2 * 3 dimension
a21, refers to the element in the matrix that is in the row 2 column 1 and that is -4
Question 6 of 10
How much would $500 invested at 6% interest compounded monthly be
worth after 5 years? Round your answer to the nearest cen
(0) - P(144
A $674,43
B. $886,41
C, 5669.11
D. $512,68
9514 1404 393
Answer:
A. $674.43
Step-by-step explanation:
The account balance is given by ...
A = P(1 +r/12)^(12t) . . . . . principal P invested at annual rate r for t years
A = $500(1 +0.06/12)^(12·5) = $500(1.005^60)
A ≈ $674.43
v=u + 2at
Where v is the final velocity (in m/s), u is the initial velocity (in m/s), a is the
acceleration (in m/s?) and t is the time in seconds).
Find v when u is 35 m/s, a is 28 m/s2, and t is 58 seconds.
Answer:
3283m/s
Step-by-step explanation:
V=U+2at
V=35+2(28)(58)
V=35+3248
V=3283m/s
Keith used the following steps to find the inverse of f, but he thinks he made a error
f(x) = 7x + 5
Answer:
Step-by-step explanation:
[tex]\Large \boldsymbol{} f(x) \ \ inverse \ \ function \ \ (f(x))^{-1} \\\\ y=7x+5 \\\\x=7y+5 \\\\ y=\dfrac{x-5}{7} \ \ or \ \ f(x)^{-1}= \dfrac{x-5}{7}[/tex]
If 4 over 7 ton of concrete covers 7 over 8 of a bridge, how many tons of concrete are required to cover the entire bridge?
Answer:
Your answer would be 32/49.
Step-by-step explanation:
4/7 tons = 7/8 x
4/7 / 7/8
32/49
The tons of concrete are required to cover the entire bridge is 32/49 tons.
What are fractions?A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 4/7.
How many tons is needed to cover the whole bridge?To determine this value, divide 4/7 by 7/8
4/7 ÷ 7/8
4/7 x 8/7 = 32/49 tons
To learn more about the division of fractions, please check: https://brainly.com/question/25779356
Find the center and radius of the circle whose equation is x 2 + y 2 - 6x - 2y + 4 = 0
Answer:
[tex]{ \tt{ {x}^{2} + {y}^{2} - 6x - 2y + 4 = 0 }} [/tex]
Center:
[tex]{ \tt{(3, \: 1)}}[/tex]
Radius:
[tex]{ \tt{radius = \sqrt{ {g}^{2} + {f}^{2} - c } }} \\ = \sqrt{36 + 4 - 4} \\ = 6 \: units[/tex]
The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller number. Find the numbers.
[ x + y = 90 ; x = 14 + 3y ]
Answer:
fourteen times six equals eighty-four, eighty-four plus six equals 90
expand this question (x+5)(x-3)
What is the value of x in the triangle below?
A. 18
B. 15
C. 6
D. 45
Answer:
it is b I already took it I just checked again
a) Arrange the following numbers so that the sum of any two neighbouring numbers is a perfect square.
7 , 11 , 9 , 14 , 16 , 2 , 25
Ex. 3+6 = 3^2 and 6+10 = 4^2
b) Find a way to arrange all of the intervenes from 1 to 17 to a list with the property from part a)
I'll do part (a) to get you started.
One possible answer to part (a) is 25,11,14,2,7,9,16
There are likely other possible answers.
The explanation is below.
==============================================================
Let's say 7 is the anchor value and we want to see which values could be its next door neighbor.
It can't be 11 since 7+11 = 18 isn't a perfect square.But 9 works because 7+9 = 16 is a perfect square (4^2 = 16)14 doesn't work because 7+14 = 21 isn't a perfect square16 doesn't work either since 7+16 = 23 isn't a perfect square2 however does work since 7+2 = 9 is a perfect squareLastly, 25 won't work because 7+25 = 32 isn't a perfect squareTo summarize this subsection, the anchor value 7 could have the neighbors 9 and 2.
So we could have 2,7,9 or 9,7,2 as a subsequence. We'll keep this in mind for later.
------------------------------------------------
Now we'll make 11 the anchor. We already checked 7 and it doesn't work.
9 doesn't work either because 11+9 = 20 isn't a perfect square
11+14 = 25 does work11+16 = 27 doesn't work11+2 = 13 doesn't work11+25 = 36 does workOf that list, only 14 and 25 are possible neighbors of the anchor value 11.
So we could have the subsequence 14,11,25 or 25,11,14.
------------------------------------------------
If 9 is the anchor, then,
9+7 = 16 works like we found earlier (section 1)9+11 = 20 doesn't work9+14 = 23 doesn't work9+16 = 25 does work9+2 = 11 doesn't work9+25 = 34 doesn't workThe values 7 and 16 are possible neighbors of 9. We could have the subsequence 7,9,16 or 16,9,7
Let's go back to the subsequence 2,7,9 and tack 16 at the end to get 2,7,9,16
------------------------------------------------
If 14 is the anchor, then,
7 doesn't work because 14+7 = 2111 does work either because 14+11 = 259 doesn't work because 14+9 = 2316 doesn't work because 14+16 = 302 does work because 14+2 = 1625 doesn't work since 14+25 = 39We could have the subsequence 11,14,2 or 2,14,11
Let's go with the first option and stick "11,14,2" in front of "2,7,9,16" to end up with the larger subsequence 11,14,2,7,9,16
We can then stick 25 at the front because 25+11 = 36 is a perfect square.
------------------------------------------------
So one possible sequence of values is 25,11,14,2,7,9,16
Here's the verification
25+11 = 36 is a perfect square (6^2 = 36)11+14 = 25 is a perfect square (5^2 = 25)14+2 = 16 is a perfect square (4^2 = 16)2+7 = 9 is a perfect square (3^2 = 9)7+9 = 16 is a perfect square (4^2 = 16)9+16 = 25 is a perfect square (5^2 = 25)Each pair of adjacent terms add up to a perfect square, so the answer is confirmed.
There are probably other solutions as well.
Side note: The video math channel "Numberphile" has a video discussing this topic in which you might be interested in. Search out "The square sum problem" with quotes (the presenter/teacher in the video is Matt Parker).
Answer:
25, 11, 14, 2, 7, 9, 16.
Step-by-step explanation:
25 + 11 = 6^2
11 + 14 = 5^2
14 + 2 = 4^2
2 + 7 = 3^2
7 + 9 = 4^2
9 + 16 = 5^2
solve
[tex]100 {5}^{2} - 500 {5}^{6} [/tex]
Please help before 9:00 pm
verify a(b-c)=ab-ac for a=1.6;b=1/-2;& c=-5/-7
Given:
[tex]a=1.6,b=\dfrac{1}{-2},c=\dfrac{-5}{-7}[/tex]
To verify:
[tex]a(b-c)=ab-ac[/tex] for the given values.
Solution:
We have,
[tex]a=1.6,b=\dfrac{1}{-2},c=\dfrac{-5}{-7}[/tex]
We need to verify [tex]a(b-c)=ab-ac[/tex].
Taking left hand side, we get
[tex]a(b-c)=1.6\left(\dfrac{1}{-2}-\dfrac{-5}{-7}\right)[/tex]
[tex]a(b-c)=1.6\left(-\dfrac{1}{2}-\dfrac{5}{7}\right)[/tex]
Taking LCM, we get
[tex]a(b-c)=1.6\left(\dfrac{-7-10}{14}\right)[/tex]
[tex]a(b-c)=\dfrac{16}{10}\left(\dfrac{-17}{14}\right)[/tex]
[tex]a(b-c)=\dfrac{8}{5}\left(\dfrac{-17}{14}\right)[/tex]
[tex]a(b-c)=-\dfrac{68}{35}\right)[/tex]
Taking right hand side, we get
[tex]ab-ac=1.6\times \dfrac{1}{-2}-1.6\times \dfrac{-5}{-7}[/tex]
[tex]ab-ac=-\dfrac{16}{20}-\dfrac{8}{7}[/tex]
[tex]ab-ac=-\dfrac{4}{5}-\dfrac{8}{7}[/tex]
Taking LCM, we get
[tex]ab-ac=\dfrac{-28-40}{35}[/tex]
[tex]ab-ac=\dfrac{-68}{35}[/tex]
Now,
[tex]LHS=RHS[/tex]
Hence proved.
Select all that apply.
The slope of the graph of a direct variation function is -3. Which of the following is true?
The equation is y = -3x.
The function is linear.
The equation of the function is y = -x .
The point (2, -6) is on the graph of the function.
a and b are correct
c is wrong
d can't be decided, because it can be true for one case, but not for others.
so only go for a and b
Answer:
B. The function is linear. (A and D COULD work)
Step-by-step explanation:
If the graph of a direct variation function has a slope of -3, then we know that the function is linear, and that m in the equation y = mx + b is -3. However, option A could be incorrect since we don't know if there is a y-intercept or not. C is wrong because of -3 being the slope, and D would only be true if A was also correct. So that leaves B. (If you know that there is more than one option, then A, B, and D are correct.)
If the product of two numbers is 1800 and its H.C.F. Is 30, find the L.C.M.
Answer:
LCM = 60
Step-by-step explanation:
Product = HCF × LCM
1800 = 30 × LCM
LCM = 1800/30
∴ LCM = 60
write a inequality phrase: you have to be at least 21 years of age
Answer:
[tex]a\geq 21[/tex]
Step-by-step explanation:
"At least" is inclusive, so you can be 21 years old.
Answer:
a≥ 21
Step-by-step explanation:
Let a = age
At least means greater than or equal to
a≥ 21
Solve for ppp. 16-3p=\dfrac23p+516−3p= 3 2 p+516, minus, 3, p, equals, start fraction, 2, divided by, 3, end fraction, p, plus, 5 p=p=p, equals
Given:
The given equation is:
[tex]16-3p=\dfrac{2}{3}p+5[/tex]
To find:
The value of p.
Solution:
We have,
[tex]16-3p=\dfrac{2}{3}p+5[/tex]
Multiply both sides by 3.
[tex]3(16-3p)=3\left(\dfrac{2}{3}p+5\right)[/tex]
[tex]48-9p=2p+15[/tex]
Isolating the variable terms, we get
[tex]48-15=2p+9p[/tex]
[tex]33=11p[/tex]
Divide both sides by 11, we get
[tex]\dfrac{33}{11}=p[/tex]
[tex]3=p[/tex]
Therefore, the required solution is [tex]p=3[/tex].
Answer:
p=3
Step-by-step explanation:
i got it right on khan
PLEASE HELP WILL GIVE BRAINSLIST
Answer: 3. 55° 2. 225° 1. 125°
Step-by-step explanation: don't want brainliest
1. What is the sum of 3/4 and 4/5?
what is the quotient
Answer:
The quotient is 4x+5 and the remainder is -13
Step-by-step explanation:
Using synthetic division
-5 4 25 12
Bringing down the 4 and multiplying
-5 4 25 12
↓ -20 -25
----------------------
4 5 -13
The quotient is 4x+5 and the remainder is -13
Answer:
4x +5 [tex]\frac{-13}{x+5}[/tex]
Step-by-step explanation:
. 4x +5 [tex]\frac{-13}{x+5}[/tex]
x + 5 | 4x^2 + 25x + 12
- 4x^2 + 20x
5x + 12
5x + 25
-13
If triangle LMQ is similar to triangle LNP, calculate the length of segment LP.
Answer:
LP = 15
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{LM}{LN}[/tex] = [tex]\frac{LQ}{LP}[/tex] , substitute values
[tex]\frac{4}{10}[/tex] = [tex]\frac{LQ}{LQ+QP}[/tex]
[tex]\frac{2}{5}[/tex] = [tex]\frac{LQ}{LQ+9 }[/tex] ( cross- multiply )
5LQ = 2(LQ + 9) = 2LQ + 18 ( subtract 2LQ from both sides )
3LQ = 18 ( divide both sides by 3 )
LQ = 6
Then
LP = LQ + QP = 6 + 9 = 15
A cash register at a store contains $277 bills. There are six more $5 bills than $10 bills. The number of $1bills is two more than 24 times the number of $10 bills. How many bills of each kind are there
Answer: See explanation
Step-by-step explanation:
Your question isn't well written, the store contains $227 and not $277.
let c be the number of $1 bills
let f be the number of $5 bills
let t be the number of $10 bills.
Therefore, the equation will be:
1c + 5f + 10t = 227
Since there are six more $5 bills than $10 bills, therefore,
f = t+6
Also, the number of $1 bills is two more than 24 times the number of $10 bills and this will be:
c = 24t + 2
Now, we substitute the equation for f and c into the main equation and this will be:
1c + 5f + 10t = 277
1(24t + 2) + 5(t + 6) + 10t = 227
24t + 2 + 5t + 30 + 10t = 227
39t + 32 = 227
39t = 227 - 32
39t = 195
t = 195/39
t = 5
Therefore, there are 5 $10 bills
Since c = 24t + 2
c = 24(5) + 2
c = 120 + 2
c = 122
Therefore, there are 122 $1 bills
Since f = t+6
f = 5+6
f = 11
Therefore, there are 11 $5 bills.
Gary's income and expenses in a month are 4,000 and 3,360 respectively.
a) What percentage of his income are expenses?
b) What percentage of his income is savings?
(SHOW YOUR WORK!)
Answer:
84%
Step-by-step explanation:
3360/4000=.84
.84=84%
Explain how to solve 5^(x-2)= 8 using the change of base formula
Answer:
x = 3.3
Step-by-step explanation:
A equation is given to us and we need to solve out for x. The given equation is ,
[tex]\sf\longrightarrow 5^{x -2}= 8 [/tex]
Take log on both sides with base as " 10" . We have ,
[tex]\sf\longrightarrow log_{10} 5^{x-2}= log_{10}\ 8[/tex]
Simplify using the property of log , [tex]\sf log a^m = m log a [/tex] , we have ,
[tex]\sf\longrightarrow ( x -2) log_{10} 5 = log_{10} 8 [/tex]
Simplify ,
[tex]\sf\longrightarrow ( x -2 ) log_{10}5 = log_{10} 2^3[/tex]
Again simplify using the property of log ,
[tex]\sf\longrightarrow (x-2) log 5 = 3 log 2[/tex]
We know that log 5 = 0.69 and log 2 = 0.301 , on substituting this , we have ,
[tex]\sf\longrightarrow ( x - 2 ) = \dfrac{ 3\times 0.301}{0.69}[/tex]
Simplify the RHS ,
[tex]\sf\longrightarrow x - 2 = 1.30 [/tex]
Add 2 both sides ,
[tex]\sf\longrightarrow \boxed{\blue{\sf x = 3.30}}[/tex]
Hence the Value of x is 3.30 .
Answer:
its actually 3.292 because we round to the nearest thousandth and thats not even the equation you use above
Step-by-step explanation:
For this equation we use the formula log a^m=m (log a) so the equation will be written as log 5 (5^x-2) = log 5 (8). You use the base, which is 5, and use log to base 5 on both sides of the equation. Then you take the exponent " x-2" and write( x-2) log 5 (5) = log 5(8). Since log a =1, you multiply that 1 by x-2, which keeps it x-2. Making the equation x-2 = log 5 (8). Next, we use the change of the base properties with the formula log b^y= log y/ log b. The equation will be written as x-2 = log 8/ log 5, since 5 is the base it stays in the bottom or basement. We then add +2 to both sides of x-2 and log 8/ log 5. To solve this equation, you can find out what log 8 and log 5 are and divide those and add +2 to solve. So log 8 = 0.903 and log 5 = 0.698970 and divide those to get 1.29190 +2 and you get the answer rounded as 3.292.
Can someone help me with this math homework please!
Answer:
Below
Step-by-step explanation:
From the graph the first local minimum is -16.18
The local maximum is 3.75
The second local minimum is -3.
Answer:
Over the interval (-3,0), the local minimum is -16.18Over the interval [0,3], the local maximum is -3.75Over the interval [0,3], the minimum is -3----------------------
Hope it helps..
Have a great day!!
Urgent i need help!!…….
Answer:
Step-by-step explanation:
These are similar triangles. We know that because we know that all right triangles are similar. The height of the red one is 8 and the height of the blue one is 4; that means that the red one is twice the size of the blue one; likewise, the blue one is half the size of the red one. That means that ALL the measurements of these triangles exist in that ratio...even the base of the blue one. If the base of the red one is 3, and the red one is twice the size of the blue one, then the base of the blue one is 3/2 or 1.5. I can't see your choices because they are too small.
A library has 160 books. 3/8 are story books, 1/4 are poetry books and the remainder are books. What fraction is comic books?
Answer:
1/8
Step-by-step explanation:
1/4*2/2=4/8
4/8+3/8=7/8
1-7/8=1/8
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
10
(-4,8)
(0,0)
. 10
10
The answer is y= -2x.
The equation of the line passing through points (0, 0) and (-4, 8) is y = -2x
What is an equation of line?The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.
Given is a graph of a line passing through points (0, 0) and (-4, 8), we need to find the equation of the line,
We know that, the equation of a line passing through two points is given by,
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Here, (x₁, y₁) and (x₂, y₂) are (0, 0) and (-4, 8)
So, the equation of the line =
y-0 = 8/(-4) (x-0)
y = -2x
Hence, the equation of the line passing through points (0, 0) and (-4, 8) is y = -2x
Learn more about equation of line, click;
https://brainly.com/question/21511618
#SPJ7
What is the surface area of a sphere with a diameter of 14 cm?
Question 6 options:
175.84 cm^2
351.68 cm^2
615.44 cm^2
2461.76 cm^2
Show your work:
9514 1404 393
Answer:
(c) 615.44 cm^2
Step-by-step explanation:
The surface area of a sphere is given by ...
A = 4πr² . . . . where r is the radius, half the diameter
A = 4(3.14)(7 cm)² = 196(3.14) cm² = 615.44 cm²
*Please Help!*
What is the volume of water, to the nearest tenth of a cubic metre, that would fill this spa tub?
First cylinder= 0.75m diameter, 0.80m height
Cylinder Underneath= 1.25m diameter, 0.70m height
Semi Sphere that holds both cylinders= 3m long
Answer:
The volume of water that will fill the spa tub is 5.9 cubic meters.
Step-by-step explanation:
Volume of water that would fill the spa tub = volume of semi sphere - (volume of the first cylinder + volume of the second cylinder)
i. volume of first cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
where r is the radius and h is the height of the cylinder.
r = [tex]\frac{0.75}{2}[/tex] = [tex]\frac{3}{8}[/tex]
= 0.375 m
h = 0.80 m
volume of the first cylinder = [tex]\frac{22}{7}[/tex] x [tex](\frac{3}{8} )^{2}[/tex] x 0.8
= 0.3536 cubic meters
ii. volume of the cylinder underneath = [tex]\pi[/tex][tex]r^{2}[/tex]h
r = [tex]\frac{1.25}{2}[/tex] = [tex]\frac{5}{8}[/tex]
= 0.625
h = 0.70 m
volume of the cylinder underneath = [tex]\frac{22}{7}[/tex] x [tex](\frac{5}{8}) ^{2}[/tex] x 0.7
= 0.8594 cubic meters
iii. volume of the semi sphere = [tex]\frac{2}{3}[/tex] [tex]\pi[/tex][tex]r^{3}[/tex]
where r is the radius = 1.5 m
volume of the semi sphere = [tex]\frac{2}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](1.5)^{3}[/tex]
= 7.0714 cubic meters
Thus,
volume of the water to fill the spa tub = 7.0714 - (0.3536 + 0.8594)
= 5.8584
The volume of water that will fill the spa tub is 5.9 cubic meters.