Answer:
x=9
if
a^b = a^c
then b=c
so in this case x=9
the interest paid for borrowing qn amount of money for 3yrs at the rate of 4%is n108 find the amount of the money borrowed
Answer:
$864.94
Step-by-step explanation:
So the amount of money over time can be given with an exponential function y=a(b)^x or more specifically y=a(1+r)^x where r is the growth rate (interest rate)
So the equation can be written as
[tex]m= P(1.04)^t[/tex] where m represents the amount of money over time, P represents the principle amount, and t represents time in years. Since we're given the amount of interest paid and not the total amount which includes the initial amount borrowed you have to subtract P from the equation. This will give us the equation that we'll use to find the initial amount
[tex]I = P(1.04)^t-P[/tex] where I represents the interest paid.
plug the values into the equation
[tex]108 = P(1.04)^3-P\\108 = P(1.124864) - P\\108 = 0.124864P\\\\864.941 = P[/tex]
How would you answer this question?
Answer:
32
Step-by-step explanation:
the pattern of sticks from the first 3 diagrams is
7 , 12 , 17 ,..
note the pattern increases by 5 each time , then continue by adding 5 to the previous value.
4th = 17 + 5 = 22
5th = 22 + 5 = 27
6th = 27 + 5 = 32
Determine the horizontal asymptote for the rational function.
Y= 5
Y= -5
Y= 1
Y= -1
Answer:
The horizontal asymptote is y=1 and
The vertical asymptote is x=5
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
By the Pythagorean theorem,
[tex]a^{2}+12^{2}=13^{2}\\\\a^{2}+144=169\\\\a^{2}=25\\ \\ a=\boxed{5}[/tex]
55. The Cone Problem Begin with a circular piece of paper with
4-in. radius as shown in (a). Cut out a sector with an arc length o
x. Join the two edges of the remaining portion to form a cone
with radius r and height h, as shown in (b).
4 in.
4 in.
(a)
(b)
(a) Explain why the circumference of the base of the cone is
8T X
(b) Express the radius r as a function of x.
(c) Express the height has a function of x.
(d) Express the volume V of the cone as a function of x.
pls helpppp
The circumference of the base of the cone is 8π - x since the base is equal to go the arc length of the remainder of the circle.
How to calculate the values?The radius r as a function of x will be:
8π - x = 2πr
r = (8π - x)/2π
r = 4 - x/2π
The height has a function of x will be:
r² + h² = 16
h² = 16 - r²
where r = 4 - x/2π
h = √16 - ✓(4 - x/2π)²
h = 4✓(4 - x/2π)²
The volume V of the cone as a function of x will be:
= 1/3 πr²h
= π/3(4 - x/2π)² 4✓(4 - x/2π)²
Learn more about cone on:
brainly.com/question/1082469
#SPJ1
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
Option C is equal to 7^1/3
sqrt(32x^3) - sqrt(16x^3) + root(4,x^3) -sqrt(2x^3)
An expression is defined as a set of numbers, variables, and mathematical operations. The simplified version of the given expression is (3√2-2)√x³.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression [tex]\sqrt{32x^3} - \sqrt{16x^3} + \sqrt{4x^3} -\sqrt{2x^3}[/tex] can be simplified as shown below.
[tex]\sqrt{32x^3} - \sqrt{16x^3} + \sqrt{4x^3} -\sqrt{2x^3}\\\\=\sqrt{x^3}(\sqrt{32}-\sqrt{16}+\sqrt{4}-\sqrt{2}})\\\\= \sqrt{x^3} (4\sqrt{2}-4+2-\sqrt2)\\\\= \sqrt{x^3} (3\sqrt{2}-2)[/tex]
Hence, The simplified version of the given expression is (3√2-2)√x³.
Learn more about Expression:
https://brainly.com/question/13947055
#SPJ1
Lightning quickly heats the air causing it to expand, which produces the sound of thunder. Sound travels approximately 1 mile in 5 seconds. Knowing D = rt, how far away is a thunderstorm when you notice a 3- second delay between the flash of lightning and the sound of thunder? Lightning quickly heats the air causing it to expand , which produces the sound of thunder . Sound travels approximately 1 mile in 5 seconds . Knowing D = rt , how far away is a thunderstorm when you notice a 3 second delay between the flash of lightning and the sound of thunder ?
Answer:
every second it travels 1/5 of a mile after 3 seconds you are 3/5 miles away
Hope This helps!
[tex]\Large\text{HELP ASAP!!!!!}[/tex]
[tex]\boxed{\stackrel\circ\circ\boxed{\textbf{what is the sin of -4\pi /3??$}}\stackrel\circ\circ}[/tex]
[tex]\dfrac{\sqrt{~~} }{[~~]}[/tex] [tex]\text{that's what the answer should look like}[/tex]
[tex]\text{Spam will NOT be tolerated!!!!!}[/tex]
Step-by-step explanation:
Did you mean.
[tex] \text{what \: is \: the \:sin \: of } \: - \frac{4\pi}{3} \: ?[/tex]
[tex] \: [/tex]
[tex] = \sin( - \frac{4\pi}{3} ) [/tex]
[tex] = \sin( - \frac{4 \times 180 \degree}{3} ) [/tex]
[tex] = \sin( - \frac{4 \times \cancel{180} \degree}{ \cancel3} ) [/tex]
[tex] = \sin( - 4 \times 60 \degree) [/tex]
[tex] = \sin( - 240 \degree) [/tex]
[tex] = \sin(0 - 240 \degree) [/tex]
[tex] = \sin(360 \degree - 240 \degree) [/tex]
[tex] = \sin(120 \degree) [/tex]
[tex] = \frac{1}{2} \sqrt{3} \: \: \text{is \: the \: answer}[/tex]
2y + 9 = 4 pls aswer the question pls pls
Step-by-step explanation:
2y+9= 4
2y=-5
y=-5/2
y= -2and 1/2
which of the following number is not a cube number
A) 10000
B)3125
C)64
D)729
Answer:
3125
Step-by-step explanation:
³√3125 comes around 14 not a whole no so not a perfect cubeAnd
10000=10³64=4³729=9³WILL MARK BRAINLIEST!!! According to the synthetic division below, which of the following statements are true? Check all that apply.
According to the given synthetic division, the statements that are true are; Options A, C and E
How to carry out Synthetic Division?
In the synthetic calculation we use the coefficient of the dividend
with the factors of the function.
Therefore;
3 , -13 , 4 are the coefficient of the dividend 3x² - 13x + 4
Therefore, the divisor is 4 and as such x = 4 is a root of f(x) = 3x² - 13x + 4
Also, it means that (x - 4) is a factor of the dividend F(x) = 2x² - 2x - 12
- The quotient is the last line of the synthetic division. Thus, the coefficients of quotient are 3, -1.
- The quotient is 1 degree less than the dividend and so the degree of the dividend is 2.
- The degree of the quotient is 1 and so the he quotient is 3x - 1.
Thus, options A, C and E are correct
Read more about Synthetic Division at; https://brainly.com/question/13133440
#SPJ1
The sum of two consecutive even numbers is 38. What is the smaller number?
Even numbers = 2x +2
Consecutive even numbers = 2x+4
then
(2x+2) + (2x+4)= 38
2x + 2 + 2x + 4 = 38
2x + 2x + 2 + 4 = 38
4x + 6 = 38
4x = 38 - 6
x = 32 :4
x = 8
2x+ 2 = 2(8)+2 = 16 + 2 = 18
2x+4 = 2(8) +4 = 16 + 4 = 20
The smallest number is 18
[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
Answer:
18 is the smaller number
Step-by-step explanation:
Let us take X for the first even number (it will also be the smallest)
x, x+1, x+2, so on..
the consecutive even number of x+2 is the next even number after x.
so you now get this equation...
x+(x+2) = 38
2x + 2 = 38
2x = 36
x=18
At a track meet, the height of John's high jump was within 6 inches of the track record of 76 inches. What is
the range of heights for John's jump?
The range:
[tex]{x|70\leq x\leq 82[/tex]
What are the next three terms in the sequence 2, -4, -16, 32
Answer:
128, -256, -1024
Step-by-step explanation:
multiply 32 by 4, multiply 128 by -2, multiply -256 by 4
20 POINTS TO THE FIRST RIGHT ANSWER!!!! PLS HELP
A sculptor is planning to order a rectangular block of composite stone to sculpt a lion. The sculptor anticipates that the lion will be 5 feet long, about 2 feet wide and at the tallest part of the lion's body, have a height of 3.5 feet. The composite stone weighs 40 pounds per cubic foot. To the nearest cubic foot, estimate the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue.
The weight of the smallest rectangular block is ____
pounds.
The weight of the smallest rectangular block is 1400 pounds.
What is density?The density refers to the heaviness of an object. It is the ratio of mass to volume.
Then we have
Density = Mass / Volume
A sculptor is planning to order a rectangular block of composite stone to sculpt a lion.
The sculptor anticipates that the lion will be 5 feet long, about 2 feet wide and at the tallest part of the lion's body, have a height of 3.5 feet.
The composite stone weighs 40 pounds per cubic foot.
To the nearest cubic foot, estimate the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue.
Then the weight of the smallest rectangular block will be
Mass = density x volume
The volume will be
V = 5 x 2 x 3.5
V = 35 cubic feet
Then the weight will be
Mass = 40 x 35
Mass = 1400 pounds
More about the density link is given below.
https://brainly.com/question/15164682
#SPJ1
Common types of data patterns that can be identified when examining a time series plot include all of the following except ______.
Answer:
Vertical is the answer
Which table represents a linear function?
Answer:
The table on the far left is a linear function.
Step-by-step explanation:
The table on the far left is the function
[tex]y = \frac{1}{2} x[/tex]
A similarity transformation maps AABC to AJKL The measure of ZA of prelmage AABC Is 105°. The scale factor of the dilation in the similarity
transformation is 1.5. If ZA In the prelmage corresponds to ZJ in the image, what is m
a 70°
b 140°
c 105°
d 35°
its reserved.
Answer:
The answer is 105.
Step-by-step explanation:
Which graph represents the following system of inequalities? x < - 2x + 4; y < x + 3; x < 3
Graph C represents the following system of inequalities. For clarification refer to the attachment.
What is the definition of inequality?Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.
Given relations;
x < - 2x + 4
y < x + 3
x < 3
Hence graph C represents the following system of inequalities.
To learn more about inequity, refer to https://brainly.com/question/20383699.
#SPJ1
Divide : (8a^2b^4 - 20a^4b^5 + 48a^6b^6) by 4a^2b^4
Hey there ! please refer to the attachment .
I hope its help you !
Which graph shows the solution to the system of linear inequalities? Y<2x-5 y>-3+1
Helppppp
Answer:
Is the second expression written correctly? It reduces to y>-2, since no x is in the equation.
Step-by-step explanation:
We can graph the two equations. See attached image. If y>2 is the correct expression, all points to the right.
If the equation was meant to read y=-3x+1, then graph the revised expression.
Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as
A data set having two values that have the highest and equal frequencies will have a bimodal distribution. Hence, option D is the right choice.
A symmetric distribution occurs when the mean, median, and mode all occur at the same location and the values of the variables occur at regular intervals.The few low scores in a negatively skewed distribution tend to push the mean to the left, thus the mean is typically lower than the median.The mode is consistently less than the mean and median in a positively skewed distribution.A continuous probability distribution having two distinct modes, that is, two separate values with the highest and equal frequencies is referred to as a bimodal distribution.Thus, a data set having two values that have the highest and equal frequencies will have a bimodal distribution. Hence, option D is the right choice.
The given question is incomplete. The complete question is:
"Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as:
A. Symmetric distribution
B. Negatively skewed distribution
C. Positively skewed distribution
D. Bimodal distribution."
Learn more about data sets at
https://brainly.com/question/14802806
#SPJ4
The absolute value of 5.8 is _________.
Answer:
5.8
Step-by-step explanation:
please help me answer this matrices question ASAP
The value of a₃₂ is 7 , Option A is the correct answer.
What is a Matrix ?Matrix is an array or an arrangement of numbers or expression in rows and column format.
The matrix is given
For a matrix of size mxn , m is the row and n is the column of the matrix.
a₃₂ = This term means 3rd row and 2nd column of the matrix
which is 7
Therefore the value of a₃₂ is 7 , Option A is the correct answer.
To know more about Matrix
https://brainly.com/question/9967572
#SPJ1
Solve the system. 2x y = −3 −2y = 6 4x write each equation in slope-intercept form. y = x y = x
The system of equation has an infinitely many solutions
How to solve the system of equations?The equations are given as:
2x + y = -3
-2y = 6 + 4x
Express 2x + y = -3 in slope-intercept form
y = - 3 -2x
Divide through by -2 in -2y = 6 + 4x
y = -3 - 2x
So, we have:
y = - 3 -2x and y = -3 - 2x
Both equations are the same.
This means that the system of equation has an infinitely many solutions
Read more about system of equations at:
https://brainly.com/question/14323743
#SPJ1
help this homework and it geometry
1) Given
2) Segment addition postulate
3) Substitution property
4) Segment addition postulate
5) Transitive property of equality
Write an equation in slope intercept form with the given information.
Goes through points (-2,-5) and (3,5)
Answer:
infinity 2 is the slope for these point .
Step-by-step explanation:
given points are
(-2,-5) and (3,5)
comparison to
(x1,y1) and (x2,y2)
here ,
[tex]slope = \frac{y2 - y1}{x2 - x1} [/tex]
slope= 5-(-5)/3-(-2)
slope =10/5
slope=2
glad to help you this may help you :)
7. Which of the verbal descriptions best matches the function below?
f(x)=0.02x+150
Gene earns 2% interest after depositing $150 into his account , Option D.
What is a Function ?A function is a law that relates an independent variable and a dependent variable with each other.
The function given is
f(x) = 0.02 x +150
Option D , Gene earns 2% interest after depositing $150 into his account
So this verbal description matches the function given as it represents , the total account balance of Gene .
Therefore Option D is the correct answer.
To know more about Function
https://brainly.com/question/12431044
#SPJ1
The radius of a sphere is 3 inches. Which represents the volume of the sphere? 12Ï€ cubic inches 36Ï€ cubic inches 64Ï€ cubic inches 81Ï€ cubic inches.
Answer: 113 inches cubed
Step-by-step explanation:
Volume of a sphere = 4/3 Pi r^3
Radius = 3 inches
Volume = 113 inches cubed
Hope I helped!
