Answer:
The in the calculation the step 3 is the first incorrect step.
Step-by-step explanation:
The function [tex]f(x) = 800(1.09)^{3x}[/tex] shows the growth due to interest that Jim earns on an investment.
To get an equivalent function we are given the following steps:
[Step 1] [tex]f(x) = 800(1.09)^{3x}[/tex]
[Step 2] [tex]f(x) = 800(1.09^{3}) ^{x}[/tex]
[Step 3] [tex]f(x) = 800(1.09 \times 3)^{x}[/tex]
[Step 4] [tex]f(x) = 800(3.27)^{x}[/tex]
The in the calculation the step 3 is the first incorrect step.
And this will be [tex]1.09^{3} = (1.09)^{3} = 1.295 \neq 3.27[/tex] (Answer)
Step 3
It is multiplying three instead of doing 9x9x9 she did 9x3
For similar triangles, the side lengths are proportional. So, you can write a proportion relating the two pairs of vertical and horizontal side lengths. For the line y = 2x, a triangle can be drawn 2 units up and 1 unit right from the origin.
Write a proportion relating the side lengths of the triangle to any other triangle that has the line as a hypotenuse, a horizontal length of x units, and a vertical length of y units.
Answer:
[tex]\frac{y}{2}=\frac{x}{1}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
The corresponding vertical sides are y and 2
The corresponding horizontal lines are x and 1
so
The proportion is equal to
[tex]\frac{y}{2}=\frac{x}{1}[/tex]
What's 286 divided by 20??
Thanks if you help! :)
Answer:
14.3
Step-by-step explanation:
percent: 14.3%
decimal: 14.3
fraction: 14 3/10
Answer:
I got 143/10 ;-;
But as a decimal it's 143.0 and percent is 14.3%
What's x for 12x+1=4x+9
Nevermind someone already answered it.
x^2-5x=14 solve for x
Answer:
x=7, -2.
Step-by-step explanation:
x^2-5x=14
x^2-5x-14=0
factor out the trinomial,
(x-7)(x+2)=0
zero property,
x-7=0, x+2=0,
x=0+7=7,
x=0-2=-2
Answer:
x = - 2, x = 7
Step-by-step explanation:
Given
x² - 5x = 14 ( subtract 14 from both sides )
x² - 5x - 14 = 0 ← in standard form
Consider the factors of the constant term (- 14) which sum to give the coefficient of the x- term (- 5)
The factors are - 7 and + 2, since
- 7 × 2 = - 14 and - 7 + 2 = - 5, thus
(x - 7)(x + 2) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 7 = 0 ⇒ x = 7
Home city bank pays 5% interest compounded quarterly on regular savings accounts. Miguel cardosa deposited 1000 for 1 year. He made no other deposits or withdrawals. How much interest did he earn during the year.
Answer:
The interest earned was $50.95
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=1\ year\\ P=\$1,000\\ r=5\%=5/100=0.05\\n=4[/tex]
substitute in the formula above
[tex]A=1,000(1+\frac{0.05}{4})^{4*1}[/tex]
[tex]A=1,000(1.0125)^{4}[/tex]
[tex]A=\$1,050.95[/tex]
Find the interest earned I
we know that
[tex]I=A-P[/tex]
substitute the values
[tex]I=\$1,050.95-\$1,000=\$50.95[/tex]
Solve the following system of equations using the substitution method. x=2y2x+5y=9
Answer:
x=2, y=1. (2, 1).
Step-by-step explanation:
x=2y
2x+5y=9
-------------
2(2y)+5y=9
4y+5y=9
9y=9
y=9/9
y=1
x=2(1)=2
how many times can 7 go into 50
Answer:
7 without going over
Step-by-step explanation:
The number 7 can go into 50 a total of 7 times with 1 remainder.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
The number 7 can go into 50 a total of 7 times because 50 / 7 = 7 with 1 remainder.
To understand this, consider that when you divide 50 by 7, you are trying to find out how many groups of 7 can be created from 50. Since 50 is a multiple of 7 (50 is divisible by 7 with 1 remainder), there will be an integer number of groups. In this case, that integer is 7, so 7 groups of 7 can be created from 50.
Learn more about the number system here:
brainly.com/question/21751836
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WILL GIVE BRAINLIEST IF CORRECT! 25 PTS
Which statement is true about the graph of this equation?
y + 4 = 4(x + 1)
A.
The graph is a line that goes through the points (1,-4) and (0,0).
B.
The graph is a line that goes through the points (1,4) and (2,8).
C.
The graph is a line that goes through the points (-4,-1) and (-3,-3).
D.
The graph is a line that goes through the points (4,1) and (5,5).
Answer:45x-5 is the answer
Step-by-step explanation:
(4,1) and 5,5 add them both
Answer:
B.) The graph is a line that goes through the points (1,4) and (2,8).
Step-by-step explanation:
1.) (4) + 4 = 4((1) +1)
2.) 8 = 4 + 4
3.) 8 = 8 --> Correct
4.) (8) + 4 = 4((2) + 1)
5.) 12 = 8 + 4
6.) 12 = 12 --> Correct
an experimental model for suspension bridges built In one section, cable runs from the top of the tower down to the roaday, touching there, and up again ,to the top of the second tower. The towers are both 16 inches tall and stand 80 inches apart. At some point along the road from the lowest point of the cable, the cable is 1.44 inches above the roadway. Find tha distance between that point and the base of the nearest tower.
The distance between the point where the cable is 1.44 inches above the roadway and the base of the nearest tower is : [tex]\[\(28 \text{ inches}}\][/tex].
To find the distance between the point where the cable is 1.44 inches above the roadway and the base of the nearest tower, we need to understand the mathematical model for the suspension bridge cable. This cable typically forms a parabolic shape.
Let's establish our coordinate system:
- Place the origin [tex]\((0, 0)\)[/tex] at the lowest point of the cable.
- The towers are at [tex]\(x = -40\)[/tex] inches and [tex]\(x = 40\)[/tex] inches since they are 80 inches apart.
- The height of the towers is 16 inches.
The equation of the parabola can be written in the vertex form [tex]\(y = ax^2\)[/tex] since the vertex is at the origin [tex]\((0, 0)\)[/tex].
At the position of the towers (x = ±40 inches), the cable is 16 inches high:
[tex]\[y(40) = 16\][/tex]
[tex]\[a(40)^2 = 16\][/tex]
[tex]\[1600a = 16\][/tex]
[tex]\[a = \frac{16}{1600} = \frac{1}{100}\][/tex]
So, the equation of the parabola is:
[tex]\[y = \frac{1}{100}x^2\][/tex]
We need to find the point where the cable is 1.44 inches above the roadway:
[tex]\[\frac{1}{100}x^2 = 1.44\][/tex]
[tex]\[x^2 = 1.44 \times 100 = 144\][/tex]
[tex]\[x = \pm\sqrt{144} = \pm 12\][/tex]
Therefore, the points where the cable is 1.44 inches above the roadway are [tex]\(x = 12\)[/tex] inches and [tex]\(x = -12\)[/tex] inches.
The distance from [tex]\(x = 12\)[/tex] inches to the nearest tower at [tex]\(x = 40\)[/tex] inches is:
[tex]\[40 - 12 = 28 \text{ inches}\][/tex]
Similarly, the distance from [tex]\(x = -12\)[/tex] inches to the nearest tower at [tex]\(x = -40\)[/tex] inches is:
[tex]\[-12 - (-40) = 28 \text{ inches}\][/tex]
Thus, the distance between the point where the cable is 1.44 inches above the roadway and the base of the nearest tower is:
[tex]\[\boxed{28 \text{ inches}}\][/tex]
yyyeeeeeeeee
1-2k-2k=5
Answer:
k=-1
Step-by-step explanation:
1-2k-2k=5
1-4k=5
4k=1-5
4k=-4
k=-4/4
k=-1
Select the correct answer.
How do you express a gain of 4 yards in a football game as a rational number?
OA. 4.5 yards
OB. +4 yards
OC. I yards
OD. - yards
E. - 4 yards
Answer:
B
Step-by-step explanation:
if you gain yards its plus 4 yards or how ever many yard to gain or lose.
Answer:
+4
Step-by-step explanation:
Because you GAIN 4
Use the following figure to answer the question.
∠ 1 and ∠ 2 are supplementary angles.
True
False
Answer:
True
Step-by-step explanation:
Because angles on a straight line are supplementary and these anglea <1 and <2 are supplementary angles
Answer: True
Step-by-step explanation:
When adding negative and positive numbers, you can use the associative and commutative properties to group all of the positive addends and then group all the negative addends. Which expression shows the second step of this method?
5 + (-1) + (-5) + (-2) + 11 + (-7) + 2
Answer:
The second step of this method is
[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=(5+11+2)-(1+5+2+7)[/tex]
The value of the given expression is
[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=3[/tex]
Step-by-step explanation:
Given expression is [tex]5+(-1)+(-5)+(-2)+11+(-7)+2[/tex]
To find the value of the given expression [tex]5+(-1)+(-5)+(-2)+11+(-7)+2[/tex]:
Arranging positive and negative addends by using the associative and commutative properties of the given expression as below:
[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=5+11+2+(-1)+(-5)+(-2)+(-7)[/tex]
[tex]=(5+11+2)-(1+5+2+7)[/tex]
[tex]=18-15[/tex]
[tex]=3[/tex]
[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=3[/tex]
The second step of this method is
[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=(5+11+2)-(1+5+2+7)[/tex]
The value of the given expression is
[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=3[/tex]
Ramona spend 8 hours making picture frames if each picture frame takes her 1/4 of hour to make how many picture frame does Ramona have?
?? “solve the missing elements for each problem. use 3.14 for area
Answer:
Problem 4:
Radius = 11 cm.
Circumference = 69.08 cm.
Problem 5:
Radius = 14 mm.
Circumference = 87.92 mm.
Problem 6:
Radius = 9 inches.
Circumference = 56.52 inches.
Problem 7:
Diameter = 32 ft.
Circumference = 100.48 ft.
Problem 8:
Diameter = 26 yards.
Circumference = 81.64 yards.
Problem 9:
Diameter = 12 cm.
Circumference = 37.68 cm.
Step-by-step explanation:
Problem 4:
Given:
Diameter GH = 22 cm
We need to find the radius EF and Circumference of the circle.
Now radius is given by half of the diameter
Also Circumference is given by π times diameter.
Radius EF = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 22 = 11 \ cm[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 22 = 69.08\ cm[/tex]
Hence Radius = 11 cm
Circumference = 69.08 cm.
Problem 5:
Given:
Diameter OP = 28 mm
We need to find the radius MN and Circumference of the circle.
Now radius is given by half of the diameter
Also Circumference is given by π times diameter.
Radius MN = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 28 = 14 \ mm[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 28 = 87.92\ mm[/tex]
Hence Radius = 14 mm
Circumference = 87.92 mm.
Problem 6:
Given:
Diameter EF = 18 inches
We need to find the radius CD and Circumference of the circle.
Now radius is given by half of the diameter
Also Circumference is given by π times diameter.
Radius CD = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 18 = 9 \ in[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 18 = 56.52\ in[/tex]
Hence Radius = 9 inches.
Circumference = 56.52 inches.
Problem 7:
Given:
Radius GH = 16 ft
We need to find the Diameter CD and Circumference of the circle.
Now Diameter is given by twice the radius.
Also Circumference is given by π times diameter.
Diameter KJ = [tex]2 \times radius = 2 \times 16 = 32 \ ft[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 32 = 100.48\ ft[/tex]
Hence Diameter = 32 ft.
Circumference = 100.48 ft.
Problem 8:
Given:
Radius LM = 13 yards
We need to find the Diameter CD and Circumference of the circle.
Now Diameter is given by twice the radius.
Also Circumference is given by π times diameter.
Diameter NO = [tex]2 \times radius = 2 \times 13 = 26 \ yards[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 26 = 81.64\ yards[/tex]
Hence Diameter = 26 yards.
Circumference = 81.64 yards.
Problem 9:
Given:
Radius NO = 6 cm
We need to find the Diameter CD and Circumference of the circle.
Now Diameter is given by twice the radius.
Also Circumference is given by π times diameter.
Diameter PQ = [tex]2 \times radius = 2 \times 6 = 12 \ cm[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 12 = 37.68\ cm[/tex]
Hence Diameter = 12 cm.
Circumference = 37.68 cm.
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
X + 10y = 29
x - y = 7
Answer:
x = 9, y = 2
Step-by-step explanation:
Given the 2 equations
x + 10y = 29 → (1)
x - y = 7 → (2)
Subtracting (2) from (1) term by term will eliminate the term in x
(x - x) + (10y - (- y)) = (29 - 7), that is
11y = 22 ( divide both sides by 11 )
y = 2
Substitute y = 2 in either of the 2 equations
Substituting in (2)
x - 2 = 7 ( add 2 to both sides )
x = 9
MNOP is a parallelogram. U is any point on side OP. Show that ar( MUN)= ar ( Δ △ PUM)+ar( UNO) △
Answer:
The Proof is below.
Step-by-step explanation:
Given:
[]MNOP is a Parallelogram
U is any point on side OP
To Show:
ar(Δ MUN)= ar ( Δ PUM)+ar (Δ UNO)
Proof:
Theorem:
If a triangle and parallelogram are on the same base and have the same altitude, the area of the triangle will be half that of the parallelogram.
If they have same altitude, they will lie between the same parallels.
Hence the area of the triangle will be equal to half that of the parallelogram.
Area of Parallelogram will be twice of Area of Triangle
∴ [tex]\textrm{Area of Parallelogram MNOP}=2\times (area\ of\ Triangle\ MUN)[/tex].............( 1 )
Also,
[tex]\textrm{Area of Parallelogram MNOP}=Ar(MUN) + Ar(PUM)+ Ar(UNO)[/tex]
Substituting equation 1 we get
[tex]2\times Ar(MUN)=Ar(MUN) + Ar(PUM)+ Ar(UNO)[/tex]
[tex]2\times Ar(MUN)-Ar(MUN) = Ar(PUM)+ Ar(UNO)[/tex]
[tex]Ar(MUN) = Ar(PUM)+ Ar(UNO)[/tex]...........Proved
Tony makes a phone call at a pay phone. The charge is 25 cents for the first four minutes,and 19 cents for each additional minute. Tony has $2.10 in change in his pocket. Write an inequality that can be used to find m, the maximum number of whole minutes he can talk on the phone
Explain to me what x is in this problem: 2/3=x/32
Answer:
x=21.33....
Step-by-step explanation:
2/3=x/32
cross product
3*x=2*32
3x=64
x=64/3
x=21.3
Cindy worked 4 hours each day for 12 days. She earned a total of $240. How much did Cindy earn per hour?
Answer:
$5 per hour
Step-by-step explanation:
12*4=48 hours
240/48=5
Does somebody know how to do this?
Answer:
Total length of running track is 371.24 m .
Step-by-step explanation:
Total running track = Running track around straight region + running track around curved region.
Running track around straight region = 2 × length of straight region
= 2×82 m
= 164 m
Running track around curved region = 2 × length of curved region
= 2 × π × radius of curved region
= 2 × 3.14 × 33 m
= 207.24 m
Therefore , total length of running track = 164 + 207.24 m
= 371.24 m
A publishing industry report predicts that magazine subscriptions will drop
by 10% each year. If this prediction is correct, then how many subscribers
will a magazine with 51,000 subscribers have in 7 years?
If necessary, round your answer to the nearest whole number.
Answer:
24,393 subscribers
Step-by-step explanation:
This is exponential decay problem. The formula for exponential decay is:
[tex]F=P(1-r)^t[/tex]
Where
F is the future value (what we are looking for, in 7 years)
P is the present amount (that is 51,000)
r is the rate of decrease per year (r = 10% = 10/100 = 0.1)
t is the time, in years (t = 7)
Now substituting, we get:
[tex]F=P(1-r)^t\\F=51,000(1-0.1)^7\\F=51,000(0.9)^7\\F=24,393.14[/tex]
Rounding to nearest whole number,
Number of subscribers after 7 years = 24,393 subscribers
Using the exponential decay formula, a magazine with an initial 51,000 subscribers will have approximately 24,393 subscribers left in 7 years if subscriptions decline by 10% annually.
Explanation:The question is asking to predict the number of magazine subscribers after a period of 7 years, assuming a 10% annual decline. To calculate this, we can use the formula for exponential decay, which is A = P(1 - r)^t, where A is the amount after time t, P is the initial principal amount (51,000 subscribers), r is the rate of decline (10% or 0.10), and t is the time in years (7 years). Calculating this, we get:
Initial subscribers: 51,000Annual decline rate: 10%Number of years: 7Subscribers after 7 years: A = 51,000(1 - 0.10)^7Now, calculate the value of A:
A = 51,000(1 - 0.10)^7
A = 51,000(0.90)^7
A = 51,000(0.4782969)
A ≈ 24,393 subscribers (after rounding to the nearest whole number).
Therefore, if the magazine subscriptions continue to decline at a rate of 10% per year, the magazine is predicted to have approximately 24,393 subscribers in 7 years.
A book on the clearance rack was marked down 65% from $21.95. Approximately, how much was the book discounted?
Answer:
$7.6825
Step-by-step explanation:
65%=0.65
0.65*21.95=14.2675
21.95-14.2675=7.6825
Answer:
7.6825
Step-by-step explanation:
Which expression represents 8 less than two times X?
OA) 2x - 8
OB) 8 - 2x
OC) 8x - 2
OD) 2-8x
Answer:
Therefore the expression is option A)
[tex]2x-8[/tex]
Step-by-step explanation:
Given:
Statement as ' 8 less than two times X'
To Find :
Expression for the statement
'8 less than two times X'
Solution:
[tex]Two\ times\ 'x'\ means=2\times x[/tex]
Now 8 less than two times X means Subtract 8 from '2x'
[tex]2x-8[/tex]
Therefore the expression is option A)
[tex]2x-8[/tex]
The length of a rectangle is 5 centimeters less than its width What are the dimensions of the rectangle if its area is 66 square centimeters?
The length of the rectangle is
The width of the rectangle is
Answer:
length of rectangle=6cm
width of rectangle=11cm
Step-by-step explanation:
let, width of rectangle=x
length of rectangle=x-5
area of rectangle=[tex]length\times(width)[/tex]
given area of rectangle=66
so 66=[tex]x\times(x-5)[/tex]
66=x^2-5x
x^2-11x+6x-66=0
x(x-11)+6(x-11)=0
(x+6)(x-11)=0
x=-6,11
here x=11 is acceptable
length of rectangle=x-5=11-5=6cm
length of rectangle=6cm
width of rectangle=11cm answer
solve and explain how you got your answer
-3(c-1) = 33
Answer:
Step-by-step explanation:
-3(c-1) = 33
c - 1 = 33/ -3
c -1 = -11
c = -11 +1
c = -10
Answer:
-10
Step-by-step explanation:
-3 (c-1 ) = 33
Divide both sides by -3
c-1 = -11
Add 1 to both sides
c = -10
What is the slope of the line represented by the equation y= -1/2x+1/4
Answer:
-1/2
Step-by-step explanation:
The format your equation in is called slope-intercept form:
y=mx+b
m stands for slope, the slope basically determines how much the line is tilted. b stands for the y intercept, the y intercept is when the line intercepts with the y axis.
Your equation is:
y= -1/2x+1/4
y= m x+ b
If a pair of jeans cost 45 dollars before the sale and the sale is taking 9 dollars off of the original price what was the percent taken off?
Answer:
20%
Step-by-step explanation:
A pair of jeans cost $45 before the sale.
The sale is taking $9 off of the original price.
Then
$45 - 100%
$9 - x%
Write a proportion:
[tex]\dfrac{45}{9}=\dfrac{100}{x}[/tex]
Cross multiply:
[tex]45\cdot x=9\cdot 100\\ \\45x=900\\ \\x=\dfrac{900}{45}\\ \\x=20\%[/tex]
Answer:
The sale price is $46.75
Step-by-step explanation:
The Ferris wheel has a radius of 70 feet. The distance between the wheel and the ground is 4 feet. The rectangular coordinate system shown has its origin on the ground directly below the center of the wheel. Write the equation of the circular wheel. (JUSTIFY)
Show your work. i will give brainliest.
Answer:
The equation of the circular wheel is [tex]x^2+(y-74)^2=(70)^2[/tex].
Step-by-step explanation:
Given :
Radius of Ferris wheel r = 70 feet.
The distance between the wheel and the ground = 4 feet.
Also, the rectangular coordinate system shown has its origin on the ground directly below the center of the wheel.
So the x coordinate of center of wheel must be 0 , and y coordinate = 70 + 4 = 74
Thus, Coordinates of center = (0,74)
The equation of circle is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Now center (h,k) = (0,74) and r = 70 , we get
[tex]x^2+(y-74)^2=(70)^2[/tex]
Hence, the equation of the circular wheel is [tex]x^2+(y-74)^2=(70)^2[/tex].
1. Which equation shows a non-proportional
relationship?
A y=-2x
By= 2X
x
Cy=2x+ 0
Dy=2x + 2
Answer:
Option D. [tex]y=2x+2[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Verify each case
case A) we have
[tex]y=-2x[/tex]
Is a equation of the form [tex]y=kx[/tex]
The value of k=-2
This equation represent a proportional relationship
case B) we have
[tex]y=2x[/tex]
Is a equation of the form [tex]y=kx[/tex]
The value of k=2
This equation represent a proportional relationship
case C) we have
[tex]y=-2x+0[/tex]
The line passes through the origin, because the y-intercept is b=0
This equation represent a proportional relationship
case D) we have
[tex]y=2x+2[/tex]
The line not passes through the origin, because the y-intercept is not equal to zero (b=2)
This equation not represent a proportional relationship