Sam initially invested $4,500 into a savings account that offers an interest rate of 3% each year. He wants to determine the number of years, t, for which the account will have less than or equal to $7,020. Create the inequality that represents this situation and plot the solution set to the inequality on the number line.
Answers
[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&7020\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill \end{cases}[/tex]
[tex]\bf 7020\geqslant 4500(1+0.03t)\implies \cfrac{7020}{4500}\geqslant 1+0.03t\implies \cfrac{39}{25}\geqslant 1+0.03t \\\\\\ \cfrac{39}{25}-1\geqslant 0.03t\implies \cfrac{14}{25}\geqslant 0.03t\implies \cfrac{~~\frac{14}{25}~~}{0.03}\geqslant t\implies \cfrac{56}{3}\geqslant t \\\\\\ 18\frac{2}{3}\geqslant t\impliedby \textit{18 years and 8 months}~\hfill \boxed{0 \leqslant t \leqslant 18\frac{2}{3}} \\\\\\ ~\hspace{34em}[/tex]
check the picture below.
bearing in mind that "t" cannot be less than 0.
Related Questions
At the beginning of year 1, Sam invests 700 at an annual compound interest rate of 5%, he makes no deposits to or withdrawals from the account. which explicit formula can be used to find the account's balance at the beginning of year 4? what is the balance?
a) 805.
b) 825.42
c) 850.85
d) 810.34
Answers
Answer:
(d) 810.34
Step-by-step explanation:
The explicit formula used for calculating the account's balance is given by:
A= P(1+R)^T
where: A= Amount (account's balance)
P= Principal (700)
R= Rate (5%)
T= Time (3 years) [since, the balance is calculated in the beginning of the forth year]
A= P(1+R)^T
A = 700(1+0.05)^3
= 700(1.05)^3
= 700*1.157
= 810.34
What are he solution(s) of the quadratic equation 98-x^2=8
Answers
Answer:
x = -3√10 and x = 3√10
Step-by-step explanation:
98-x^2=8
x^2 = 98 - 8
x^2 = 90
x = +/- 3√10
Answer:
[tex]\pm3\sqrt{10}[/tex]
Step-by-step explanation:
The solution to an equation is when the equation is equal to 0 (also known as the roots/x intercepts.)
[tex]98-x^2=8\\-x^2=-90\\x^2=90\\x=\pm\sqrt{90} \\x=\pm3\sqrt{10}[/tex]
A spinner is divided into four equal sections labeled 1, 2, 3, and 4. Another spinner is divided into three equal sections labeled A, B, and C. Simon will spin each spinner one time.
How many of the possible outcomes have an even number or a B?
Answers
Answer:
The possible outcome could be 4 or 3
Step-by-step explanation:
Answer:
2/3
Step-by-step explanation:
There are 12 possible outcomes. Of the 12, 6 are even and 4 have B's. That would give up 10/12. But then you would subtract the possible outcomes that are BOTH even AND have a B. Only 2 possible outcomes have an even number and the letter B. So 10 minus 2 is 8. That would give you 8/12. Simplify and you will get your answer of 2/3!
Just took the test, so trust me on this fellow K12ers!
NEED HELP WITH ALL THESE PROBLEMS !!
Answers
Answer:
1) ASA 2) In explanation 3) I cant see all of the problem
Step-by-step explanation:
For Number 1 you need one more thing to prove that the triangles are congruent. You could see that there is a pair of vertical angles and vertical angles are congruent so you could use that. Angle DEA is congruent to Angle CEB. When there is a side in between two congruent angles, that is ASA.
For Number 2 it really is almost the same as number 1. First you write the given, then you write that angle DEA is congruent to angle CEB and the reason for that is that vertical angles are congruent. Lastly, you say that triangle ADE is congruent to triangle CBE.
Evaluate the expression when b=4 and y= -5
-b+5y
Answers
Answer:
-29
Step-by-step explanation:
-b+5y
We know that b=4 and y= -5
We can substitute these into the expression
-(4) +5(-5)
-4 -25
-29
What’s the actual distance = yards?
Answers
Answer:
120 yards
Step-by-step explanation:
A map scale is a ratio.
1 inch : 30 yards
Multiply both sides of the ratio by 4.
4 * 1 inch : 4 * 30 yards
4 inches : 120 yards
Answer:
So we know 4 inches is 120 yds
Step-by-step explanation:
We can use ratio's to solve this problem
1 inch 4 inch
------------ = --------------
30 yds x yds
Using cross products
1 * x = 30*4
x = 120
So we know 4 inches is 120 yds
The formula used for this is a^2+b^2=c^2, I don't really get this problem.
Answers
Answer:
127.3
Step-by-step explanation:
The formula you gave is is known as the Pythagorean Theorem.
It is used to find the hypotenuse (longest side) of a right triangle with the lengths of the other two legs (sides).
Here, a is the hypotenuse of two adjacent triangles. Both triangles are right triangles, and have legs (not including the hypotenuse) of 90 ft.
Now, the formula is a^2 + b^2 = c^2.
A and b are the two shorter legs of the triangle: 90 and 90. Let's insert these values into the formula.
90^2 + 90^2 = c^2
90^2 is 8100, and 8100 plus 8100 is 16200.
16200 = c^2 (c is the hypotenuse, or a)
Now, we just have to find the square root of 16200.
sqrt16200=127.27....
When we round this to the nearest tenth, we get 127.3.
What construction tool would be used to measure an angle?
Answers
Answer:
A protractor.
Step-by-step explanation:
A rectangle has a width of 9 cm, and a diagonal of 15 cm. Find the length.
Answers
Answer:
87857570
Step-by-step explanation:
Please Help ! I Dont Know What The Answer Is
Answers
Answer:
2x2=6
Step-by-step explanation:
Distance formula
D = ( x2 - x1)2 + (y2 - y1)2
Use the distance formula to find the distance between each set of the points:
(1,4) and (-2,3)
Answers
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(-2-1)^2+(3-4)^2}\implies d=\sqrt{(-3)^2+(-1)^2} \\\\\\ d=\sqrt{9+1}\implies d=\sqrt{10}[/tex]
To find the distance between two points (1,4) and (-2,3) using the distance formula, perform the relevant calculations and steps.
Explanation:To find the distance between two points using the distance formula, you can follow these steps:
Identify the coordinates of the two points. In this case, the coordinates are (1,4) and (-2,3).Plug the values of the coordinates into the distance formula: D = (√((x2 - x1)^2 + (y2 - y1)^2)).Calculate the difference between the x-coordinates and the y-coordinates separately. For this example, (x2 - x1) = (-2 - 1) = -3, and (y2 - y1) = (3 - 4) = -1.Square the differences calculated in the previous step: (-3)^2 = 9 and (-1)^2 = 1.Add the squared differences together: 9 + 1 = 10.Take the square root of the sum to find the distance: √10 ≈ 3.16.So, the distance between the points (1,4) and (-2,3) is approximately 3.16 units.
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Can someone do this for me thank you
Answers
Answer:
I think is (A)
They got same y intercept
they both cross at 0
but they are opposite graph like X
Step-by-step explanation:
What is the value of X im the figure?
Answers
Answer:
x=36
Step-by-step explanation:
< CAB and <EAD are vertical angles and vertical angles are equal
<CAB = <EAD
36 = x
An animal shelter has 12 cats. Of these cats, 5 weigh no more than 7 lbs. What is the approximate percentile rank of the cats that weigh 7 lbs?
Answers
Answer:
84 lbs
Step-by-step explanation:
Solve equation for a=
Answers
Answer:
Alright well solve for a by multiplying both sides of the equation, then isolating the variable
a = 2b/5 + c/5 Hope this helps have a nice day :)
Step-by-step explanation:
That should be right
If Michael bought the 5 m how many inches did she walk
Answers
Answer:
1 meter = 39.370 inches.....so 5 meters = (5)(39.370) = 196.85 inches
For every 20 litres of petrol a car can run for 75 km.
How much petrol do you need (to 1 DP) to ensure the car has enough petrol of a trip that is 196 km?
Answers
Answer:
52.3 litres.
Step-by-step explanation:
The car consumption is 75/20 = 3.75 km/litre.
Volume of petrol needed to travel 196 km
= 196 / 3.75 = 52.3 litres.
Does the point (2,2) lie on the circle (x-4)^2+(y-2)^2=4
Answers
Answer:
Yes, see attached plot
Step-by-step explanation:
PLEASE HELP ME!
Sketch the linear function f(x) = 1/2(3x + 1)
1. Which key feature of the graph is true?
A) y-intercept (0, −1)
B) x-intercept (1/6,0)
C) x-intercept (1/3, 0)
D) y-intercept (0, 1/2)
Answers
Answer:
it's C
Step-by-step explanation:
Answer: c
x-intercept ( 1 /3 , 0)
Step-by-step explanation:
Students in band are selling oranges and grapefruit to earn money for a trip. Mrs.Whitten purchased three boxes of oranges and two boxes of grapefruit from a student for a total of $22.50. Mr. Rutig purchased one bag of oranges and four boxes of grapefruit, spending a total of $28.50. How much is one box of oranges?
Answers
Answer:
The cost of one box of oranges = $3.3
Step-by-step explanation:
Let x be cost of one box of oranges and y be the cost of one box of grapefruit.
We have been given that Mrs. Whitten purchased 3 boxes of oranges and 2 boxes of grapefruit from a student for a total of $22.50. We can represent this information as:
[tex]3x+2y=22.50...(1)[/tex]
Mr. Rutig purchased 1 box of oranges and four boxes of grapefruit, spending a total of $28.50. We can represent this information as:
[tex]x+4y=28.50...(2)[/tex]
We will solve our system of linear equations using substitution method.
From equation (1) we will get,
[tex]y=\frac{22.50-3x}{2}[/tex]
Substituting y's value in equation (2) we will get,
[tex]x+4*(\frac{22.50-3x}{2})=28.50[/tex]
[tex]x+2*(22.50-3x)=28.50[/tex]
Upon distributing 2 we will get,
[tex]x+45-6x=28.50[/tex]
[tex]x-6x=28.50-45[/tex]
[tex]-5x=-16.5[/tex]
[tex]x=\frac{-16.5}{-5}[/tex]
[tex]x=3.3[/tex]
Therefore, the cost of one box of oranges is $3.3.
how would you write 834,209 in word form
Answers
Answer:
eight hundred thirty four thousand two hundred nine
All you got to do is write the places and the number.
Plzzz mark brainlest and thank em would be very much thankful
which of the following numbers must be added to complete the square in the equation below? x^2+6x-19=23 A. 19 B. -9 C. 3 D. 9
Answers
Answer:
the answer is D
Step-by-step explanation:
Answer:
D. 9
Step-by-step explanation:
Is y = 1/4x^0.5 a power function? Explain your reasoning.
Answers
Answer:
[tex]y =\displaystyle\frac{1}{4}x^{0.5}[/tex]
It is a power function.
Step-by-step explanation:
We are given the following function in the question:
[tex]y =\displaystyle\frac{1}{4}x^{0.5}[/tex]
We have to check whether the given function is a power function or not.
Power Functions :
A power function is of the form:[tex]f(x) = ax^p,[/tex]
where a is a constant and not equal to zero and p is a real number.
Comparing the given function, we get:
[tex]a = \displaystyle\frac{1}{4}\\\\p = 0.5[/tex]
Hence, the given function is a power function.
The equation y = 1/4x^0.5 is a power function because it fits the general form of a power function, y = ax^n, with a constant coefficient and a real number exponent.
Explanation:Yes, the function y = 1/4x^0.5 is indeed a power function. A power function is of the form y = ax^n, where a is a constant and n is a real number, representing the power of x. In the given function, a is equal to 1/4, and n is 0.5, which is equivalent to the square root of x (since raising a number to the 0.5 power is the same as taking its square root).
Therefore, we can express the square root of x as x raised to the power of 1/2, fitting the form of a power function.
How many solutions does the system of the equation have? y=-4x+2
24x+6y=6
Answers
Answer:
0 solutions
Step-by-step explanation:
they have the same slope and different y intercepts so they never intersect
Answer:
This equation has no solution
Step-by-step explanation:
To find our many solution the system of equation has, we need to solve simultaneously, we can either solve by substitution method, by elimination method or both method.
We will be using substitution method to solve.
Here are the system of equation;
y= -4x+2 ----------(1)
24x+6y=6---------(2)
First, we are going to substitute equation (1) in equation (3)
{what we mean by substituting equation (1) in equation (2) is then any where we see y in equation (2), we will be replacing it by[-4x + 2]}
24x + 6(-4x + 2) = 6
Then, we will go ahead and open the bracket
24x - 24x + 12 =6
This simply shows that there is no solution to this system of equation
A farm tree is going out of business. It has 45 maple trees and 27 pine trees left for sale. How much money would the owners make if they sell all the trees?
Answers
Who knows how to solve this problem ”Surface Area-Prisms”?
Answers
Answer: You lay out the 3 demential shape into a net then find the area of the net. There are 2 surfaces that are 81 square feet. and 4 surfaces that are 18 feet. 81 + 81 + 18 + 18 + 18 + 18 = 234.
The surface area is 234 Square Feet. Hope this helps and brainliest is always appreciated. :)
Answer: 234
Step-by-step explanation:
Surface area of a rectangular prism: 2lengthheight + 2lengthwidth + 2heightwidth
Length: 9 | Height: 9 | Width: 2
2(9x9) + 2(9x2) + 2(9x2) = 234
divide 9 by w, then subtract v from the result
Answers
Answer:
9/w=x(your result)
x-v=( your final answer )
Please mark my answer as brainliest
Step-by-step explanation:
A zookeeper thinks there is a problem with the naked-mole rat population at the zoo. He starts keeping track of the animals in the tunnels. 7 days into his monitoring he counts 120 mole rats. 13 days in he counts 108.
1.) write an equation in point-slope form that represents the situation (define your variables)
2.) convert your equation to slope-intercept form
Answers
(y - y1) = m(x - x1) -- this means y (which will stay the same throughout the equation) minus a known or given y value equals the slope (m), parenthesis x (which will also stay the same throughout the equation) minus a known or given x value.
1.) An equation in point-slope for this would be.... (y - 120) = -2(x - 7) -- 120 being your known y value and 7 being your known x value.
2.) The equation in slope intercept form
(which is y=mx+b) would be y = -2x+134.
(y - 120) = -2(x - 7)
(y - 120) = -2*x + (-2*-7)
y - 120 = -2x + 14
+120 +120
y = -2x + 134
In this exercise we have to use the knowledge of equations to write the intersection equation, so we have to:
The formula for setting up an equation is given by:
[tex](y - y1) = m(x - x1)[/tex]
1.) So by the formula above, substituting for the values given in the statement, then:
[tex](y - 120) = -2(x - 7)[/tex]
2.) The equation in slope intercept form will be:
[tex](y - 120) = -2(x - 7)\\(y - 120) = -2*x + (-2*-7)\\y - 120 = -2x + 14\\y = -2x + 134[/tex]
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Write the value of c that makes x^2+12x+c a perfect square trinomial.
Answers
Answer:
c = 36
Step-by-step explanation:
Use the formula (b/2)^2 to solve for the max or min.
ax^2 + bx + c
b = 12
(12/2)^2
6^2 = 36
You can check you work
y = x^2 + 12x + 36
y = (x + 6) (x + 6) It works!
Answer:
D 36
Step-by-step explanation:
URGENT!! Which shape has six square, flat sides that are equal in size?
Answers
Answer: cube
Step-by-step explanation:
Think of a box .... it has 4 sides, a top, and a bottom = 6 total sides
The shape with six equal square, flat sides is known as a cube.
Explanation:A cube is a three-dimensional geometric shape characterized by six equal square faces. Each face of the cube is identical, and the shape is formed by connecting these faces at right angles. This regular polyhedron is fundamental in mathematics and has practical applications in various fields. Cubes are extensively used in geometry, trigonometry, and calculus to illustrate concepts such as volume and surface area. In addition to its mathematical significance, cubes are prevalent in everyday objects like dice and building blocks. Understanding the properties of cubes is crucial in engineering and architecture, where it aids in designing structures and solving spatial problems efficiently.
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