Answer:
A. [tex]\displaystyle 10\:units[/tex]
Step-by-step explanation:
Use the Distance Formula:
[tex]\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = D \\ \\ \sqrt{[-3 + 2]^2 + [-6 - 4]^2} = \sqrt{[-1]^2 + [-10]^2} = \sqrt{1 + 100} = \sqrt{101} ≈ 10,04987562 ≈ 10[/tex]
Since we are talking about distance, we ONLY want the NON-NEGATIVE root.
I am joyous to assist you anytime.
Final answer:
The approximate length of a line segment connecting points A(3, 6) and B(2, -4) is found using the distance formula and it is approximately 10 units.
Explanation:
To calculate the approximate length of a line segment connecting points A and B, we use the distance formula. The distance formula is derived from the Pythagorean theorem and is:
d = \/((x2 - x1)² + (y2 - y1)²)
Given points, A(3, 6) and B(2, -4), we can plug these coordinates into the formula:
d = \/((2 - 3)² + (-4 - 6)²)
Now, calculate the squares and sum:
d = \/((-1)² + (-10)²)
d = \/(1 + 100)
d = \/(101)
The square root of 101 is approximately 10.05, which is close to 10 units.
Therefore, the approximate length of the line segment connecting points A and B is 10 units, which corresponds to option A.
The top band in the state charges C(x)=55x+15,000, where x is the total number of attendees at the concert. The venue charges $70 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?
The venue will break even after selling 1000 tickets.
The value will be $70,000 at that point.
Step-by-step explanation:
Given,
Charges of band;
C(x) = 55x+15000
Per ticket charges by Venue = $70
V(x) = 70x
For breaking even,
C(x) = V(x)
[tex]55x+15000=70x\\15000=70x-55x\\15000=15x\\15x=15000[/tex]
Dividing both sides by 15
[tex]\frac{15x}{15}=\frac{15000}{15}\\x=1000[/tex]
The venue will break even after selling 1000 tickets.
Putting 1000 in V(x)
[tex]V(1000)=70(1000)\\V(1000)=70000[/tex]
The value will be $70,000 at that point.
Keywords: function, multiplication
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Change to slope-intercept form. Then find the y-intercept, first point, and second point.
-x+3y>6
(choices in photo)
Answer:
1) [tex]y> \frac{x}{3}+2[/tex] 2) (0,2) 3) The first and second Points must have x coordinate <-6, or y-coordinate y >2 e.g. (-7,2), (-6,3)
Step-by-step explanation:
1) To Rewrite it as Slope-intercept form, is to isolate the y on the left side and on the right side the rest of the inequality.
[tex]-x+3y>6\Rightarrow 3y>x+6 \Rightarrow y> \frac{x+6}{3}\Rightarrow y> \frac{x}{3}+2[/tex]
2) Since this is a linear inequality the y intercept is given by "b" parameter.[tex]y> mx+b \Rightarrow y> \frac{x}{3}+2 \Rightarrow b=2[/tex]
So the y-intercept is y > 2, coordinate point (0,2). In the graph, we have a dashed line over 2.
3) Since there no choices, the points that satisfy this inequality lie within the green area. We know that the points for this inequality must satisfy x < -6 or y> 2:
Testing for (-7,2) for x<-6 ⇒-7 <-6
[tex]-x+3*y>6\\-(-7)+3*2>6\\7+6>6\\13>6\:\\True\\[/tex]
Testing for (-6,3) for y>2 ⇒3>2
[tex]-x+3*y>6\\-(-6)+3*3>6\\6+9>6\\15>6\:True\\[/tex]
Lines c and d are parallel. The equation of line c is y=−3x−5. What is the equation of line d?
Answer: y = -3x - 5
Step-by-step explanation: since the two lines are parallel, it implies that
m1 = m2. From the equation given,
m1 = -3 , m2 = -3
Substantial for m2 in y = mx + c
We now have
y = -3x - 5 since the new line is not passing through any coordinate.
Answer:
The answer is y=-3x-2
I hope it's not too late;)
Step-by-step explanation:
g(x) = x2 + x - 2
Find g(x - 3)
Answer:
x^2-5x+4
Step-by-step explanation:
(x-3)^2+(x-3)-2
x^2-3x-3x+9+x-3-2
x^2-6x+9+x-5
x^2-5x+9-5
x^2-5x+4
What expression is equivalent to x-5/(x-5)(x-4)
Answer:
[tex]\large\boxed{\dfrac{1}{x-4}\ \text{for}\ x\neq5\ \wedge\ x\neq4}[/tex]
Step-by-step explanation:
[tex]\dfrac{x-5}{(x-5)(x-4)}\\\\\text{Domain:}\ (x-5\neq0\ \wedge\ x-4\neq0)\Rightarrow(x\neq5\ \wedge\ x\neq4)\\\\\dfrac{x-5}{(x-5)(x-4)}\qquad\text{cancel}\ (x-5)\\\\=\dfrac{1}{x-4}[/tex]
MR Arsalan bought a plot of land for rs 108 000 and sold it for a profit of 20% at what price did he sold at
Answer:
The plot of land was sold for rs 129,600
Step-by-step explanation:
The cost of the plot of land = rs 108,000
Profit calculation ( 20% x 108,000) = rs 21,600
Price land was sold = (108,000 + 21,600) = 129,600
Robin can clean
72
7272 rooms in
6
66 days.
How many rooms can Robin clean in
9
99 days?
Robin can clean 108 rooms in 9 days, given she cleans 72 rooms in 6 days; this is determined by calculating her daily cleaning rate and extending it over the 9-day period.
The student asks how many rooms Robin can clean in 9 days if she can clean 72 rooms in 6 days. To solve this problem, we first need to determine the rate at which Robin cleans rooms per day, which is done by dividing the total number of rooms by the total number of days. Once we have the daily rate, we can then multiply this rate by 9 to find out how many rooms can be cleaned in 9 days.
First, we calculate the daily rate:
Rate = Total Rooms / Total Days
Rate = 72 rooms / 6 days
Rate = 12 rooms/day.
Now, we multiply the daily rate by 9 days:
Rooms in 9 days = Rate times Number of Days
Rooms in 9 days = 12 rooms/day times 9 days
Rooms in 9 days = 108 rooms.
Therefore, Robin can clean 108 rooms in 9 days.
can someone help me please
The circumference of a circle is 3.2mm.
Find the length of the diameter.
Give your answer rounded to 3 SF.
The diameter of circle is 1.018 mm.
Step-by-step explanation:
Given,
Circumference of circle = 3.2 mm
We know that;
Circumference = 2πr
[tex]3.2=2\pi r\\[/tex]
Putting π=22/7
[tex]3.2=2*\frac{22}{7}*r\\3.2=\frac{44}{7}r[/tex]
Multiplying both sides by 7/44
[tex]\frac{7}{44}*3.2=\frac{7}{44}*\frac{44}{7}r\\\\\frac{22.4}{44}=r\\\\r=0.509[/tex]
Diameter = 2r
Diameter = 2*0.509
Diameter = 1.018 mm
The diameter of circle is 1.018 mm.
Keywords: circle, circumference
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A soccer game is 90 minutes long. 36 minutes have passed. What percentage of the game has passed?
Answer:
40%
Step-by-step explanation:
Percentage Passed = 36 ÷ 90 × 100 = 40%
Can someone help me with this problem? I just can't seem to get the answer.
Answer:
[tex]\frac{9}{4}[/tex] or [tex]2\frac{1}{4}[/tex] or [tex]2.25[/tex]
Step-by-step explanation:
1 cm = 25000cm = 1/4 km. 9*1/4=9/4=2 1/4= 2.25
i have 150 i share one third how much did i share
Answer:
50
Step-by-step explanation:
150 divided by 3 is 50 and since you shared only one third the answer will be 50
Answer:50
Step-by-step explanation:
One third equals 1/3 of 150
1/3 ×150 =50
Solve |12x + 1| = 10
(9/2, 11/2)
(-9/2, 9/2)
(-112.9/2)
|12x + 1| = 10
Remove the absolute value term and make two equations:
12x +1 = 10
12x +1 = -10
Now solve for both x values:
12x +1 = 10
Subtract 1 from both sides:
12x = 9
Divide both sides by 12:
x = 9/12
12x +1 = -10
Subtract 1 from both sides:
12x = -11
Divide both sides by 12:
x = -11/12
The answer would be (-11/12, 912)
What is the average rate of change of the function f(x)=120(.1)^x from x=0 to x=2
Answer:
- 59.4
Step-by-step explanation:
The given function is [tex]f(x) = 120(0.1)^{x}[/tex]
Therefore, at x = 0, [tex]f(0) = 120(0.1)^{0} = 120[/tex] and
at x = 2, [tex]f(2) = 120(0.1)^{2} = 1.2[/tex]
Hence, the average rate of change of the given function from x = 0 to x = 2 will be
[tex]\frac{f(2) - f(0)}{2 - 0}[/tex]
= [tex]\frac{1.2 - 120}{2 - 0}[/tex]
= - 59.4 (Answer)
The cost y (in dollars) for x ounces of peanuts is
represented by the equation y = 0.23x. The cost y
(in dollars) for x ounces of pecans is represented by
the equation y = 0.45x. Which statement is true?
Select all that apply.
A The cost for peanuts is $0.22 per ounce less than
the cost for pecans.
B The cost for peanuts is greater than the cost
for pecans.
C The cost for 8 ounces of peanuts is $3.60.
D The cost for 8 ounces of pecans is $3.60.
Answer:
Options A and D are correct.
Step-by-step explanation:
The cost y (in dollars) for x ounces of peanuts is represented by the equation
[tex]y=0.23x[/tex] .... (1)
It means the cost of each ounce of peanuts is $0.23.
The cost y (in dollars) for x ounces of pecans is represented by the equation
[tex]y=0.45x[/tex] .... (2)
It means the cost of each ounce of pecans is $0.45.
$0.45 > $0.23
It means the cost for pecans is greater than the cost of peanuts. Option B is incorrect.
[tex]\$0.45-\ $0.23=\$0.22[/tex]
The cost for peanuts is $0.22 per ounce less than the cost for pecans. Option A is correct.
Substitute x=8 in equation (1).
[tex]y=0.23(8)=1.84[/tex]
The cost for 8 ounces of peanuts is $1.84. Option C is incorrect.
Substitute x=8 in equation (2).
[tex]y=0.45(8)=3.6[/tex]
he cost for 8 ounces of pecans is $3.60.. Option D is correct.
A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5
Inches and a height of 3 inches. The other two candles are scaled versions of the smallest, with scale factors of 2 and 3. How much wax is
needed to create one set of candles?
OA 27 cubic inches
B.
C.
D.
36 cubic inches
53 cubic inches
86 cubic inches
E.
98
cubic inches
Next
The amount of wax needed to create one set of candles is 84.75 cubic inches.
What is a cylinder?A cylinder is a 3-D figure that has a radius and a height.
The volume of a cylinder is given as πr²h.
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume.
= 3.14 x 2 x 2 x 5
= 62.8 cm³
We have,
Let's calculate the volume of each candle and then add them together to find the total wax needed for one set of candles.
For the smallest candle, the radius is 0.5 inches and the height is 3 inches, so the volume is:
V1 = π x (0.5)² x (3) = 0.75π cubic inches
For the medium-sized candle, the radius is twice as big, or 1 inch, and the height is twice as big, or 6 inches. So the volume is:
V2 = π x (1)² x (6) = 6π cubic inches
For the largest candle, the radius is three times as big, or 1.5 inches, and the height is three times as big, or 9 inches.
V3 = π x (1.5)² x (9) = 20.25π cubic inches
To find the total wax needed for one set of candles, we add up the volumes:
V (total) = V1 + V2 + V3
= 0.75π + 6π + 20.25π
= 27π cubic inches
= 27 x 3.14
= 84.78 cubic inches
Therefore,
The amount of wax needed to create one set of candles is 84.75 cubic inches.
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It takes 2 wooden sticks and 1.5 square feet of paper to make a kite, and it takes 12 wooden sticks and 8 square
feet of paper to make a lamp.
Min-Young wants to make kites and lamps using at least 87 wooden sticks and more than 63 square feet of
paper.
Let K denote the number of kites she makes and L the number of lamps she makes.
Write an inequality that represents the condition based on the number of wooden sticks. Write an inequality that represents the condition based on the number of square feet of paper.
Answer:
2K + 12L ≥ 87 and 1.5K + 8L > 63
Step-by-step explanation:
It takes 2 wooden sticks and 1.5 square feet of paper to make a kite, and it takes 12 wooden sticks and 8 square feet of paper to make a lamp.
If K denotes the number of kites that Min-Young made and L denotes the number of lamps she made then
2K + 12L is the number of wooden sticks that she used which is greater than equal to 87
i.e. 2K + 12L ≥ 87 ........ (1)
Again, 1.5K + 8L is the number of square feet of paper that she used which is greater than 63 sq. feet
i.e. 1.5K + 8L > 63 ........... (2)
Hence, inequalities (1) and (2) are the required answer. (Answer)
Answer:
1) 2K + 12L ≥ 87
2) 1.5K + 8L > 63
Step-by-step explanation:
Expand
Your answer should be a polynomial in standard form
(
+1)(2-6)
Answer:
x^2 - 6x + x - 6
= x^2 - 5x - 6
what is the degree of differential equation? ?
Answer:
Degree = 1
Step-by-step explanation:
Given:
The differential equation is given as:
[tex]\frac{d^2y}{dx^2}+(\frac{dy}{dx})^2+6y=0[/tex]
The given differential equation is of the order 2 as the derivative is done 2 times as evident from the first term of the differential equation.
The degree of a differential equation is the exponent of the term which is the order of the differential equation. The terms which represents the differential equation must satisfy the following points:
They must be free from fractional terms.Shouldn't have derivatives in any fraction.The highest order term shouldn't be exponential, logarithmic or trigonometric function.The above differential equation doesn't involve any of the above conditions. The exponent to which the first term is raised is 1.
Therefore, the degree of the given differential equation is 1.
If f (x) = 3 x squared and g (x) = 4 x cubed + 1, what is the degree of (f circle g) (x)?If f (x) = 3 x squared and g (x) = 4 x cubed + 1, what is the degree of (f circle g) (x)?
options are
2
3
5
6
Answer:
degree = 6
Step-by-step explanation:
Given [tex]f(x)=3x^2[/tex], and [tex]g(x)=4^3+1[/tex], we can find the composition of functions: [tex]fog(x)[/tex] by applying the definition of composition and performing the needed algebra.
Recall that the composition of functions is defined as: [tex]fog(x)=f(g(x))[/tex], where we use as input for the function f(x) the actual expression in terms of "x" of the function g(x):
[tex]f(g(x))=f(4x^3+1)\\f(g(x))=3(4x^3+1)^2\\f(g(x))=3\,(4x^3+1)\,(4x^3+1)\\f(g(x))=3\,[16x^6+4x^3+4x^3+1]\\f(g(x))=3\,[16x^6+8x^3+1]\\f(g(x))=48x^6+24x^3+3[/tex]
Therefore, the degree of this expression is "6" (the highest power at which the variable "x" appears)
Answer:
the answer is 6
Step-by-step explanation:
don't have one
The volume of a rectangular prism is 72 cubic centimeters. The prism is 2 centimeters wide and 4 centimeters high. What is the length of the prism?
Answer:
The length of prism is 9 centimetres.
Step-by-step explanation:
Given:
The volume of a rectangular prism is 72 cubic centimeters.
The prism is 2 centimeters wide and 4 centimeters high.
Now, to find the length of prism:
Let the length be [tex]l[/tex].
Width = 2 centimeters.
Height = 4 centimeters.
Volume = 72 cubic centimeters.
So, putting the formula to get the length of prism:
[tex]Volume = length\times width\times height[/tex]
[tex]72=l\times 2\times 4[/tex]
[tex]72=l\times 8[/tex]
Dividing both sides by 8 we get:
[tex]9=l[/tex]
Length = 9 centimetres.
Therefore, the length of prism is 9 centimetres.
Tarzan loaded 3 trucks in 6 minutes. At that rate, how many trucks would he load in 5 hours?
Answer:
150
Step-by-step explanation:
60 minutes in 1 hour
3x10= 30 in one hour
30x5=150 30 trucks in 5 hours
Tarzan can load 150 trucks in 5 hours.
To calculate how many trucks Tarzan can load in 5 hours based on the rate that he loaded 3 trucks in 6 minutes. First, we convert 5 hours into minutes to match the units of the given rate. There are 60 minutes in 1 hour, so 5 hours is 300 minutes (5 hours x 60 minutes/hour). Next, we need to find out how many 6-minute intervals there are in 300 minutes, which is 300 minutes / 6 minutes/intervals = 50 intervals. Since Tarzan loads 3 trucks per interval, we multiply the number of intervals by the number of trucks per interval to get the total number of trucks loaded in 5 hours: 50 intervals x 3 trucks/interval = 150 trucks.
What is the process of converting a fraction to a decimal?
8/12 in 0.667 (right?), but i dont actually know the process to figuring it out.
thank youu
You would use long division to determine that 8/12 = 0.667 approximately. The steps would go something like this
-------------
Step 1) Write 8 under a long division bar and place 12 to the left and outside the bar
Step 2) Change the 8 into 8.0000 (you can have as many trailing zeros as you want)
Step 3) While 12 doesn't go into 8, 12 does go into 80. So you can think of 8.0 as 80. Ask yourself "how many times does 12 go into 80?". The answer is 6 times because 6*12 = 72 (note how 7*12 = 84 is too big). So we write a "6" above the 8.0000 such that it is above the first "0". So far we have 0.6 as the quotient.
Step 4) Multiply that 6 by 12 to get 72. We write the 72 under the 80 and then subtract to get 80 - 72 = 8. Pull down the second 0 from "8.0000" to change that 8 into 80.
Step 5) We effectively repeat steps 3 and 4 again. So thats why we get another 6 as the next part of the quotient, and why the 6's repeat forever. The only reason why there's a 7 at the end is because of rounding.
-----------------------
The long division is shown in the image attachment below. The gridlines are there to show how things line up though when you write out the long division steps (to show to your teacher) you wont use any grid lines.
side note: the fraction 8/12 reduces to 2/3. You divide both top and bottom by the GCF 4. So 8/4 = 2 and 12/4 = 3.
which expression represents 4 times as much as 12
Answer:
4x+12
Step-by-step explanation:
An expression is a mathematical sentence that doesn't end in an equal sign. This question is asking for you to find four times as much as 12, but doesn't explain what number or phrase you need to find it for. We would replace the unknown number with the variable X.
I may be confusing this with another subject, so sorry if I am! Hope this helps!
The expression which represents 4 times as much as 12 is, [tex]4x=12[/tex]
Let us consider that number is x.
Since, 4 times of number is equal to 12.
So that, [tex]4*x=12\\\\4x=12[/tex]
Hence, the expression which represents 4 times as much as 12 is, [tex]4x=12[/tex]
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Devon needs a wood board with an area of 516 square yard to complete a project. If the wood board is 13 yard wide, how long must the board be?
Answer:
[tex]L=\frac{15}{16}\ yd[/tex]
Step-by-step explanation:
The correct question is
Devon needs a wood board with an area of 5/16 square yard to complete a project. If the wood board is 1/3 yard wide, how long must the board be?
we know that
The area of a rectangle is equal to
[tex]A=LW[/tex]
where
L is the length
W is the width
we have
[tex]A=\frac{5}{16}\ yd^2\\\\W=\frac{1}{3}\ yd[/tex]
substitute
[tex]\frac{5}{16}=L(\frac{1}{3})[/tex]
solve for L
[tex]L=\frac{5}{16}(3)[/tex]
[tex]L=\frac{15}{16}\ yd[/tex]
The length of the wood board must be approximately 39.69 yards.
Explanation:To find the length of the board, we need to divide the total area by the width of the board. The area of the board is 516 square yards and the width is 13 yards.
Therefore, the length of the board can be found by dividing 516 by 13.
516 ÷ 13 = 39.69 yards.
So, the board must be approximately 39.69 yards long to complete the project.
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3. READING Alejandro read 4 pages in a book in 6
minutes. How long would you expect him to take to
read 6 pages at this rate?
Alejandro read 4 pages in 6 minutes, then it would take him 9 minutes to read 6 pages
Solution:
Given that Alejandro read 4 pages in a book in 6 minutes
Therefore,
4 pages = 6 minutes
Let us find the time taken to read 1 page
time taken to read 1 page = time taken to read 4 pages divided by 4
[tex]\text{ time taken to read 1 page } = \frac{6 minutes}{4} = \frac{3}{2} minutes[/tex]
Thus to read 6 pages at this rate, multiply time taken to read 1 page by 6
[tex]\rightarrow \frac{3}{2} \times 6 = 9[/tex]
Therefore it would take 9 minutes to read 6 pages
Identify the equation of the linear function through the points (- 2,- 7) and (1,2). Then state the rate of change of the function. What is the equation of the linear function? A. y = 3x - 1 B. y = - 3x - 1 C. y = 3x + 1 D. y = -3x + 1 The rate of change is ( ? ).
Answer:
y = 3x - 1
The rate of change of the function is 3.
Step-by-step explanation:
The equation of the linear function through the points (- 2, - 7)and (1,2) will be given by
[tex]\frac{y - ( - 7)}{- 7 - 2} = \frac{x - (- 2)}{- 2 - 1}[/tex]
⇒ (y + 7) = 3(x + 2)
⇒ y = 3x - 1 (Answer)
Now, the rate of change of the function is the slope of the line i.e. 3. (Answer)
We know the equation of a straight line which passes through the points [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] is given by
[tex]\frac{y - y_{1}}{y_{1} - y_{2}} = \frac{x - x_{1}}{x_{1} - x_{2}}[/tex]
How many feet are in 100 inches? Write your answer two ways: in feet and inches and in feet only
Answer: 8 ft and 4 in, 8 1/3 ft
Step-by-step explanation:
100/12=50/6=25/3=8.3333333...
1/3 of a foot is 1/3x12 which is 12/3 which is 4 in.
Final answer:
100 inches is equal to 8 feet and 4 inches or 8.33 feet.
Explanation:
To solve this problem, you can convert 100 inches to feet using the unit equivalence:
1 foot = 12 inches
Multiply the number of inches by the unit equivalence:
100 inches ÷ 12 inches per foot = 8 feet and 4 inches
A computer can sort x objects in t seconds, as modeled by the functio
below:
1=0.005x2 + 0.002.x
How many objects are required to keep the computer busy for exactly
seconds?
Round to the nearest whole object.
Question:
A computer can sort x objects in t seconds, as modeled by the function below:
t=0.005x^2+0.002x
How many objects are required to keep the computer busy for exactly 9 seconds?
Round to the nearest whole object.
Answer:
42 objects are required to keep the computer busy for exactly 9 seconds
Solution:
Given function is:
Computer can sort x objects in t seconds, as modeled by the function below:
[tex]t = 0.005x^2+0.002x[/tex]
We have to find number of objects required to keep the computer busy for exactly 9 seconds
Therefore t = 9
Substitute t = 9 in given function
[tex]9 = 0.005x^2+0.002x\\\\0.005x^2+0.002x - 9 = 0[/tex]
Let us solve the above equation by quadratic formula,
[tex]\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Using the above formula,
[tex]\text{ for } 0.005x^2+0.002x - 9 = 0 , \text{ we have } a = 0.005 ; b = 0.002 ; c = -9[/tex]
Substituting the values of a = 0.005 ; b = 0.002 ; c = -9 in above quadratic formula we get,
[tex]\begin{aligned}&x=\frac{-0.002 \pm \sqrt{0.180004}}{0.01}\\\\&x=\frac{-0.002 \pm 0.4242}{0.01}\\\\&x=\frac{-0.002+0.4242}{0.01} \text { or } x=\frac{-0.002-0.4242}{0.01}\\\\&x=42.22 \text { or } x=-42.62\end{aligned}[/tex]
Ignoring negative value,
x = 42.22 ≈ 42
Thus 42 objects are required to keep the computer busy for exactly 9 seconds
A total of $11,000 is invested in two accounts. Part was invested at 4% and the rest was invested at 7%. If the investments earn $680 peer year, how much was invested at each rate? I=prt
Answer:
The amount invested at 4% was $3,000 and the amount invested at 7% was $8,000
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=1\ year\\ P_1=x\\P_2=11,000-x\\I=\$680\\r_1=4\%=4/100=0.04\\r_2=7\%=7/100=0.07[/tex]
substitute in the formula above
[tex]I=P_1(r_1t)+P_2(r_2t)[/tex]
[tex]680=0.04x+(11,000-x)0.07[/tex]
solve for x
[tex]680=0.04x+770-0.07x[/tex]
[tex]0.07x-0.04x=770-680[/tex]
[tex]0.03x=90[/tex]
[tex]x=\$3,000[/tex]
so
[tex]\$11,000-x=\$11,000-\$3,000=\$8,000[/tex]
therefore
The amount invested at 4% was $3,000 and the amount invested at 7% was $8,000