Final answer:
To find out how much of the $13,000 was loaned at 8%, set up a system of equations based on the total amount of the loan and the total interest received. Solve the equations to find that $7,250 was loaned at an 8% interest rate.
Explanation:
The student is dealing with a problem related to the allocation of two different simple interest rates for portions of a loan. To find out how much was loaned at 8%, we set up two equations representing the amounts loaned at each rate and the total interest earned. Let's assume the amount loaned at 8% is x and the amount loaned at 16% is y. The following system of equations can be formed:
x + y = 13000 (total amount loaned)0.08x + 0.16y = 1500 (total interest earned)By solving this system of equations, we can determine the value of x and y.
The first step is to express y in terms of x from the first equation: y = 13000 - x. Next, we substitute this expression into the second equation: 0.08x + 0.16(13000 - x) = 1500. Simplifying this gives us 0.08x + 2080 - 0.16x = 1500, which further simplifies to -0.08x = -580. Dividing by -0.08, we find x = 7250. Therefore, $7,250 was loaned at 8%.
Find the solution of the inequality
−4x+2≤−10
Question 3 options:
x≤2
x≥2
x≤3
x≥3
Answer:
option D
x≥3
Step-by-step explanation:
Given in the question an inequality
−4x + 2 ≤ −10
rearrange x terms to the left and constant to the right
-4x ≤ −10 - 2
-4x ≤ -12
cancel - on both sides, due to sign change inequality will also be change
4x ≥ 12
x ≥ 12/4
x ≥ 3
So, the solution of the inequality is x ≥ 3, x is greater than or equal to 3.
Answer:
x ≥ 3
Step-by-step explanation:
We have given a inequality.
−4x+2 ≤ −10
We have to find the solution of given inequality.
Adding -2 to both sides of given inequality, we have
-4x+2-2 ≤ -10-2
-4x ≤ -12
Cancelling negative sign from both sides of above inequality , we have
4x ≥ 12
Dividing by 4 to both sides of above equations, we have
x ≥ 3 which is the solution of inequality.
what fraction is equevalent to 1/4
Answer:
6/8
Step-by-step explanation:
all you have todo is multiply 2 on top and the bottom
Answer:
Step-by-step explanation:
2/8 3/12 4/16 5/20 6/24 7/28 8/32 9/36 10/40 11/44 12/44. .25 This is the decimal of 1/4
the list below shows the heights, in meters, of five different buildings 180,170,120,180,160
Answer:170
Step-by-step explanation:
Place the numbers in ascending order that should give you
120,160,170,180,180
Then find the number that is in the middle that would be 170, there for your answer is 170
Mike started saving money by putting 50 dollars aside. Each month, he adds more money than the month before. At the end of 36 months, he has saved 4950. How much more does he add each month?
Answer:
He add $5 more each month
Step-by-step explanation:
* Lets consider this problem as an arithmetic sequence because
he add every month x dollars more
∵ He start with 50 dollars ⇒ a (1st amount)
∵ He add x dollars every month ⇒ d
∵ He did that for 36 months ⇒ n
∵ He saved 4950 dollars ⇒ Sn
∵ Sn = n/2[2a + (n - 1)d]
* Where Sn is the total money after n months
a is the first amount he saved
d is the money he add more each month
∴ 4950 = 36/2[2(50) + (36 - 1)(x)]
∴ 4950 = 18[100 + 35x]
∴ 4950/18 = 100 + 35x
∴ 35x = 275 - 100 = 175
∴ x = 175/35 = 5 dollars
Answer:
Mike added $5 more each month.
Step-by-step explanation:
We are given that Mike started saving money by putting $50 aside. Each month, he adds more money than the previous month and so by the end of 36 months, he saved $4950.
Assuming this to be an arithmetic sequence:
[tex]S_n = \frac{n}{2} (2a+(n-1)d)[/tex]
where [tex]S_n=4950[/tex], [tex]n=36[/tex], [tex]a=50[/tex] and [tex]d= x[/tex].
Substituting the given values in the above formula to find how much more money does he add each month.
[tex]4950 = \frac{36}{2} (2 \times 50+(36-1)d)[/tex]
[tex]4950=1800+630x[/tex]
[tex]x=\frac{3150}{630}[/tex]
[tex]x=5[/tex]
Therefore, Mike added $5 more each month.
Determine which rectangle was transformed to result in rectangle E
Answer:
Rectangle C
Step-by-step explanation:
Rectangle C was transformed to Rectangle E.
To see how this occurs, let's follow point F (-2, 5) through the two transformations.
(a) Reflection across the x-axis
The x-coordinate does not change, but the y-coordinate changes sign.
Thus, F ⟶ F' (-2, -5).
(b) Translating up two units
The x-coordinate does not change, but the y-coordinate increases by 2..
Thus, F' ⟶ F" (-2, -3).
You can follow the same transformations for the other three corners of rectangle C.
Rectangle C ⟶ Rectangle E
What is the measure of MRN
Answer:
16
Step-by-step explanation:
180-109=71
71+93=164
180-164=16
A person operating a machine can mow 0.75 acres in ½ hour. What is the rate, in acres per hour, that the person can mow? Write your answer as a decimal.
1.50 acres is the answer.
Final answer:
The mowing rate is 1.5 acres per hour
Explanation:
To find the rate at which a person can mow in acres per hour, we need to use the data provided that a person can mow 0.75 acres in ½ hour. To convert this to a rate in acres per hour, we divide the acres mowed by the hours it took to mow them:
To find the rate at which the person can mow, we need to divide the number of acres mowed by the time taken. In this case, the person can mow 0.75 acres in 1/2 hour.
So, the rate at which the person can mow is 1.5 acres per hour
Rate (in acres per hour) = Acres mowed / Hours taken = 0.75 acres / 0.5 hours = 1.5 acres per hour
Thus, the person can mow at a rate of 1.5 acres per hour.
Convert 6 10/36 to an improper fraction in lowest terms
ANSWER
[tex] \frac{113}{18} [/tex]
EXPLANATION
We want to convert
[tex]6 \frac{10}{36} [/tex]
to improper fraction.
Let us first reduce the fractional part to get;
[tex]6 \frac{5}{18} [/tex]
We now multiply 6 by 18 and add 5 and then express the result over 18.
This will give us;
[tex] = \frac{6 \times 18 + 5}{18} [/tex]
[tex] = \frac{108 + 5}{18} [/tex]
[tex] = \frac{113}{18} [/tex]
To convert the mixed number 6 10/36 to an improper fraction, first simplify the fraction to 5/18. Then multiply the whole number by the denominator (6 * 18 = 108) and add the numerator (108 + 5) to get 113/18, which is in its lowest terms.
To convert the mixed number 6 10/36 to an improper fraction in its lowest terms, follow these steps:
First, simplify the fractional part of the mixed number by dividing the numerator and denominator by their greatest common divisor. In this case, 10/36 can be simplified because 2 is the greatest common divisor of 10 and 36. So, 10 \/ 2 = 5 and 36 / 2 = 18, which gives us 5/18.
Next, convert the mixed number to an improper fraction by multiplying the whole number by the denominator of the fraction then adding the numerator. 6 (the whole number) \\times 18 (the new denominator) = 108. Then add the numerator: 108 + 5 = 113.
The result is the improper fraction 113/18.
This improper fraction 113/18 is already in its lowest terms as the numerator and denominator have no common factors other than 1.
What’s the answer [x+2]=4
X + 2 = 4
= X = 4 - 2= 2
X=2
Happy to help! Marking my answer as the Brainliest would really be aprreciated.
I need help with this problem
Answer:
3695.5 m
1530.73 m
Step-by-step explanation:
Given in the question,
The distance probe travels at an angle of depression 67.4 from the ship to the ocean surface = 4000m
We will use trigonometry identities
sinФ = opposite / hypotenusecosФ = adjacent/ hypotenuse1)
distance of probe from top of sea to surface = x
cos(90 - 67.5) = x / 4000
x = 3695.5 m
2)
horizontal distance from ship to probe = y
sin(90-67.5) = y / 4000
y = 1530.73 m
Type the correct answer in the box
Answer:
5
2
2
Step-by-step explanation:
Given in the question the polynomial
x^5 - 9x^4 + 13x³ + 57x² - 86x - 120
1)has total of 5 zeroes
Regardless of odd or even, any polynomial of positive order can have a maximum number of zeros equal to its order.
2)
maximum of 2 positive real roots
Using Descartes' Rule of Signs
x^5 - 9x^4 + 13x³ + 57x² - 86x - 120
------------ -----------
1 2
There are 2 sign changes in the positive-root case. This number 2 is the maximum possible number of positive zeroes.
3)maximum of 2 negative real roots
Using Descartes' Rule of Signs
When f (–x), we have
- x^5 - 9x^4 - 13x³ + 57x² + 86x - 120
--------- ----------
1 2
number of sign changes = 2
The area of a rectangle is 229.2 m2. If the length is 15 m, what is the perimeter of the rectangle
Answer:
[tex]\large\boxed{P=60.56\ m}[/tex]
Step-by-step explanation:
The formula of an area of a rectangle:
[tex]A=lw[/tex]
l - length
w - width
We have
[tex]A=229.2\ m^2\\\l=15\ m[/tex]
Substitute:
[tex]15w=229.2[/tex] divide both sides by 15
[tex]w=15.28\ m[/tex]
The formula of a perimeter of a rectangle:
[tex]P=2(l+w)[/tex]
Substitute:
[tex]P=2(15+15.28)=2(30.28)=60.56\ m[/tex]
Ava and her little sister, April, both have the same birthdays on the same day. Ava is 12 years old, April is nine years old. Did you know that Ava was once double the age of April?How many years ago was that? WORTH 50 PTS PLZ ANSWER
Answer:
6 years ago
Step-by-step explanation:
12 - 6 = 6
9 - 6 = 3
3 * 2 = 6
Answer:
6 Years ago
Step-by-step explanation:
6 years ago, Ava was 6 and April was 3, making Ava double her age.
0=(x-1)^2-4
show work <33
Answer:
x=-1,3
Step-by-step explanation:
0=(x-1)^2-4
Add 4 to each side
0+4=(x-1)^2-4+4
4 = (x-1)^2
Take the square root of each side
sqrt(4) = sqrt((x-1)^2)
±2 = x-1
Separate into 2 equations
2 = x-1 -2 = x-1
Add 1 to each side
2+1 = x-1+1 -2 +1 =x-1+1
3 =x -1 =x
There are two solutions
x=-1,3
Mr.Nelson sold 147 bags of popcorn and 216 bottles of water in 3 days. At this rate, how many more bottles water than bags of popcorn will Mr.Nelson selling 5 days
Answer:
115
Step-by-step explanation:
72 water per day
49 popcorn per day
360 water in 5 days
245 water in 5 days
360-245=115
Please mark Brainliest
Answer:
115 bottles of water
Step-by-step explanation:
To make this easier, let us find out how many items he sells in one day. We can do this by dividing his original sales by 3, since it took him 3 days to sell the original.
[tex]\frac{147}{3} = 49[/tex]
[tex]\frac{216}{3} = 72[/tex]
We now know it took Mr. Nelson one day to sell 49 bags of popcorn and 72 bottles of water.
To find out how much Mr. Nelson sold in 5 days, all we need to do is multiply the numbers by 5.
[tex]49 * 5 = 245[/tex]
[tex]72*5=360[/tex]
It takes Mr. Nelson 5 days to sell 245 bags of popcorn and 360 bottles of water. However, the question is asking how many MORE bottles of water than bags of popcorn will he sell in five days.
Since we have how many he sold in five days, we need to get the difference of the two answers by subtracting them:
[tex]360-245=115[/tex]
Apply the distributive property to factor out the greatest common factor.9+15=9+15=9+15=
The factored expression of 9 + 15 is 3(3 + 5)
How to apply the distributive property?The expression is given as
9 + 15 =
Express 9 and 15 as a product of 3
9 + 15 = 3 * 3 + 3 * 5
Factor out 3
9 + 15 = 3(3 + 5)
Hence, the factored expression of 9 + 15 is 3(3 + 5)
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Find h, assuming the triangles formed are similar.
h =
Here is your answer
h= 15
REASON :
Since triangles formed are similar,
so its corresponding sides are proportional.
i.e. 6/h= 8/20
On solving we get,
h= 6/8 ×20
h= 120/8
h= 15
HOPE IT IS USEFUL
Answer:
[tex]h=15 units[/tex]
Step-by-step explanation:
It is given that the two triangles are similar, thus using the similarity conditions, we have
[tex]\frac{6}{h}=\frac{8}{20}[/tex]
Simplifying the above expression, we get
[tex]h={\frac{6{\times}20}{8}[/tex]
⇒[tex]h=3{\times}5[/tex]
⇒[tex]h=15 units[/tex]
Therefore, the value of h will be 15 units.
The line plot shows the length (in feet) of the girls hair in Mr. Wood’s Class. What is the difference in length between the girls with the shortest and longest hair? Please show work, thank you!
Answer:
1
Step-by-step explanation:
Because if the longest amount is 2 feet and the shortest is 1 feet 2 minus 1 equals 1.
A right rectangular prism has a length of 5 cm, a width of 4 cm, and a height of 3 cm. The dimensions of the prism are doubled. What is the surface area of the enlarged prism?
Answer:
376 square centimeters
Step-by-step explanation:
When doubled, the new length is 5*2=10 cm, new width is 4*2=8 cm, and new height is 3*2=6 cm.
The surface area of a rectangular prism is given by : [tex]2(lw+wh+lh)[/tex]
Where l is length, w is width, and h is height
Plugging in the new values we get:
[tex]2(lw+wh+lh)\\=2((10)(8)+(8)(6)+(10)(6))\\=2(80+48+60)\\=2(188)\\=376[/tex]
The surface area of the enlarged prism = 376 cm^2
Answer: 376 cm²
Step-by-step explanation:
If the dimensions are doubled then:
length=10cm
width=8cm
height=6cm
You must apply the formula for calculate the surface area of a rectangular prism, whih is shown below:
[tex]SA=2(wl+lh+hw)[/tex]
Where l is the length, w is the width and h is the height.
WHen you substitute values, you obtain the following result:
[tex]SA=2[(8cm*10cm)+(10cm)(6cm)+(6cm)(8cm)][/tex]
[tex]SA=376cm^2[/tex]
A rectangular prism has a surface area of 400 cm 2. If it is 10 cm long and 10 cm wide, what is its height? 4 cm 5 cm 8 cm 40 cm
Answer:
2((10)(10) + 10h + 10h) = 400
100 + 20h = 200
20h = 100
h = 5 cm
Urvi solved a fraction division problem using the rule “multiply by the reciprocal.” Her work is shown below.
Answer:
D. Urvi multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.
Step-by-step explanation:
We know that Urvi solved a fraction division problem using the rule “multiply by the reciprocal.”
According to this rule, “multiply by the reciprocal”, we need to take the reciprocal of the divisor (denominator) and multiply with the dividend in its original form.
Looking at the calculations made by Urvi, we can see that she took the reciprocal of the dividend and not the divisor.
Therefore, the correct answer option is D. Urvi multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.
Answer: it d
Step-by-step explanation:
Because the the the answer is the letter D
A swimming pool is 15 feet wide, 50 feet long, and has an average depth of 5 feet. How many cubic feet of water will it hold
it can hold water equal to volume of swimming pool.
so volume of swimming pool = L × B ×H
= 50 ×15 × 5 = 3750 cubic feet
The amount of water it will hold is 3750 feet³
Step-by-step explanation:According to the problem we need to find the volume of the pool
Volume = length x width x height
Volume = 15 x 50 x 5
Volume = 3750 feet³
So the amount of water it will hold is 3750 feet³
There are 1,760 yards in a mile. How many full laps would Danny have to run around the block to run a mile?
2 my brotha boi only 5,560 or so feet and more than that so its certainly 2 laps.
Danny have to run 7 laps to cover 1760 yards.
What is Perimeter?The perimeter of a shape is the distance around its edge.
A rectangle's perimeter is the total distance covered by its boundaries or sides. Because a rectangle has four sides, the perimeter of the rectangle is the total of the four sides.
The yard is 80 feet yards and 60 yards long.
So, the perimeter of block
= 2(80+ 66)
= 2 x 146
= 292 yards
So, to cover 1760 yards the number of laps to run is
= 1760 / 292
= 6.027
= 7 laps
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find the solution of this system of equations 6x+3y=12 6x-5y=60
Answer:
(5, - 6)
Step-by-step explanation:
Given the 2 equations
6x + 3y = 12 → (1)
6x - 5y = 60 → (2)
Multiply (2) by - 1 and add to (1) will eliminate the term in x
- 6x + 5y = - 60 → (3 )
Add (1) and (3) term by term
(6x - 6x) + (3y + 5y) = (12 - 60)
8y = - 48 ( divide both sides by 8 )
y = - 6
Substitute y = - 6 into (1) or (2) and siolve for x
Using (1), then
6x - 18 = 12 ( add 18 to both sides )
6x = 30 ( divide both sides by 6 )
x = 5
Solution is (5, - 6)
The solution to the system of equations 6x + 3y = 12 and 6x - 5y = 60 is x = 2 and y = -6.
Explanation:The subject of this question is to find the solution to a system of two linear equations. These equations are: 6x + 3y = 12 and 6x - 5y = 60.
To find the solution to these, one way is to subtract one equation from the other to eliminate x. When we subtract the second equation from the first, we get: (6x+3y) - (6x-5y) = 12 - 60. This simplifies to 8y = -48.
Therefore, y = -48 ÷ 8 which gives the solution y = -6. Substituting y = -6 into the first equation gives us 6x = 12 - 3*(-6), which becomes 6x = 12 to get x = 2.
So the solution to this system of equations is x = 2 and y = -6.
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can someone help me with this? graph the quadratic function label the vertex axis of symmetry and x intercepts. Describe the Domain and range of the function.
Answer:
x-12(+4)
Step-by-step explanation:
7x+4x=11x+1x=12x +4.
Number 10 I don’t know how to do
Yes he is correct
Step-by-step explanation:Given a triangle ABC, the sum of the lengths of any two sides of the triangle is greater than the length of the third side. In the words of Euclid: In any triangle two sides taken together in any manner are greater than the remaining one.
If we add the two sides 12 and 18 we get 30 so the third side must be greater than 30. He said greater than 6 so he is right too
What function can be used to model data pairs that have common ratio
Answer:
Step-by-step explanation:
y = mx, or y = kx, where m or k is the common ratio, or slope, or constant of proportionality.
PLEASE HELP
What money is added to cost of items or services?
A gross income
B income tax
C sales tax
D budget
The answer is C: Income tax
Answer:
C. Sales tax
Step-by-step explanation:
This is added to items that you buy.
Given the function f(x)= -5x²-x+20, find f(3).
Answer: -28
Step-by-step explanation:
f(3) = -5 x (3)^2 - 3 + 20
= -45-3+20
= -28
Hope this helps!
Answer:
-28
Step-by-step explanation:
Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the following equation.
Point: (−1,−2)(−1,−2)
Equation: 3x−y=53x−y=5
Parallel Equation: y=
Answer:
y = -3x -5
Step-by-step explanation:
Parallel lines are parallel because they never intersect. As such, they have the same slope. The equation 3x - y = 5 can be converted to slope intercept form to find the slope. The slope of the line y = -3x - 7 is -3. Substitute m = -3 and the point (-1,-2) into the point slope form of a line.
[tex]y -y_1 = m(x-x_1)\\y --2 = -3(x --1)\\y + 2 = -3(x+1)\\[/tex]
You can convert the equation to slope intercept form by using the distributive property.
y + 2 = -3(x+1)
y + 2 = -3x - 3
y = -3x - 5