Payment Every Month = $2,514.58
Total of 1 Payments = $2,514.58
Total Interest = $14.58
What is simple intertest ?
Simple interest is calculated based on the principal of a loan or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accumulated.
Solution:
Principal value = $2500
Interest rate = 7%
Time = One month
Formula for simple interest calculation:
[tex]=\frac{Principalamount*rate *time}{100} \\=\frac{2500*7*(\frac{1}{12}) }{100}\\ =14.588[/tex]
Total Simple interest on $2500 for month $14.588.
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4x−4<8 and 9x+5>23 find x
Answer:
Step-by-step explanation:
for the first one, it is x=2
for the second one, it is x=9
Find the product of:
(3x - 4)(2x^2 + 2x - 1).
A. 6x^3 + 2x^2 - 5x + 4
B. 6x^3 + 14x^2 - 11x + 4
C. 6x^3 - 14^2 - 5x + 4
D. 6x^3 - 2x^2 - 11x + 4
Answer:
6x^3 -2x^2-11x + 4
Step-by-step explanation:
(3x - 4)(2x^2 + 2x - 1)
(3x - 4)(2x^2 + 2x - 1)
[(3x)(2x^2 + 2x - 1)] + [-4(2x^2 + 2x - 1)]
6x^3 + 6x^2 - 3x -8x^2 - 8x + 4
6x^3 + [6x^2-8x^2] [- 3x- 8x] + 4
6x^3 -2x^2-11x + 4
Answer:
[tex]6x^3-2x^2-11x+4[/tex]
Step-by-step explanation:
Given expression:
[tex](3x-4)(2x^2+2x-1)[/tex]
Distribute the parentheses:
[tex]\implies 3x(2x^2+2x-1)-4(2x^2+2x-1)[/tex]
[tex]\implies 3x \cdot 2x^2+3x \cdot 2x +3x \cdot -1 -4 \cdot 2x^2-4 \cdot 2x-4 \cdot -1[/tex]
[tex]\implies 6x^3+6x^2 -3x -8x^2-8x+4[/tex]
Collect like terms:
[tex]\implies 6x^3+6x^2-8x^2 -3x -8x+4[/tex]
Combine like terms:
[tex]\implies 6x^3-2x^2-11x+4[/tex]
Can someone please explain how to do this? I don’t need the answer I just don’t know how to solve it.
Let [tex]P[/tex] be the number of plain cakes sold, and [tex]D[/tex] the number of decorated cakes sold.
Each plain cake sells for $7, so [tex]P[/tex] cakes sells for [tex]\$7P[/tex].
Similarly, each decorated cakes goes for $11, so [tex]D[/tex] cakes are worth [tex]\$11D[/tex].
The baker sells all but 3 cakes, so
[tex]P + D = 117[/tex]
After the sale, the baker earns a total of $991, so
[tex]7P + 11D = 991[/tex]
Now just solve the system of equations for [tex]P[/tex] and [tex]D[/tex]. This is easily done by substitution or elimination.
(The selected answer is actually the correct one.)
if we multiply or divide both sides of a linear equation with a non zero number, then the solution of the linear equation
hi
"does not change " or "remain the same "
picture explains everything please help ASAP
Answer: Choice B is correct.
You roll two number cubes one red and one blue. the table shows the probability
Answer:
where is the table?
Step-by-step explanation:
How does the graph of g(x) = (x − 2)3 + 6 compare to the parent function of f(x) = x3?
The graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.
How does the graph of g(x) compare to the one of f(x)?
Here we have:
[tex]f(x) = x^3\\\\g(x) = (x - 2)^3 + 6[/tex]
You can notice that if we take f(x), and we shift it 2 units to the right, we have:
g(x) = f(x - 2)
Then if we apply a shift upwards of 6 units, then we have:
g(x) = f(x - 2) + 3
Replacing f(x) by the cubic parent function, we have:
[tex]g(x) = (x - 2)^3 + 6[/tex]
So we conclude that the graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.
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1. Factor and simplify: cos² xcsc² x-cos²xcot² x
Answer:
Cos² x
Step-by-step explanation:
Trigonometry:[tex]\sf Cos^2 \ x *Csc^2 \ x-Cos^2 \ x *Cot^2 \ x = Cos^2 \ x (Csc^2 \ x - Cot^2 \ x)[/tex]
[tex]\sf = Cos^2 \ x \left(\dfrac{1}{Sin^2 \ x} - \dfrac{Cos^2 \ x}{Sin^2 \ x}\right)\\\\= Cos^2 \ x \left(\dfrac{1-Cos^2 \ x}{Sin^2 \ x}\right)\\\\\boxed{\bf Indentity: \ 1 - Cos^2 \ x = Sin^2 \ x}\\\\\\= Cos^2 \ x \left(\dfrac{Sin^2 \ x}{Sin^2 \ x}\right)\\\\= Cos^2 \ x[/tex]
i have no idea whats going on. PLEASE HELPPP
Answer:
36 meters
Step-by-step explanation:
You are given an angle and the length of the side adjacent. You want to find the length of the side opposite, so the relevant trig relation is ...
Tan = Opposite/Adjacent
SetupThe height of Yuri's balcony is the sum of the heights of Kim's balcony and the height of Yuri's balcony above that. Each of those height is the side opposite a given angle in a right triangle. These can be found by solving the tangent relation for the opposite side:
Tan = Opposite/Adjacent
(Adjacent)(Tan) = Opposite
height of Kim's balcony = (30 m)tan(40°)
height above Kim's balcony = (30 m)tan(20°)
__
height of Yuri's balcony = height of Kim's + height above Kim's
height of Yuri's balcony = (30 m)tan(40°) +(30 m)tan(20°)
height of Yuri's balcony = (30 m)(tan(40°) +tan(20°))
Evaluationheight of Yuri's balcony ≈ (30 m)(0.8391 +0.3640) ≈ 36.092 m
The height of Yuri's balcony is about 36 meters.
Identify m∠EFH.
The figure shows triangle G F H. Angle G is equal to 76 degrees. A measure of angle H is given by the formula 3 times x minus 3 degrees. Side G F lies on ray G F with endpoint G. Angle H F E is an exterior angle and its measure is given by the formula 8 times x plus 8 degrees.
Based on the calculations, the magnitude of m∠EFH is equal to 112°.
How to find the magnitude of m∠EFH?In Geometry, the sum of two (2) non-adjacent interior angles in a triangle is equal to its exterior angle. Thus, we have:
(3x - 3) + 76 = 8x + 8
3x + 73 = 8x + 8
73 - 8 = 8x - 3x
65 = 5x
x = 65/5
x = 13.
From triangle GFH, we have:
m∠EFH = ∠F = 8x + 8
m∠EFH = 8 (13) + 8
m∠EFH = 104 + 8
m∠EFH = 112°.
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25 POINTS!!!!
The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 7 units, the value of k is ________??
The answer is k = 7.
As the graph has been shifted down 7 units, the translation can be represented as :
g(x) = f(x) - 7
(0.5)x - k = (0.5)x - 7
k = 7
A graduate school entrance exam has scores that are normally distributed with a mean of 560 and a standard deviation of 90. What percentage of examinees will score between 600 and 700
26.8% of examinees will score between 600 and 700.
This question is based on z score concept.
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.
[tex]z={x-\mu \over \sigma }[/tex]
where:
μ is the mean
σ is the standard deviation of the population
Given:
μ = 560
σ = 90
For
600≤ X≤700
for x = 700
Z score =x - μ/σ
=(700 - 560)/90
= 1.55556
P-value from Z-Table:
P(560<x<700) = P(x<700) - 0.5 = 0.44009
for x = 600
Z score =x - μ/σ
=(600 - 560)/90
= 0.44444
P-value from Z-Table:
P(560<x<600) = P(x<600) - 0.5 = 0.17164
∴ P(600<x<700) = P(560<x<700) - P(560<x<600)
= 0.44009 - 0.17164
=0.26845
∴26.8% percentage of examinees will score between 600 and 700.
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given that 4x-y=5 4y-z=7 and 4z-x=18 what is the value of x+y+z
Answer:
x + y +z= 10
Step-by-step explanation:
4x - y = 5 ---------(I)
4y - z = 7 ---------(II)
4z - x = 18 ---------(III)
Add all the three equations,
4x - y + 4y - z + 4z - x = 5 + 7 + 18
4x - x -y + 4y -z + 4z = 30
3x + 3y + 3z = 30
Divide the entire equation by 3
[tex]\sf \dfrac{3x}{3}+\dfrac{3y}{3}+\dfrac{3z}{3} = \dfrac{30}{3}[/tex]
x + y + z = 10
Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
2x - y = 7
2y = 4x - 14
Since there are same number of either side, hence the solution has infinite number of solution
System of equationsSystem of equations are equation that consist of two or more equations with unknown variables.
Given the equations
2x - y = 7
2y = 4x - 14
This can also be written as
2x - y = 7
y = 2x - 7
Substitute equation 2 into 1
2x - (2x - 7) = 7
2x-2x+7= 7
7 = 7
Since there are same number of either side, hence the solution has infinite number of solution
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Volume = length x width x height
1.
? ft
? ft
? ft
If the volume of the cube is 1 ft³,
Find the equation of the line that
is perpendicular to y = 6x-2 and
contains the point (6, -2).
y =
= [2²] x + [ ]
Answer:
y = - [tex]\frac{1}{6}[/tex] x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 6x - 2 ← is in slope- intercept form
with slope m = 6
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{6}[/tex] , then
y = - [tex]\frac{1}{6}[/tex] x + c ← is the partial equation
to find c substitute (6, - 2 ) into the partial equation
- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1
y = - [tex]\frac{1}{6}[/tex] x - 1 ← equation of perpendicular line
The sum of an integer and 7 more than the next consecutive integer is 66. find the integer
If the sum of an integer and 7 more than the next consecutive integer is 66 then the integers are 29 and 30.
Given that the sum of an integer and 7 more than the next consecutive integer is 66.
Integer is a number that is written without a fraction component. It can be positive as well as negative.
let the first integer be x.
Consecutive integer will be x+1.
Sum of integer and 7 more than the next consecutive integer is 66.
Sum according to the given information=x+x+1+7
=2x+8
2x+8=66
2x=66-8
2x=58
x=58/2
x=29
Next integer=29+1-30.
Hence if the sum of an integer and 7 more than the next consecutive integer is 66 then the integers are 29 and 30.
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The rug for the kitchen has an area of 80 square feet. the width is 40 feet. what is the length?
HELPPPP‼️‼️
19. In a school election, 250 votes are tallied for 3
candidates: Eric, Kai, and Sarah. If Eric got 50
votes, and Kai gets 60% of the remaining votes,
how many votes did Sarah get?
Answer:
The answer is 75 and here's why.
Let's figure out the amount of remaining votes to prove this.
250 total votes - 150 votes for candidate a = 100 votes.
minus ↑ sign
Candidate B received 25% of the votes, so let's find 25% of 100
100 * 0.25 = 25 votes
Candidate B only got 25 votes (that's kinda sad, poor guy)
100 - 25 votes = the # of votes candidate C got
Candidate C got 75 votes!
The value of a company’s stock is represented by the expression x2 – 2y and the company’s purchases are modeled by 2x 5y. the company’s goal is to maintain a stock value of at least $5,000, while keeping the purchases below $1,000. which system of inequalities represents this scenario? x2 – 2y > 5000 2x 5y < 1000 x2 – 2y > 5000 2x 5y ≤ 1000 x2 – 2y ≥ 5000 2x 5y < 1000 x2 – 2y ≤ 5000 2x 5y ≤ 1000
Answer:
answer is (c)
May it help you
Option C. The inequality can then be written as x² - 2y ≥ 5000 and 2x + 5y <1000
How to write the inequality
Stock = x² - 2y
Purchase = 2x + 5y
Stock is said to be at least 5000 dollars. We can write this as
x² - 2y ≥ 5000
Then the purchase is said to be below 1000. This is written as 2x + 5y <1000
The inequality can then be written as x² - 2y ≥ 5000 and 2x + 5y <1000
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What is the angle at a
Answer and Step-by-step explanation:
We are given a triangle, a quadrilateral inside a triangle. and exterior angles of the triangle at linear bisectors.
We can figure out the interior angles of the shape to find a by using the linear bisector theorem, in which a line separated by another line will have two angles that will add to 180 degrees.
For the bisected line with the angle of 60 degrees, the other angle will have to equal 120. We know this by taking 60 from 180.
The perpendicularly bisected line will always have 90 degrees for the angles, so the interior angle will be 90 degrees.
For the bisected line with the angle of 80 degrees, the other angle will have to equal 100. We know this by taking 80 from 180.
Now, we have angles to determine a.
Quadrilaterals consist of 4 interior angles, which, when added together, equals 360 degrees.
360 - 90 - 100 - 120 = a
260 - 90 - 120 = a
140 - 90 = 50 = a
So, angle a is equal to 50 degrees.
#teamtrees #PAW (Plant And Water)
Students in a ninth grade class measured their heights, h, in centimeters. The height of the shortest student was 155 cm, and the height of the tallest student was 190 cm. Which inequality represents the range of heights?
A. h > 155 or h < 190
B. 155 ≤ h ≤ 190
C. 155 < h < 190
D. h ≥ 155 or h ≤ 190
Answer:
a h>155 or h<190
Step-by-step explanation:
The height of the shortest student is 155 cm and the height of the tallest student is 190 cm, then the inequality shows the range is 155 ≤ h ≤ 190. Hence, option B is correct.
What is an inequality?Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.
As per the provided data in the question,
The height of the shortest student is 155 cm and,
The height of the tallest student is 190 cm.
It means that the height rage is starting from 155 cm and ending at 190 cm.
The shortest height should be at least equal to 155 cm and the greater height is maximum 190 cm.
Therefore, the inequality according to this is 155 ≤ h ≤ 190.
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I needed help solving this question please if u can
Answer:
1) 4x + 5y = 20 4x + 5y = 20
-2x + 3y = 12 --> 2(-2x + 3y) = 2(12)
2) 4x + 5y = 20
-4x + 6y = 24
3) 4x + 5y = 20
-4x + 6y = 24
0x + 11y = 44
4) 11y = 44
5) y = 4
6) 4x + 5y = 20
4x + 5(4) = 20
7) 4x + 20 = 20
8) 4x = 0
9) x = 0
10) The solution is the point (0, 4)
Graph by hand or using a calculator to determine the solution to the given system. Put in slope-intercept form first if necessary.
The solution to the system of equations is (8, -4)
How to solve the system?The system of equations is given as;
y = -1/4x - 2
y = 3/8x - 7
See attachment for the graph of the equations
From the attached graph, we have the point of intersection to be
(x, y) = (8, -4)
Hence, the solution to the system of equations is (8, -4)
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Consider the function represented in this table. f(x) -1 -21 0 -9 1 3 2 15 Which of these tables could represent the inverse of function f? X X -1 0 1 2 q(x) 21 9 -3 -15
If f(-1)=-21,f(0)=-9,f(1)=3,f(2)=15 then the inverse of function f(x) is p(-21)=-1,p(-9)=0,p(3)=1,p(15)=2 which is option d.
Given that f(-1)=-21,f(0)=-9,f(1)=3,f(2)=15 and we are required to find the inverse if the function.
Function is relationship between two or more variables expressed in equal to form. In a function each value of x must have corresponding value of y.
The given function is as under:
f(-1)=-21,
f(0)=-9,
f(1)=3
f(2)=15
In the inverse of the function the value of x becomes the value of y and the value of y becomes the value of x. So the inverse of the function is as under:
p(-21)=-1,
p(-9)=0,
p(3)=1,
p(15)=2
Hence if f(-1)=-21,f(0)=-9,f(1)=3,f(2)=15 then the inverse of function f(x) is p(-21)=-1,p(-9)=0,p(3)=1,p(15)=2 which is option d.
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does this inequality have a solution? 6(x+2)>x-3
Answer:
x > - 3
Step-by-step explanation:
6(x + 2) > x - 3 ← distribute parenthesis on left side
6x + 12 > x - 3 ( subtract x from both sides )
5x + 12 > - 3 ( subtract 12 from both sides )
5x > - 15 ( divide both sides by 5 )
x > - 3
[tex]\textbf{Heya !}[/tex]
✏[tex]\bigstar\textsf{Given:-}[/tex]✏
[tex]\sf{6(x+2) > x-3}[/tex]✏[tex]\bigstar\textsf{To\quad find:-}[/tex] ✏
x -- ?✏[tex]\bigstar\textsf{Solution \quad Steps:-}[/tex] ✏
use the distributive property
[tex]\sf{\longmapsto 6x+12 < x-3}[/tex]
subtract both sides by x and 12
[tex]\sf{\longmapsto{5x < -15}[/tex]
divide both sides by 5
[tex]\sf{\longmapsto x < -3}}[/tex]
`hope it's helpful to u ~
Instructions: Find the missing side. Round your answer to the nearest tenth.
x=
Check
30
X
17
Sine rule:
30/sin(17) = x/sin(90)
x sin(90)
30 x sin(90) / sin(17) = x
x = 102.6091086
So, x = 102.6 to the nearest tenth.
Hope this helps!
5 Jack works as a part-time waiter. He earns $60 per weekday and $98 per day on weekends. (a) On a particular week, he works from Tuesday to Sunday. How much was he paid for that week? (b) Find his average wage rate per day.
Can someone help me out on this please having trouble on both and show work please !!
The difference of the expression is as follows:
(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5) = - 6y⁴ + 4y² - 12
3(x - 5) - (2x + 4) = x - 19
How to find the difference of the expression?The difference of the expression can be found when we combine the like terms.
Therefore,
(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5)
6y⁴ + 3y² - 7 - 12y⁴ + y² - 5
6y⁴ - 12y⁴ + 3y² + y² - 7 - 5
- 6y⁴ + 4y² - 12
3(x - 5) - (2x + 4)
3x - 15 - 2x - 4
3x - 2x - 15 - 4
x - 19
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She needs to know the length of each side so she can buy fencing. What is the length of line segment FJ
Using the Pythagorean theorem, the length of line segment FJ is: 42 ft.
How to Apply the Pythagorean Theorem?To find the length of line segment FJ, we need to apply the Pythagorean theorem to find the length of the segment from F to the point, say point O, on FJ where a right triangle FOG will be gotten.
Thus, we have:
FO = √(GF² - GO²)
FO = √(30² - 24²)
FO = 18 ft.
FJ = FO + GH
Plug in the values
FJ = 18 + 24
FJ = 42 ft.
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