Chris opened up a new credit card and credit line with U.S bank. He is paying a 15% APR on all new purchases
A. if he has a balance of 2,800 on his credit card, how much does he owe in interest to the bank next month?
B. if he sends in a payment to U.S bank for $140, how much of that will go towards paying off his principle balance
Answer:
Which one does not belong to the group
AandBhave coordinates (-1,1.5) and (3,2).
Tangents to the curve have been drawn at A and B.
Calculate the gradient of the curve at A and at B.
An organization supports 125 villages financially. This figure is only 11% as compared to the organization's worldwide support. How many villages does the organization support worldwide?
If organisation supports 125 villages financially and it is 11% of world wide then the total villages in world wide that needs help is 1136.36 villages.
Given An organization supports 125 villages financially. This figure is only 11% as compared to the organization's worldwide support.
If 125 villages are 11% of worldwide villages who need help financially then we have to find 100% value according to organisation figure which can be calculated as under:
if 125 is 11% then 1% will be 125/11
then 100% will be 125/11*100
=12500/11
=1136.36
=1136 Approx
Hence 1136 villages are totally present worldwide which need help financially.
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Use the formula to solve the equation x^2 + 9x + 8 = 0.
Answer:
[tex]x=-8, -1[/tex]
Step-by-step explanation:
Given the equation [tex]x^{2} +9x+8=0\\[/tex],
By the quadratic formula,
[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex],
[tex]x=\frac{-(9)+-\sqrt{(9)^{2}-4(1)(8) } }{2(1)}=\frac{-9+-\sqrt{49 } }{2}=\frac{-9+-7 }{2}[/tex]
We have two different solutions for x where [tex]x=\frac{-9-7 }{2}[/tex] and [tex]x=\frac{-9+7 }{2}[/tex]
So, x = [tex]-16/2=-8[/tex] and [tex]x=-2/2=-1[/tex]
Therefore, the solutions to this quadratic equation is x = -8, -1, by the quadratic formula.
1-sinA+cosA / sinA+cosA-1 = 1+cosA/sinA
Solution:
[tex]\dfrac{\left[\left(\sin ^{2} A+2 \times \sin A \times (1-\cos A)+(1-\cos A)^{2}\right]\right.}{\left[\left(1-\cos ^{2} A\right)-(1-\cos A)^{2}\right]}[/tex]
[tex]\dfrac{\left[\left(1-\cos ^{2} A\right)+2 \times \sin A \times (1-\cos A)+(1-\cos A)^{2}\right]}{\left[(1-\cos A)(1+\cos A)-(1-\cos A)^{2}\right]} [/tex]
[tex]\dfrac{(1-\cos A)[1+\cos A+2 \sin A+1-\cos A]}{[1-\cos A][1+\cos A-1+\cos A]} [/tex]
[tex]\dfrac{[2+2 \sin A]}{[2 \times \cos A]}[/tex]
[tex]\dfrac{2(1+\sin A)}{2 \times \cos A}[/tex]
[tex]\dfrac{1+\cos A}{\sin A} [/tex]
Hence Proved.
a television set was priced $1659 after a 30% discount. What original price before the discount?
=======================================================
Work Shown:
x = price before the discount
30% of x = 0.30x = amount saved
x - 0.30x = 0.70x = price after discount = 1659
0.70x = 1659
x = 1659/(0.70)
x = 2370
First we'll have to convert the percent into decimal.
We'll have to divide the value by 100.
[tex]\frac{30}{100}[/tex]
[tex]\bold{=0.30}[/tex]
Now, we can find the original price.
[tex]\large\boxed{\bold{Formula:OP= \frac{price}{1-Discount}}}[/tex]
We have all the necessary values to find the original price.
Let's solve!
Substitute the values according to the formula.
[tex]OP=\frac{1659}{1-0.30}[/tex]
OP= $2370
Therefore, the original price of the television set is $2370
Find (f • g) (x) Assume x>0
Answer:
[tex]\textsf{B.} \quad (f \cdot g)(x)=10x[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}f(x)=\sqrt{50x}\\g(x)=\sqrt{2x}\end{cases}[/tex]
[tex]\begin{aligned}\textsf{As }(f \cdot g)(x) & = f(x) \cdot g(x)\\\implies (f \cdot g)(x)& = \sqrt{50x} \cdot \sqrt{2x}\end{aligned}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}:[/tex]
[tex]\begin{aligned}\implies (f \cdot g)(x) &= \sqrt{50x2x}\\& = \sqrt{100x^2}\end{aligned}[/tex]
Rewrite 100 as 10²:
[tex]\implies (f \cdot g)(x)=\sqrt{10^2x^2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^bc^b=(ac)^b:[/tex]
[tex]\implies (f \cdot g)(x)= \sqrt{(10x)^2}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]
[tex]\implies (f \cdot g)(x)=10x[/tex]
What are the x-coordinates of the solutions to this system of equations?
x² + y² = 16
y = x + 4
The x-coordinates are -4 and 0.
find the inequality for 20 points pls
First find the Slope-intercept form of the graph:
b=1
Given the points: (0,1)&(3,0)
slope= [tex]\frac{y1-y2}{x1-x2} =\frac{1-0}{0-3} =\frac{-1}{3}[/tex]
The line is not a dashed line, so that means the values on the slope (blue) are also counted
All the y values below the slope are counted, the inequality is:
y[tex]\leq \frac{-1}{3}x +1[/tex]
Hope it helps!
Express your answer as a decimal. 63÷12=
Answer:
5.25
Step-by-step explanation:
Answer:
5.25Step-by-step explanation:
type 63 : 12 in your calculator
see the example in the attachment.
Situation:
A 45 gram sample of a substance that's
used to sterilize surgical instruments has
a k-value of 0.15.
N = Noe kt
No initial mass (at time t = 0)
N= mass at time t
k= a positive constant that depends on
the substance itself and on the units
used to measure time
t-time, in days
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
Enter the correct answer.
DONE
+?
The substance's half-life is 4.7 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.15
What is exponential decay?During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.
We have an exponential function:
[tex]\rm N = N_oe^{-kt}[/tex]
Plug N = N⁰/2
[tex]\rm N_o/2 = N_oe^{-kt}[/tex]
[tex]\rm \dfrac{1}{2} = e^{-0.15t}[/tex]
Solving for t:
t = 4.62≈ 4.7 days
Thus, the substance's half-life is 4.7 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.15
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You went to an electronics store and would like to buy a TV priced at $1200. You only have $1000 to
spend and the store gives 15% discount on the TV. Can you buy the TV? Explain
Which expression is not a polynomial?
x³
x² - 2x
x³ +1
12x
Answer:
12x
Step-by-step explanation:
It has no exponent so it is not a polynomial
Which graph shows the greatest integer function?
The graph of the greatest integer function is graph A.
What is graph?A graph is a diagram or a pictorial representation of data or values that show the relationship between quantities or objects.
Given are graphs we need to find the graph of the greatest integer function,
The graph of the greatest integer function is graph A because since it is a greatest integer function, it includes the highest integer, but excludes the lowest since it is the highest integer when x is less than or equal to an integer but greater than x-1.
Hence the graph of the greatest integer function is graph A.
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PLS HELPPPP I NEED AN ANSWER ASAP WILL GIVE BRAINIEST
What are the alternate exterior angle pairs in the picture below?
∠1 and ∠2, ∠7 and ∠8
∠1 and ∠8, ∠2 and ∠7
∠1 and ∠7, ∠2 and ∠8
Answer:
∠1 and ∠2, ∠7 and ∠8
Answer:
∠1 and ∠7, ∠2 and ∠8
Step-by-step explanation:
just took the quiz
Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
D
Step-by-step explanation:
Trust me
Pls answer fast
(√3 + √11)² + (√3 - √11)²
(√3 + √11)² + (√3 - √11)²
(a+b)² = a² + b² + 2ab ( a - b )² = a² + b² - 2abNow ,
(√3 + √11)² + (√3 - √11)²
(3 + 11 + 2√3√11)+ (3 +11 - 2√3√11)
14 + 2√33+ 14 - 2√33
14 + 14 = 28
Hence , The value of (√3 + √11)² + (√3 - √11)² is 28 .
Answer:
28
Step-by-step explanation:
(a + b)² + (a - b)² = 2a² + 2b²
(√3 + √11)² + (√3 - √11)²
= 2√3² + 2√11²
= 28
A system of equations has 1 solution. If 4x - y = 5 is one of the equations, which could be the other equation?
A.y=-4x+5
B. Y=4x -5
C.2y=8x-10
D.-2y=-8x-10
answer :
A. y = – 4x + 5
Step-by-step explanation:
make y = 4x-5 equal to each of the answer choices and see if you get an answer
STEPS:
1.
make 4x - y = 5 into a y= equation
4x - y = 5 is y = 4x-5
2.
then make y = 4x-5 equal to each of the answer choices and see if you get an answer
A.
4x-5 = -4x+5
8x = 10
x = 10/8 = 5/4
yes, it has one solution
its also an intersecting line because
one line has 4x and the other has -4x
4x and -4x are slopes and opposite signs so
the lines are intersecting
B.
4x-5 = 4x-5
since they are the same on both sides of the equal sign they have
infinite solutions
they are also both the same line
C.
2y=8x-10 when simplified is y=4x-5
so its just like choice B
they are also both the same line
4x-5 = 4x-5 which is
0 = 0
since they are the same on both sides of the equal sign
infinite solutions
they are also both the same line
D.
-2y=-8x-10 when simplified is y=4x+5
4x-5 = 4x+5 when you work it out you get the answer
0 = 5
since when you solve the equation and get 0 = 5
that means its there is no solution
its also parallel line because both lines have 4x as a slope
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The amount of money that kailyn earns varies directly with the number of hours she works. if she works for 15 hours and makes 146.25, how much will she make in 40 hours.
Answer:
$390
Step-by-step explanation:
The wage rate for Kailyn is ($146.25/15 hours) = $9.75/hour
40 hours would result in:
(40 hours)*($9.75/hour) = $390
Given the following formula,A school needs to buy new notebook and desktop computers for its computer lab. The notebook computers cost $300 each, and the desktop computers cost $225 each. How much would it cost to buy 18 notebooks and 12 desktop computers? How much would it cost to buy n notebooks and dd desktop computers?
Total cost, 18 notebooks and 12 desktop computers:
Total cost, n notebooks and dd desktop computers:
The cost to buy 18 notebooks and 12 desktop computers will be $8100.
The cost to buy n notebooks and d desktop computers will be 300n + 225d
What is the cost of a given material?The cost of a given material is the amount attached and to be paid for getting that material.
From the given information:
The cost of notebook computers = $300The cost of desktop computers is $225 eachThe cost to buy 18 notebooks and 12 desktop computers will be:
= 300(18) + 225(12)
= 5400 + 2700
= $8100
The cost to buy n notebooks and d desktop computers will be:
= 300(n) + 225(d)
= 300n + 225d
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Select the correct answer.
Consider the given functions.
A table with values of x and f of x is given along with a non-linear equation g of x equals 2 power x minus 5 and a graph solving the equation
Select the true statement regarding the end behavior of the functions.
Using limits, it is found that the true statement regarding the end behavior of the function is given by:
B. As the value of x increases, f is the only function to approach 0.
How to find the end behavior of a function?The end behavior of a function is given by the limit of the function as x goes to infinity.
In this problem, we have that:
[tex]\lim_{x \rightarrow \infty} f(x) = 0[/tex], as we can see from the table, when x increases, y decreases. [tex]\lim_{x \rightarrow \infty} g(x) = 2^{\infty} = \infty[/tex].[tex]\lim_{x \rightarrow \infty} h(x) = \infty[/tex], from the graph.Hence statement B is correct.
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Determine the endpoints of the midsegment connecting side YX and side YZ
Answer:
endpoint of midsegment connecting side YX is (4, 3)
endpoint of midsegment connecting side YZ is (5, -1)
Step-by-step explanation:
Mid point of a line segment - it is the middle point of a line segment. It is equidistant from both endpoints and it is the centroid both of the segment and of the endpoints.
according to the graph;
Y is (1, 2), Z is (9, -4), X is (7, 4)
therefore using mid point formula we can determine the endpoints of midsegments connecting side YX and YZ
if (x , y) and (x1, y1) are the endpoints of a line then;
The coordinates of mid point are given by the formula = (x+x1)/2, (y+y1)/2
using the above formula mid point of YX is
(7+1)/2, (4+2)/2 = (4, 3)
and the mid point of line YZ is
(9+1)/2, (-4+2)/2 = (5, -1)
hence the answer is (4,3) and (5, -1)
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Given the graph of the function, f(x), what is the value of f (–2)?
f (–2) =
Using the graph of the function concept, the numeric value at x = 2 is f(-2) = 0.
How to find the numeric value of a function?To find the numeric value of a function at x = a, we look at the value of y(vertical axis) where x = a has a closed interval.
Researching the problem on the internet, looking at it's graph, it is found that when x = -2, there is a closed interval at y = 0, hence f(-2) = 0.
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Answer:
0A: (-∞, ∞)B: (-2, ∞)Step-by-step explanation:
solve simulteneusly equation 6p-4r=4 and p-2r=5
Answer:
r = - 3.25, p = -1.5
Step-by-step explanation:
→ Rearrange p - 2r = 5
p = 5 + 2r
→ Substitute into 6p - 4r = 4
6 ( 5 + 2r ) - 4r = 4
→ Expand
30 + 12r - 4r = 4
→ Simplify and solve
r = - 3.25
→ Substitute into p - 2r = 5
p + 6.5 = 5
→ Minus 6.5 from both sides
p = -1.5
A rectangular field with sides as shown below has to be fenced all around. If fencing posts have to be fixed at 1-metre intervals, how many posts are needed?
1. 167
2. 334
3. 668
4. 6840
Step-by-step explanation:
the perimeter of a rectangle is
2×length + 2×width
so, here
2×95 + 2×72 = 190 + 144 = 334 m
so, yes, the answer 2. 334 is correct.
The solution is Option B.
The total number of posts is the total perimeter of the rectangular field and the value of N = 334 posts
What is the Perimeter of a Rectangle?
The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P = 2 ( Length + Width )
Given data ,
Let the number of posts be = N
Fencing posts have to be fixed at 1-metre intervals
The perimeter of the rectangular field = number of posts
Now , the equation will be
The length of the rectangular field = 95 m
The width of the rectangular field = 72 m
Perimeter P of the rectangle = 2 ( Length + Width )
Substituting the values in the equation , we get
Perimeter of the rectangle P = 2 ( 95 + 72 )
On simplifying the equation , we get
Perimeter of the rectangle P = 2 ( 167 )
Perimeter of the rectangle P = 334 m
Now , the number of posts = perimeter of the rectangular
So , the number of posts N = 334 posts
Therefore , the value of N is 334
Hence , the number of posts is 334 posts
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If m/BAD = 22°,
what is X?
A
C
22⁰
B
D
Answer:
x = 136
Step-by-step explanation:
x = 180 - 22 - 22
= 136
Please help me out…
Polygon ____ and polygon ____ are similar to polygon 1.
Answer:
Polygon 3 and polygon 4 are similar to polygon 1.
Step-by-step explanation:
I believe this is the answer from the looks of it. If it's not 3, then try 2. I know one of them is definitely 4 though. I hope this helps!!
HELP ANGJHHGG plssssssssssssssssssfghgg
Answer:
5377
Step-by-step explanation:
this is a vector question where how far is the Resultant. that is, it is determined by the magnitude of the Hypotenuse.
using Pythagoras theorem
Hypotenuse ²= Opposite ²+Adjacent²
Hypotenuse ²= 2865²+4550²
Hypotenuse ²= 8208225+20702500
Hypotenuse ²=28910725
Hypotenuse=√28910725
Hypotenuse=5376.86944234282
Hypotenuse= 5377 approximated
[tex]\frac{4x}{x-1} -\frac{5x}{x-2}=\frac{2}{x^{2} 3x+2}[/tex]
The value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2
How to solve the equation?The equation is given as:
[tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex]
Start by taking the LCM
[tex]\frac{4x(x - 2) - 5x(x - 1)}{(x - 1)(x -2)} = \frac{2}{x^2 - 3x + 2}[/tex]
Expand the denominator
[tex]\frac{4x(x - 2) - 5x(x - 1)}{x^2 -3x +2} = \frac{2}{x^2 - 3x + 2}[/tex]
Cancel out the common factor
4x(x - 2) - 5x(x - 1)= 2
Expand
[tex]4x^2 - 8x - 5x^2 + 5x = 2[/tex]
Evaluate the like terms
[tex]-x^2 - 3x = 2[/tex]
Rewrite as:
[tex]x^2 + 3x + 2 = 0\\[/tex]
Expand
[tex]x^2 + 2x + x + 2 = 0[/tex]
Factorize
x(x + 2) + 1(x + 2) = 0
Factor out x + 2
(x + 1)(x + 2) = 0
Solve for x
x = -1 or x = -2
Hence, the value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2
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Plsss helppppp I neeed this
Based on the calculations on the bisector of ST, the value of ST are equal to 38 and 30 respectively.
How to find the bisector of ST?In order to determine the bisector of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
For exercise 1, we have:
ST = SM + MT
ST = 19 + 19
ST = 38.
For exercise 2, we have:
First of all, we would determine the value of x as follows;
3x - 6 = x + 8
3x - x = 8 + 6
2x = 14
x = 14/2
x = 7.
ST = SM + MT
ST = 3x - 6 + x + 8
ST = 3(7) - 6 + 7 + 8
ST = 30.
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