Answer:
Step-by-step explanation:
Help with this precalc question
The principal amount invested at the rate of 6% for 3 years, then the investment results in $717.38.
What is compound interest?Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.
As per the given information in the question,
Principle, P = $600
Rate, r = 6%
Time, t = 3 years.
Compound quarterly, r = 6/4
t = 4 × 3 = 12
Use the formula,
[tex]A = P(1+\frac{r}{100} )^t[/tex]
A = 600(1 + 6/4 × 100)¹²
A = 600 × (203/200)¹²
A = $717.38
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f(x) = -x³ + 3x² +9
x=4
[tex]{ \pink{ \boxed{ \red{ \sf{f(4) = - 7}}}}}[/tex]
Step-by-step explanation:
[tex]{ \green{ \sf{f(x) = { - x}^{3} + 3 {x}^{2} + 9}}}[/tex]
[tex]{ \green{ \sf{f(4) = ( { - 4})^{3} + 3( {4})^{2} + 9}}}[/tex]
[tex]{ \green{ \sf{f(4) = - 64 + 3(16) + 9}}}[/tex]
[tex]{ \green{ \sf{ f(4) = - 64 + 48 + 9}}}[/tex]
[tex]{ \green{ \sf{f(4) = - 64 + 57}}}[/tex]
[tex]{ \blue{ \boxed{ \orange{ \sf{f(4) = - 7}}}}}[/tex]
tan(tan^-1x)=x where?
Tan of arc tan x is equal to x when the angle x is 0 degrees
What is tan as used in math?Tangent is the ratio of the side opposite the angle we know or want to know over the side adjacent to that angle, and is sometimes abbreviated as tan.
In a right angle triangle, the formula for tan is as below
Tangent (tan) = opposite / adjacent
Arc tan (tan^(-1)) is the inverse of tan = adjacent / opposite
Arc tan is equal to tan when the angel is zero degree
therefore, tan (tan^(-1) x) = x
when x = 0
tan^(-1) 0 = 0
tan 0 = 0
tan (tan^(-1) 0)
tan (0)
0
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complete question
At what point does tan(tan^-1(x))=x
Calculate (A) amount to be credited and (B) balance outstanding: (Round your answers to the nearest cent.) Invoice: $3,000; Terms 2/10, n/30 Invoice date: July 5 Payment amount $600 Date paid: July 14
The amount to be credited, based on the invoice amount and the payment, is $612.24. The balance outstanding is $2, 387.76
How to find the balance outstanding?Credit terms of 2/10, n/30 mean that if a buyer pays their payables in 10 days, they get a 2% discount. If they don't, then they'd have to pay the full thing in 30 days.
The days till the partial payment was made was:
= July 14 - July 5
= 9 days
The discount of 2% would apply on the payment of $600 so the amount to be credited is:
= 600 / (1 - 2%)
= $612.24
The balance would then be:
= Invoice amount - credited amount
= 3, 000 - 612.24
= $2, 387.76
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What is the image point of (-8, 1) after the transformation D₂ 0 R180 ?
The image point of (-8, 1) after the transformation D₂ о R180° is equal to (16, -1).
Given that,
The point is (-8,1)
We must locate the point's picture.
In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).
We have the following for a 2 scale factor dilation:
Point A (-8, 1)
= (-8 × 2, 1 × 2)
= Point A' is (-16, 2)
By applying a rotation of 180° to the given point, the coordinates of its image is given by:
(x, y)→(-x, -y)
Points A' = (-16, 2)
Points A' = (-(-16), -(1)) = (16, -1).
Therefore, The image point of (-8, 1) after the transformation D₂ о R180° is equal to (16, -1).
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{ ( - 4, 2 ), ( - 1, 0 ), ( - 3, 1 ), ( 2, - 3 ) } Write the set using set notation and in ascending order.
By using set notation, the elements of the given data set in ascending order include {-4, -3, -3, -1, 0, 1, 2, 2}.
What is a listing method?In Mathematics, a listing method can be defined as a technique which is used to list all the elements or members of a data set, while separating each of them with a comma and enclosing the data set within curly braces.
Generally speaking, set notation is typically used in mathematics for listing the elements of a set such as objects, numbers, or outcomes, especially by making use of curly brackets.
For this exercise, the elements of the given data set would be listed in ascending order as follows:
Set = {-4, -3, -3, -1, 0, 1, 2, 2}
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=
4(7x), what is the value of a(-2)
The value of the function f(x) = 4 ( 7x ) for x = -2 is equal to f( -2 ) = -56.
As given in the question,
Given expression is equal to :
f(x) = 4 ( 7x )
Calculate the value of the given function for x = -2 is given by :
Substitute value of x = -2 we get.
f(-2)
= 4 ( 7 ( -2) )
Seven is positive and 2 is negative , multiplication of positive to negative is always negative.
So, 7 ( -2 ) is -14 Substitute in above equation we get,
= 4 ( -14 )
= -56
Therefore, the value of the function f(x) = 4 ( 7x ) for x = -2 is equal to
f( -2 ) = -56.
The complete question is :
If f(x) = 4 (7x) , what is the value of f(-2)?
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Abigail Henderson has $1360 budgeted for spending money on an upcoming trip to country and country be countries currency is trading $1.30 per Curren$y a and country bees currencies trading at $1.60 per currency be she plans to spend more time In country a so she wants to four times as much of currency a as currency be
Abigail Henderson's budget of $1,360 and the $1.30 and $1.60 trading price of the currency of country A and country B gives;
The equation that represents the total cost is; 1.3·x + 1.4·y = 1,360The number of each currency Abigail plans to buy are;
The number of units of currency of country A, x = 800The number of units of the currency of country B, y = 200What is a budget?A budget provides an estimation of a person, business, or country's income and expenditure over a specified period or duration.
The amount Abigail Henderson budgeted = $1,360
The per currency exchange rate for country A = $1.30
The per currency exchange rate for country B = $1.60
The number of currency A Abigail wants = 4 × The number of currency B
Which gives; x = 4·y
The equation that represents Abigail's total cost of buying currencies is presented as follows;
1.3·x + 1.6·y = 1,360
Plugging in the value of x gives;
1.3 × (4·y) + 1.6·y = 1,360
6.8·y = 1,360
y = 1,360 ÷ 6.8 = 200
The number of currency of country B, Abigail purchases, y = 200
The number of currency of country A Abigail plans to buy, x = 4 × 200 = 800
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A family wants to save $100 each month. They record their progress toward this goal at the end of each month. What would a recording of $0 mean?
A recording of $0 for the family simply means that they have not saved anything or have spent all the savings.
What is savings?Savings simply means keeping of miney for a period of time in order to cater for future expenses. Saving is defined as income that is not spent or deferred consumption. Saving methods include putting money aside in a deposit account, a pension account, an investment fund, or as cash. Saving also entails lowering expenses, such as recurring costs.
Here, the family wants to save $100 each month and they record their progress toward this goal at the end of each month.
A recording of $0 simply means no savings.
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convert the following percents to a decimal. show steps. help fast pls
10%
15%
17.5%
0.125%
113%
202.125%
Answer:
below
Step-by-step explanation:
0.1
0.15
0.175
0.00125
1.13
2.02125
How many liters of paint are in a 5 gallon bucket round your answer to the nearest liter
Answer:
19 liters
Step-by-step explanation:
Solve the proportion: 3/x=15/45
Answer:
[tex]x = 9[/tex]
Step-by-step explanation:
1 ) Cross-multiply...
[tex]\frac{3}{x}[/tex] ÷ [tex]\frac{15}{45}[/tex]
[tex]3[/tex] × [tex]45 = 15[/tex] × [tex]x[/tex]
[tex]135=15x[/tex]
2 ) Flip the equation...
[tex]15x=135[/tex]
3 ) Divide both sides by 15...
[tex]\frac{15x}{15}[/tex] = [tex]\frac{135}{15}[/tex]
[tex]x = 9[/tex]
Hope this helps! :)
What’s the answer???
Answer:
2nd
Step-by-step explanation:
Which expression is equivalent to 5x - 5x + 3x - 3x?
Answer:
0
Step-by-step explanation:
subtracting same numbers give you zero
The equation of line s is y= – 4x– 5/3 . Line t includes the point ( – 3,3) and is parallel to line s. What is the equation of line t?
The equation of the parallel line t is y = -4x - 9
How to determine the line equation?The equation of line s given as
y = -4x - 5/3
Also, from the question
The point on line t is given as
Point = (-3, 3)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = -4
This means that the slope of y = -4x - 5/3 is -4
The slopes of parallel lines are equal
This means that the slope of the line t is -4
The equation of the parallel line is then calculated as
y = m(x - x₁) +y₁
Where
m = -4
(x₁, y₁) = (-3, 3)
Substitute the known values in the above equation
y = -4(x + 3) + 3
Evaluate
y = -4x - 12 + 3
Evaluate the sum
y = -4x - 9
Hence, the parallel line has an equation of y = -4x - 9
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A relation contains the points (1,-4), (3, 2), (4, -3), (x, 7), and (-4, 6).
For which value of a will the relation be a function?
O-4
O-3
O 3
O 4%
For x = -3 the relation will be a function.
We know that a relation is a function when for each input there is exactly one output.
In this question, we need to find the value of x for which the relation will be a function.
We need to select the value of x such that x ≠ 1, 3, 4, -4
This means x must be -3
Therefore, For x = -3 the relation will be a function.
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Use PMT=
nearest dollar.
-nt
to determine the regular payment amount, rounded to the
The price of a home is $210,000. The bank requires a 15% down payment and one
point at the time of closing. The cost of the home is financed with a 30-year fixed-
rate mortgage at 6.5%.
a. Find the required down payment.
b. Find the amount of the mortgage.
c. How much must be paid for the one point at closing?
d. Find the total cost of interest over 30 years, to the nearest dollar.
B)
OA) a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $2100
d. total cost of interest over 30 years: $196,167
a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $1785
d. total cost of interest ver 30 years: $227,667
Oc) a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $2100
d. total cost of interest over 30 years: $227,667
OD) a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $1785
d. total cost of interest over 30 years: $406,167
Answer:
B
a. down payment: $31,500b. amount of mortgage: $178,500c. points paid at closing: $1785d. total cost of interest over 30 years: $227,667Step-by-step explanation:
You want to know the 15% down payment, the mortgage amount, the value of 1 point, and the total interest cost for a 6.5% 30 year loan on a $210,000 home.
Look at the Answer ChoicesThe answer choices all have the down payment as $31,500 and the loan value as $178,500. A "point" is one percent of the loan value (not the home value), so ...
1 point = 0.01 × $178,500 = $1785 . . . . . . eliminates choices A and C
The difference between choices B and D is in the value of the interest paid. Your experience with 30-year loans in this interest rate range tells you that the interest paid is between 1 and 2 times the loan value. That is, the chice $227,667 is more likely correct than the choice $406,167.
Comparing these two numbers, we see they differ by 178,500, which is the value of the loan. That is, we can guess that 406,167 is the total amount repaid, not just the interest.
Answer choice B is the only one that makes sense.
Work the problemIf you like, you can work the problem.
down payment = 15% × $210,000 = $31,500
loan amount = $210,000 -31,500 = $178,500
one point = 0.01 × $178,500 = $1785
The monthly payment is found using the amortization formula:
A = P(r/12)/(1 -(1 +r/12)^(-12t))
A = 178500(0.065/12)/(1 -(1 +0.065/12)^(-12·30)) ≈ 1128.24
The monthly payment amount is about $1128.
So, the total repaid is 360 payments of $1128.24, or $406,167.
The interest paid is this amount less the principal:
interest paid = $406,167 -178,500 = $227,667
Emi is a veterinarian. In a given week, 50% of the 16 dogs she saw were boxers. Antonio is also a veterinarian. In the same week, 7 of the 35 dogs he saw this week were Boxers. Each wants to record the part, the whole, and the percent.
Emi will need to locate the whole in this case because she already has the part and the percentage.
What is a whole?In mathematics, the total number of items being analyzed, in this case, the total number of dogs, is represented by a whole.
The term "part" refers to a quantity that is typically smaller than the total and describes particular qualities. For instance, 20 of the 30 students in a classroom enjoy playing basketball. The part is 20 then.
The relationship between the part and the whole is represented by the percentage, which is a number followed by the symbol%. In this instance, the proportion of boxers and overall dogs are related.
Emi already knows the percentage (50%), the part (16), and the total number of dogs, which in this case is 32, as a result of this.
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A bottle maker assumes that 24% of his bottles are defective. If the bottle maker is right, what is the probability that the proportion of defective bottles in a sample of 546 bottles would differ from the population proportion by greater than 4%? Round your answer to four decimal places.
The probability that the proportion of defective bottles in a sample of 546 bottles would differ from the population proportion by greater than 4% is: 10.9069.
What is the probability that the population proportion will be greater than 4%?To obtain the correct value, we need to use the formula for the Z score. This formula requires that we subtract the average or mean value from the data point provided and divide the remaining value by the standard deviation.
Here is the formula:
z = (x-μ)/σ
First population proportion = 0.24
The sample proportion, hat p = 0.04
Z score =
[tex]0.04 - 0.24 / \sqrt 0.24 (1 - 0.24) / 546[/tex]
So, the Z score will
= -10.9469
So, when the z score = - 10.9469, the probability that Z is greater than - 10.9469, is = 10.9069
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Write an equation of the line that passes through (-3,1) and is perpendicular to y= 1/2x +3
Answer: y=-2x-5
Check this in desmos
factor and graph the equation -0.01x² +0.5x
The graph and factor to the given equation are x= 50 or x=0.
What is equation?
An equation may be a formula in arithmetic that expresses the equality of 2 expressions by connecting them with the sign =.
Main body:
I am assuming the equation as : -0.01[tex]x^{2}[/tex] + 0.5x =0
Now first removing the decimal from the equation ,
-[tex]x^{2}[/tex]/100 + 5x/10 = 0
-[tex]x^{2}[/tex] + 50 x = 0
switching signs , we get
[tex]x^{2}[/tex] - 50x= 0
taking x as common
x(x-50) =0
so either x = 0
or
x- 50 = 0
x =50
Hence the value of x are 0 or 50.
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On one campus, 620 undergraduate students work 50 or more weeks. If this student body is average in terms of work habits, about
how many undergrads would you expect there to be on the entire campus?
Answer:
Step-by-step explanation:
The equation: -2(x - 5) = 4x is solved in several steps below. For each step, select the reason that best justifies it.
Equations:
2x + 10 = 4x
-2x + 10 + 2x = 4x + 2x
10 = 6x
10/6 = 6x/6
5/3=x
Options:
Simplifying
Subtraction Property of Equality
Multiplication Property of Equality
Addition Property of Equality
Distributive Property
Division Property of Equality
The order of reasons that best justifies each step of the equation's solution is as follows;
-2x + 10 = 4x (Distributive property)-2x + 10 + 2x = 4x + 2x (Addition property of Equality)10 = 6x (Simplifying)10/6 = 6x/6 (Division property of Equality)5/3 = x (Simplifying).What are the reasons that justify the steps of the solution?It follows from the task content that the reasons which best justify each step of the solution be identified.
Therefore; Given the equation; -2(x - 5) = 4x; we have;
-2x + 10 = 4x (Distributive property)-2x + 10 + 2x = 4x + 2x (Addition property of Equality)10 = 6x (Simplifying)10/6 = 6x/6 (Division property of Equality)5/3 = x (Simplifying).Ultimately, the reasons which best justifies each of the steps as required are as provided above.
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Answer: Justification for each step is provided below.
Step-by-step explanation:
Original Equation: -2(x - 5) = 4x
-2x + 10 = 4x --> Distributive property - simplify the left side
-2x + 10 + 2x = 4x + 2x --> Addition property of Equality - add 2x to both sides
10 = 6x --> Simplifying
10/6 = 6x/6 --> Division Property of Equality - divide each side by 6
5/3 = x --> Simplifying
Considering the Matrix: Give the solution in terms of x. Show work.
1 0 -.05 I 2
0 1 2 I 1
0 0 0 I 0
The solution to the system of equations, in terms of x, considering the augmented matrix, is of:
y = -40x + 81.x = 20x - 40.Augmented matrix of system of equationsThe augmented matrix of a system of equations is built as follows:
Each of the columns before the | represents the coefficients of a variable.The column after the | represents the numeric value of the expression.In this problem, there are three columns before the |, the there are three variables given as follows:
x,y and z.
The expression from the first row is:
x -0.05z = 2.
The expression from the second row is:
y + 2z = 1.
The third row is all zero, meaning that there is a free variable, hence the solution to the system is written as a function of x as follows:
x - 0.05z = 2
0.05z = x - 2.
z = (x - 2)/0.05
z = 20x - 40.
Hence the solution for y is:
y = 1 - 2z
y = 1 - 40x + 80
y = -40x + 81.
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Given the polynomial f(x) = 2x3 + 7x2 + x − 10, which of the following is true?
a (x + 2) is a factor since f(2) = 0.
b (x − 2) is a factor since f(2) = 0.
c (x + 2) is a factor since f(−2) = 0.
d (x − 2) is a factor since f(−2) = 0.
Answer:
Step-by-step explanation:
Given:
2[tex]x^{3}[/tex]+7[tex]x^{2}[/tex]+x-10
factor it
I used MatLab roots(x) to find these so I kinda cheated :P
-2.5, -2 , 1
so we know -2 is a factor and, then
x+2=0 is a factor
so the "x+2" answer C)
simplify tana+cota help asap
Using trigonometric ratios, tan a + cot a = (cos a + sin a) / sin a * cos a
Trigonometric RatioThe six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trigonometric ratios are evaluated with respect to sides and angles.
In the question given, the trig ratio is
tan a + cot a
We can simplify this as
tan a = sin a / cos a
cot a = 1 / tan a = 1 / sin a / cos a = cos a / sin a
Adding both ratios together
tan a + cot a = (sin a / cos a) + (cos a / sin a)
tan a + cot a = (cos a + sin a) / sin a * cos a
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Explain the steps for (-1/5) divided by 3/10 x (-2.4).
Answer: The correct answer is 14/7
Step-by-step explanation: This is the correct answer because it's explaining how to do it
What is the equation of the line in standard form?
A. x-2y=4
B. x+2y=4
C. 2x+y=2
D. 2r-y-2
Answer:
D. 2x -y = 2
Step-by-step explanation:
You want to know the standard-form equation of the line through points (-1, 4) and (2, 2) as shown on the graph.
Intercept formThe graph shows the x-intercept of the line is a=1, and the y-intercept of the line is b=-2. This means the intercept form of the equation is ...
x/a +y/b = 1
x/1 +y/(-2) = 1
Standard formMultiplying this equation by 2 gives ...
2x -y = 2 . . . . the standard form equation for the line
__
Additional comment
The standard form equation can also be developed from the coordinates of points on the line:
(y2 -y1)x -(x2 -x1)y = (y2 -y1)x1 -(x2 -x1)y1
(2 -(-4))x -(2 -(-1))y = (2 -(-4))(-1) -(2 -(-1))(-4)
6x -3y = -6 +12
Dividing by 3 gives the standard form equation ...
2x -y = 2
(PLEASE OPEN) Need help with triangle proofs, please.
The triangle proof that shows that angle Q and angle S are congruent to each other is explained below.
What is the Side-angle-side Congruence Theorem (SAS)?The side-angle-side congruence theorem (SAS) states that if the two sides and an included angle in one triangle is congruent to two corresponding sides and an included angle in the other triangle, then both triangles are congruent to each other.
If two triangles are congruent to each other, the CPCTC theorem states that all their corresponding parts are also equal or congruent to each other.
The triangle proof is given as:
Statements Reasons
1. PR bisects ∠PQS 1. Given
2. ∠1 ≅ ∠2 2. Definition of bisection
3. PQ ≅ PS 3. Given
4. RP ≅ PR 4. Reflexive property
5. ΔQPR ≅ ΔSPR 5. SAS theorem
6. ∠Q ≅ ∠S 6. CPCTC
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Given m || n, find the value of x and y.
(3y-17) (6x+20)°
(7x+13)
n
Answer:
Value of x = 7° & y = 45°
Step-by-step explanation:
According to the question m || n.
For x:
[tex] \rm \implies (7x + 13) \degree = (6x + 20) \degree \\ \\ \rm \implies 7x - 6x = 20 \degree - 13\degree \\ \\ \rm \implies x = 7 \degree[/tex]
For y:
[tex] \rm \implies (3y - 17)\degree + (6x + 20) \degree = 180\degree \\ \\ \rm \implies (3y - 17)\degree + (6 \times 7 + 20)\degree = 180\degree \\ \\ \rm \implies (3y - 17)\degree + (42 + 20)\degree = 180\degree \\ \\ \rm \implies 3y - 17\degree + 62\degree = 180\degree \\ \\ \rm \implies 3y + 45\degree = 180\degree \\ \\ \rm \implies 3y = 180\degree - 45\degree \\ \\ \rm \implies 3y = 145\degree\\ \\ \rm \implies y = \bigg( \frac{145}{3} \bigg) ^\degree \\ \\ \rm \implies y = 45\degree[/tex]