Based on the cost of the car and the simple interest loan amount, the amount of Darren's monthly payment is $363.33
What is the monthly payment?First, find the simple interest on the loan:
= 12,000 x 3% x 3 years
= $1,080
The total amount to be repaid:
= 1,080 + 12,000
= $13,080
The monthly payment is:
= 13,080 / (12 x 3 years)
= $363.33
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Answer: its 363.33
Step-by-step explanation:
Simplify each expression.
[tex](y-3)(y^2+9)(y+3) - (2y^2 -y)^2 - 19[/tex]
The simplified expression of the expression given as (y - 3)(y^2 + 9)(y + 3) - (2y^2 - y)^2 - 19 is (y^4 - 81) - (2y^2 - y)^2 - 19
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to simplify the expression?The expression is given as
(y - 3)(y^2 + 9)(y + 3) - (2y^2 - y)^2 - 19
Rewrite the above expression as
(y + 3)(y - 3)(y^2 + 9) - (2y^2 - y)^2 - 19
Apply the difference of two squares formula
So, we have
(y^2 - 9)(y^2 + 9) - (2y^2 - y)^2 - 19
Evaluate the product
So, we have
(y^4 - 81) - (2y^2 - y)^2 - 19
Hence, the simplified expression of the expression given as (y - 3)(y^2 + 9)(y + 3) - (2y^2 - y)^2 - 19 is (y^4 - 81) - (2y^2 - y)^2 - 19
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The price of an item plus 6% sales tax
The expression of the statement is 1.06x
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the expression of the statement?The statement is given as
The price of an item plus 6% sales tax
Let the price of the item be x
So, we have the sales tax amount to be
Sales tax amount = x * 6%
Evaluate the product
So, we have
Sales tax amount = 0.06x
So, the total amount is
Total = x + 0.06x
Evaluate the sum
So, we have
Total = 1.06x
Hence, the expression of the statement is 1.06x
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Solve for t -7/4= 5/2t
Solve for T
Answer:
t=−7/6
I hope this helps.
which option please help
Step-by-step explanation:
when lines are parallel gradiant should be the same in both equations
or m in y=mx+c
A)
1. y=-3x-6
2. y=-3x+6
therefore A is parallell
B)
1. y=44x+7/2
2.y=2/3x-17
therefore not parallel
c)
1. y=8x/7-17/7
2. y=-23x/21+30/21
therefore not parallel
d)
1. y=-8x/7+6
y=-7x/8-12
therefore not parallel
might have missed something-am tired. let me know if you have an issue.
if f(x) is the height in cm of a sunflower plant that is x days old which of the following statements best describes the meaning of f(60) = 210
Write the phrase as an expression. Twice a number w
Answer: w2
Step-by-step explanation:
It is just w2, or w*2, or w x 2. You just have the number w twice.
Estimate each value to the nearest whole number.
5.4²
Hey there!
(5.4)^2
= 5.4^2
= 5.4 * 5.4
= 29.16
Therefore, your answer should be:
29.16
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Suppose your teacher offers to give the whole class a bonus if everyone passes the next math test. The teacher says she will give everyone a 10-point bonus and increase everyone's grade by (9%) of their score.
a. You earned a 75 on the test. Would you rather have the 10 -point bonus first and then the \(9 \%\) increase, or the (9%) increase first and then the 10 -point bonus?
b. Is this the best plan for all students? Explain.
Function f(x) to represent the 10-point bonus. f(x) = x+10
Function g(x) to represent the 9% increase. g(x) = X +0.09x
g(x) = 1.09x
Use a composite function to find your grade if the 10-point bonus is applied before the 9% increase.
(g.f)x = g(f(x))
f(75) = 85
g(85) = 92.65
Use a composite function to find your grade if the 9% increase is applied before the 10-point bonus.
(f.g)(x) = f(g(x))
g(75) = 1.09(75) = 81.75
f(x) = 81.75+10 = 91.75
You would want 10 point bonus applied before percentage increase. the 10 point bonus is flat increase.
whereas the percentage increased larger if multiplying by a bigger number your grade would be almost 1% higher with is option
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On a slow weekend, you spend at least two hours on homework. on a busyweekend, you spend as much as five hours on homework. write an ablosue value inequality that repersents the number of hours you spend doing homework on a typical week day. math problem
The absolute value inequality that represents the number of hours spent on doing homework is 2 ≤ x ≤ 5
Let us assume that one spends x hours doing homework on a typical weekday. Then we can write
The inequality expression for a slow weekend is given as;
X ≥ 2
In the same vein, the inequality expression for a busy weekend is given as;
X ≤ 5
Pooling the two inequalities expression we have;
2 ≤ x ≤ 5
Two inequality expression could be written simultaneously if they can be expressed individually. They are commonly referred to as a “double” inequality and is often written in the form a ≤ f (x) ≤ b
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4x - 11x + 32 = 4 if the value for x is 5
Answer:
no solution or -3=4
Step-by-step explanation:
There are 75 men at a party and 60 women. How many more percent more men are there then women?
Need help, had a brain fart
There are 11.2% more men than women
How to calculate the percentage ?The First step is to calculate the percentage of men in attendance
There are 75 men and 60 women
Total number of people in attendance= 75 +60
= 135
75/135 × 100
= 0.556 × 100
= 55.6
The percentage of women in attendance
= 60/135 × 100
= 0.444 × 100
= 44.4
Next step is to subtract both percentages
= 55.6 - 44.4
= 11.2
Hence there are 11.2% more men that women
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A teacher asked students why it is necessary to check for extraneous roots when squaring both sides of the equation. Which of the following answers is the best? Is this answer complete? Explain.
(A) Because the squared equation can have negative roots.
B) Because squaring is multiplication, and any multiplication is a potential source of extraneous roots.
(C) Because when you square both sides of the equation, you add to the solution set the roots of the equation a=-b .
(D) Because any operation with an equation may result in extraneous roots.
Because the squared equation can have negative roots.
If the equation you're given already includes the squared variable (and you don't multiply by the variable yourself), then you don't need to worry about the extraneous root. Both solutions will be correct because the variable was already squared.
You only need to worry about the extraneous root in the case of a quadratic equation if you made the equation quadratic by multiplying by a variable. Any time you square a negative number or a variable (which may be negative), you risk losing information by making it positive. That means that, if you square a variable (especially for variables on both sides of the equation, which can easily hide a negative) or a negative number, you should always do a quick plug-in and check.
Because the squared equation can have negative roots.
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Which postulate proves these two triangles are congruent
The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.
What is a triangle?A triangle is a polygon that has three angles and three sides. The sum of angles in a triangle is 180 degrees.
Types of triangles are isosceles, scalene and equilateral triangles. Two angles are said to be complementary if their sum is 90 degrees.
Two triangles are said to be congruent if all their corresponding sides and angles are congruent. This means that the triangles have equal angles and equal sides.
The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.
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If y varies directly as x and y= 64 when x=4 find x when y=48
Answer:
If y varies directly as x and y= 64 when x=4 find x when y=48
x=3
Use the properties of exponential and logarithmic functions to solve each system. Check your answers.
log (2 x-y)=1
log (x+y)=3 log 2
The solved logarithmic function is 2x - y = e and x + y = 8 for log (2x - y) = 1 and log (x + y) = 3 log 2 respectively.
What is a logarithmic and exponential function?
Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet, e. For example log 10 = 1 and e^2.
Solving the given expressions: log (2x - y) = 1 and log (x + y) = 3 log 2
Applying given properties of logarithmic and exponential function;
log a + log b = log (ab)
4 log x = log x⁴
e^(log x) = 1
e^(x + y) = (e^x) × (e^y)
Take expression, log (2x - y) = 1
Applying exponential on both sides, we get,
e^(log 2x - y) = e^1
2x - y = e
To Check Results,
Taking logarithm both sides,
log (2x - y) = log e
log (2x - y) = 1
Thus, the answer is verified.
Take expression, log (x + y) = 3 log 2
Applying exponential on both sides, we get,
e^(log (x + y) = e^(3 log 2)
x + y = e^(log 8)
x + y = 8
To Check Results,
Taking logarithm both sides,
log (x + y) = log 8
log (x + y) = 3 log 2
Thus, the answer is verified.
Hence, the solved expression is 2x - y = e and x + y = 8 for log (2x - y) = 1 and log (x + y) = 3 log 2 respectively.
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6. a right triangle has a line of symmetry. select all conclusions that must be true. a. all sides of the triangle have the same length. b. all angles of the triangle have the same measure. c. two sides of the triangle have the same length. d. two angles of the triangle have the same measure. e. no sides of the triangle have the same length. f. no angles of the triangle have the same measure.
Answer:
C.
D.
Step-by-step explanation:
For right triangle has a line of symmetry two sides of the triangle have the same length and two angles of the triangle have the same measure.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
A right angle triangle is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular.
If a right triangle has a line of symmetry then two sides of triangle will have same length and two angles are equal.
For a triangle to have a line of symmetry, it must be an isosceles triangle, meaning two of it’s sides and two of it’s angles must be the same.
From there it follows that for a right triangle to have a line of symmetry it must be an isosceles right triangle, meaning it must either have two 90-degree angles, or two identical non-90-degree angles.
Hence for right triangle has a line of symmetry two sides of the triangle have the same length and two angles of the triangle have the same measure.
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Ifa box of apples is distributed among 28 children , each gets 3 . iF 7 children were not present , their share would also ne distriibuted among the others How many apples would each children get
Answer:
First subtract 28 by 7.
28 - 7 = 21
Then multiply 28 times 3
28 times 3 is 84
Then finally divide 84 by 21
84/21 = 4
Each of the children would get 4 apples
Step-by-step explanation:
Me ayudan? La necesito para mañana
Answer:
1. 9/10 x 3 = 93/10
2. 9/8
Espero que esto ayude a tener un buen día!
Can someone help me with this please? I need the answers and the work shown please... thank you!
Answer:
Below
Step-by-step explanation:
Ok, there is a few ways to slove this problem. You could just try to plug in both xs and see which is true, or you could actually do the math. I will do the math.
Alright, the first question is a corrseponding angle, so they are equal to each other. Set it up like this:
3x-1=x+5
Now, you need to get the variable by itself, so do that.
3x-1=x+5
+1 +1
3x=x+6
-x -x
2x=6
/2 /2
x=3
The arrow will go to the right.
Now, you have a same side exterior angle. When you add these together, they will equal 180 degrees, so set up the equation like this.
8x+10+6x+2=180
Now, solve
8x+10+6x+2=180
Combine like terms (8x+6x)+(10+2)
14x+12=180
-12 -12
14x=168
/14 /14
x=12
Your arrow will go down.
Same side interior angles is your next problem, and it is like same side exterior angles as it equal 180. Set up your equation accordingly
10x-8+5x+8=180
Combine like terms (10x+5x)+(8-8)
15x=180
/15 /15
x=12
Your arrow will go down.
These are opposite side exterior angles, so they will equal each other. Set up the equation accordingly.
9x+18=10x-8
Get the variable on one side and by themselves
9x+18=10x-8
+8 +8
9x+26=10x
-9x -9x
26=x
Your arrow will go upper corner right
This problem is opposite side exterior angles, so they will equal each other. Set up the equation accordingly.
2x+5=3x-7
+7 +7
2x+12=3x
-2x -2x
12=x
Your arrow will go up
Now, you have a same side exterior angle. When you add these together, they will equal 180 degrees, so set up the equation like this.
8x+5+2x-15=180
Combine like terms (8x+2x)+(5-15)
10x-10=180
+10 +10
10x=190
/10 /10
x=19
Arrow goes diagonal right down
The angles are opposite side interior angles, so they are equal to each other. Set up your equation like this:
4x-4=-3x+52
+4 +4
4x=-3x+56
+3x +3x
7x=56
/7 /7
x=8
That is your finish!
Solve each equation.
2⁵x⁺¹=32
After solving the equation, x = 4/5 is the value of x in [tex]2^{5x+1} = 32[/tex]
⇒ [tex]2^{5x+1} = 32[/tex]
⇒ [tex]2^{5x+1} = 2^5[/tex]
⇒ 5x + 1 = 5
⇒ 5x = 5 - 1
⇒ 5x = 4
⇒ x = 4/5
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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For a result to be considered _____, the chances of its occurring as a result of random error are often less than 5 percent.
For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.
What is Random error?A coincidental discrepancy between the observed and true values of anything is known as a random error (e.g., a researcher misreading a weighing scale records an incorrect measurement).
It's not always a mistake when there is random error; rather, it happens when measurements are made. Even when you measure the same item repeatedly, there will always be some variation in your results because to changes in the environment, the instrument, or your own perceptions.
Your measurements are equally likely to be greater or lower than the genuine values due to random error, which has unexpected effects.
According to the given data,
For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.
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a_1=4 and an=a_{n-1}+6
The value of the fifth term based on the expression a + (n - 1) + 6 is 14.
How to calculate the value?From the information, it should be noted that the first term has been given and the nth series has been given.
It should be noted that the fifth term will be:
= a + (n - 1) + 6
where
a = 4
n = 5
Therefore, a + (n - 1) + 6
= 4 + (5 - 1) + 6
= 4 + 4 + 6
= 14
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a_1=4 and an=a + {n-1}+6. Find the fifth term
Ms. Moya has received 13 Starbucks cards from students and generally gets 2 more
each year she teaches. Ms. Powers has only ever been given 1 Starbucks gift card but
plans to get 5 more each year she teaches. Which equation models the situation to find
the number of years before they have the same number of Starbucks cards?
Answer:
13+2=15+2=17+2=19+2=21
1+5=6+5=11+5=16+21
(The Pink Answer)
What is the solution of (x+2)³/₄=27 ?
(A) x=27 (B) x=79 (C) x=81 (D) x=83
The solution (B) x=79.
Rewriting the equation to find the solution -
(x+2)³/₄=27
Raising both sides of the equation with exponent ⁴/₃
((x+2)³/₄)⁴/₃ = 27⁴/₃
Cancelling the exponents on Left Hand Side of the equation. Writing the value on Right Hand Side of the equation in exponent form
x + 2 = (3³)⁴/₃
Cancelling 3 on Right Hand Side of the equation
x + 2 = 3⁴
Solving Right Hand Side of the equation
x + 2 = 81
Shifting 2 to Right Hand Side of the equation
x = 81 - 2
Performing subtraction on Right Hand Side of the equation
x = 79
Hence, the solution is (B) x=79.
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5. Table Item The table shows the time and
distance Hector walked in a 5-kilometer-long
walk for charity. The distance is proportional
to the time walked. Complete the table to
show the times of his last three walks.
(Lesson 3)
Distance (km) Time (min)
1.5
13.5
2010
4.5
5
The distance being proportional to the time Hector walked 2 km in 18 minutes.
Two variables are proportional if they can be written in the form ak=b where k is the proportionality constant.
Here the proportionality constant is speed.
Speed is defined as the distance covered in unit time. The unit of speed can be written as kilometer per hour, miles per hour or meters per second.
The distance is proportional to the time walked therefore:
1.5/2=13.5/T₁
or, T₁=18
Similarly:
1.5/4.5=13.5/T₂
or, T₂=40.5 minutes
again,
1.5/5=13.5/T₃
or, T₃=45 minutes.
Hence the total time taken to complete the distances 2,4.5 and 5 is given by 18,40.5 and 45 minutes.
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Two financial institutions offer different deals to new customers. The first bank offers an interest rate of 3 % for the first year and 2 % for the next two years. The second bank offers an interest rate of 2.49 % for three years. You decide to invest the same amount of principal in each bank. To answer the following, assume you make no withdrawal or deposits during the three-year period.
c. Write a function that represents the total amount of money in both accounts at the end of three years.
The function that represents the total amount of money in both accounts at the end of three years as
First Bank - 107 P / 100
Second Bank - 10747 P / 10000
Simple interest :
Simple interest can be calculated as follows
S.I = PRT / 100
Let the amount invested in two banks be 'P'
First Bank :
Given the first bank offers an interest rate of 3% for the first year and 2% for the next two years as
R₁ = 3%, R₂ = 2% T₁ = 1, T₂ = 2
Now the simple interest for the first bank is
S. I = PR₁T₁ / 100 + PR₂T₂ / 100
= P(3*1 / 100 + 2*2 / 100)
= P(3 / 100 + 4 / 100)
= 7P/100
The total amount of money in the first bank at the end of three years is
= S.I + P
= 7P / 100 + P
= 107 P / 100
Second Bank:
Given the second bank offers an interest rate of 2.49% for the three years as
R = 2.49, T = 3
Now the simple interest for the second bank is
S. I = PRT / 100
= P(2.49 * 3 / 100 )
= P(7.47 / 100)
= 7.47P/100
The total amount of money in the second bank at the end of three years is
= S.I + P
= 7.47P / 100 + P
= 107.47 P / 100
= 10747 P / 10000
Therefore, the function that represents the total amount of money in both accounts at the end of three years as
First - 107 P / 100
Second - 10747 P / 10000
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to determine the number of cashiers needed when a grocery store opens each
morning, the manager of the store wanted to estimate the typical number of items each
customer purchased. the manager took all the receipts from the first 30 minutes the
store was open on a particular day and recorded the number of items purchased by
each customer. the manager constructed the following boxplot from the information
on the receipts.
From the box-and-whisker plot of the distribution, we have that:
The center of the distribution is the median of 32.The range of the distribution is described by two measures, the IQR of 35 - 22 = 13 and the range of 62 - 17 = 45.The distribution is left skewed.What is the missing information?The plot of the distribution is missing, as is given at the end of the answer.
It asks to describe:
The center of the distribution.The variability of the distribution.The shape of the distribution.What does a box-and-whisker plot shows?A box and whisker plot shows five things:
The minimum value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum value.For the plot in this problem, we have that:
Minimum: 17.Q1: 22.Median: 32.Q3: 35.Maximum: 62.Hence:
The center of the distribution is the median of 32.The range of the distribution is described by two measures, the IQR of 35 - 22 = 13 and the range of 62 - 17 = 45.The distribution is left skewed, as Q3 - Q2 < Q2 - Q1.More can be learned about box-and-whisker plots at https://brainly.com/question/12343132
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Carol has a balance of $520 in her checking account. She writes three
checks each for $120 from the account. She also deposits 2 paychecks for
$240 each. What is her balance now?
w
dealer in
stail
Answer:
$640
Step-by-step explanation:
3 checks at $120 each = 3 x 120 = $360
This will reduce the balance so we should treat it as -360
2 paychecks at 240 = 2 x 240 = $480
This will increse the balance so we should treat it as +480
Net balance = 520 - 360+480=640
Balance = $640
help
Which expression is equivalent to 5(2.47y − 2.03)?
12.35y + 10.15
12.35y − 10.15
12.35y + 2.03
12.35y − 2.03
Step-by-step explanation:
I will first expand. Whatever is in the brackets will be multiplied by 5=5(2,47y)+5(-2,03)
=12.35y-10,15
0.6r = 4.5
giving brainlest n a lot of points