Given the equation :
[tex]y=3x^3-3[/tex]It is a cubic function because the power of x = 3
The cubic function is not linear function
The linear function has the form : y = m * x + b
The power of x for the linear function = 1
so, the answer is : No
A sinking fund is established to discharge a debt of $70,000 in 10 years. if deposits are made at the end of each 6-month period and interest is paid at the rate of 9%, compounded semiannually, what is the amount of each deposit? (round your answer to the nearest cent.)
The amount of each deposit is $210000
What is compound interest?Compound interest is when you reinvest your income. Compound interest distinctively means "interest on interest" and is the reason so many investors are so successful.
The computation of the each deposit is shown below:
Given that
Future value be $70,000
Time period = 10 × 2 = 20
And, the rate = 9% ÷ 2 = 4.5%
Now the formula is as follows
= (Future value × rate of interest) ÷ (1 + rate of interest)^time period - 1
= ($70,000 × 4.5) ÷ (1 + 0.025)²⁰⁻¹
= $315,000 ÷ 1.5
= $210000
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if f(x) has a remainder of -2 when divided by x-7, what is f(7)?
If f(x) has a remainder of -2 when divided by x-7, f(7) is -2.
The leftover is -2 when the function f(x) is divided by x-7, according to the question.
hence the result will be -2 if we use the value x = 7 in the function.
This has the same meaning as "f(7)" because "f(7)" also means to enter "x = 7" in the function and "-2" as the response.
Therefore, if f(x) is divided by x-7 with a remainder of 2, f(7) is equal to -2.
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Find the domain and range and intercepts.g of x = 3 / x-4
a) Domain; all real numbers except 4
b) Range; all real numbers except y = 0
c) Y-intercept = -0.75
d) x-intercept does not exist
Here, we want to find the domain, range and intercepts
The domain refers to the possible x-values
From the question, the function will hold for all values of x, except x = 4, where we will have an undefined expression
Thus, the domain is all real numbers, except x= 4
For the range, we are referring to the possible y-values
From the given equation the possible y values are all real numbers except y = 0
To find the intercepts, let us write g(x) as y
The equation is thus;
[tex]\begin{gathered} y\text{ = }\frac{3}{x-4} \\ \end{gathered}[/tex]To get x-intercept, substitute y = 0
By doing this, we have no x-intercept
To get the y-intercept, we simply substitute x = 0
That means;
[tex]\begin{gathered} y\text{ = }\frac{3}{0-4} \\ y\text{ = }\frac{3}{-4} \\ y\text{ = -0.75} \end{gathered}[/tex]one angle of a triangle mesures 24 more than the smallest angle in the triangle. the third angle measures twice the measure of the smallest angle
What is the measure of the smallest angle?
24
39
52
54
The answer, the measure of the smallest angle is 39° in the triangle.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angle of triangle = 180
Let x be the smalletst angle
2nd angle will be x+24
and 3rd angle will be 2x
So sum of all angles x+2x+x+24=180
4x=180-24
x=156/4
x=39
Hence the measure of the smallest angle will be 39°
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5. The circle graph shows the favorite music genre of radio listeners. Which of the following 2 categories combinedmake up the biggest percentage?Music PreferenceClassical 10%a. Alternative and classicalb. Country and rock15%AlternativeRock 35%C.Jazz and countryCountry25%Jazz 15%d. Rock and Classical
rock with 35% and country with 25% are the highest percentages, therefore the answer is: B
a frame is 9 inch wide and 6 inch tall. if it is reduced to a width of 3 inch the how tall will it be?
The height of the frame will remain the same.
The height of the frame is 6 inch
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
A frame:
The frame can be considered as a rectangle.
Wide = 9 inch
Height = 6 inch
_______
| |
| | 6-inch (height)
| |
|_______|
9-inch (wide)
If wide = 3 inches the height remains the same.
Thus,
The height of the frame will remain the same.
The height of the frame is 6 inch
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Enter the value of 5.6( 7+13)
Answer:
112
Step-by-step explanation:
According to pemdas we do what’s in parentheses first and then multiply
5.6(7+13)
5.6(20)
112
Hopes this helps please mark brainliest
What is the equation for the line in slope-intercept form?
Answer:
y = -2x - 4
Step-by-step explanation:
Slope intercept form : y = mx + b
Where
m = slopeb = y intercept Finding Y - InterceptThe y intercept is the point where the line crosses the y axis.
Here, just by looking at the graph we can say that the y intercept is at (0,-4) because that is where the line passes the y intercept.
This means that b = - 4
Finding the slopeWe can find the slope using the following formula
Slope = (y2-y1)/(x2-x1)
Where, (x1,y1) and (x2,y2) are any given points on the line
The points used can vary however I have chosen (0,-4) and (-2,0)
Defining our variables we get (x1,y1) = (0,-4) and (x2,y2) = (-2,0)
So we have x1 = 0 , x2 = -2 , y1 = -4 and y2 = 0
We now plug this in to the formula
Slope = (y2-y1)/(x2-x1)
==> plug in x1 = 0 , x2 = -2 , y1 = -4 and y2 = 0
Slope = (0-(-4))/(-2-0)
==> remove parenthesis
Slope = (0+4)/(-2-0)
==> simplify addition and subtraction
Slope = 4/-2
==> simplify fraction
Slope = -2
So the slope or "m" is -2
Plugging the y intercept and slope into y intercept formAgain we have y = mx + b
m = slope so m = -2 and b = y intercept so b = -4
Plugging this in, we acquire y = -2x - 4
What are the first five terms of the arithmetic sequence defined explicitly by the formula an=14 - 3n
11, 8, 5, 2, -1
Option D is correct
Explanation:The given arithmetic sequence is:
[tex]a_n=14-3n[/tex]For the first term, substitute n = 1 into the arithmetic sequence
[tex]\begin{gathered} a_1=14-3(1) \\ a_1=14-3 \\ a_1=11 \end{gathered}[/tex]For the second term, substitute n = 2 into the arithmetic sequence
[tex]\begin{gathered} a_2=14-3(2) \\ a_2=14-6 \\ a_2=8 \end{gathered}[/tex]For the third term, substitute n = 3 into the arithmetic sequence
[tex]\begin{gathered} a_3=14-3(3) \\ a_3=14-9 \\ a_3=5 \end{gathered}[/tex]For the fourth term, substitute n = 4 into the arithmetic sequence
[tex]\begin{gathered} a_4=14-3(4) \\ a_4=14-12 \\ a_4=2 \end{gathered}[/tex]For the fifth term, substitute n = 5 into the arithmetic sequence
[tex]\begin{gathered} a_5=14-3(5) \\ a_5=14-15 \\ a_5=-1 \end{gathered}[/tex]Therefore, the first five terms are:
11, 8, 5, 2, -1
Find the GCF and LCM for 24 & 30.
GCF-
LCM-
Answer:
The GCF of 24 & 30 would be 6. The LCM of 24 & 30 would be 120.
Step-by-step explanation:
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Blake works at a grocery store and is paid every two weeks. He earned $486.50 this week. His pay will increase by 10% next week. What will his total
pay be for the two week period?
Answer:
$1,021.60
Explanation:Blake earn $486.50 in 1 week.
"The next week, his pay will increase by 10%"
2 weeks:
= $486.50 * 1.10(+10%)
= $535.15
Blake paid after two weeks. He got
= $486.50 + $535.10
= $1,021.60
Find the equation of the line passing through the given pair of points. Write the equation in slope-intercept form.(-4,-2), (3,7)
Equation of a line in slope intercept form:
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
To find the slope use the two given points in the next formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{points: }(-4,-2)(3,7) \\ \\ m=\frac{7-(-2)}{3-(-4)} \\ \\ m=\frac{7+2}{3+4}=\frac{9}{7} \end{gathered}[/tex]Use the slope and one of the points to find the y-intercept:
[tex]\begin{gathered} y=mx+b \\ (3,7) \\ \\ 7=\frac{9}{7}(3)+b \\ \\ 7=\frac{27}{7}+b \\ \\ 7-\frac{27}{7}=b \\ \\ b=\frac{49-27}{7} \\ \\ b=\frac{22}{7} \end{gathered}[/tex]Then, the equation of the line passing through the given pair of points is:
[tex]y=\frac{9}{7}x+\frac{22}{7}[/tex]If a loan is taken out for $278 at 10% and costs the borrower $174.12 in simple interest, how many years was the loan for? ROUND YOUR ANSWER TO THE NEAREST WHOLE YEAR
Data:
Loan=$278 at 10%
A simple interest is calculated for payments on the initial capital.
If the total interest was $174.12.
If the interest is on a year. You calculated the interes of one year. The 10% of $278:
[tex]278\cdot\frac{10}{100}=27.8[/tex]In a year the interest is $27.8.
Then, $174.12 divided into $27.8 is the number of years of the loan:
[tex]\frac{174.12}{27.8}=6.26\approx6[/tex]Then, the loan was for 6 yearsWhich of the following equations is equivalent to 4x + 2y = 12? A. 2y = -4x + 12 B. y=-2x + 6 C. y = 2X - 6 D. y = 8x + 24
Let's find the equivalent equation to:
4x + 2y = 12
2y = 12 - 4x
Dividng by 2 at both sides:
2y/2 = 12/2 - 4x/2
y = 6 - 2x
We can see that choices B and C are not correct because the signs.
If we multiply by 2 at both sides, we have:
2y = 12 - 4x
We can see that if we change the order at the right side of the equation, we have:
2y = -4x + 12
I think now you are ready to select the correct choice, Deppreso.
Last year the book fair sold 200 bookmarks compared to the 180 sold this year. What is the percent of change in the number of bookmarks sold?
Answer:
Step-by-step explanation:
1. Subtract 200 from 180
200 - 180 = 20
2. Divide the difference of the number of bookmarks by last years
20 / 200 = 0.1
3. Multiply 0.1 by 100 to get the percentage
0.1 x 100 = 10 %
4. Since this is a reduction in number of bookmarks sold, then it would be a -10% change in the number of bookmarks sold.
A dance club had 3 times as many members as an art club. the art club had 3,598 fewer members than the dance club. how many members did the art club have?
There are 1799 members in art club .
What is an linear equation ?A linear equation has the algebraic form y=mx+b, where m is the slope and b is the y-intercept, and consists of a first-order (linear) term and a constant. When x and y are the variables, the aforementioned is sometimes referred to as a "linear equation of two variables."
Each line in the Euclidean plane is conceived of as a collection of all the answers to a linear equation with two variables. Lines represent the solutions of linear equations in the Euclidean plane. This is where the word "linear," which is used to characterize this class of equations, originates.
Calculationd-dance club
a-art club
Lets set system of equations:
d=3a
a=d-3598
--------------
a=3a-3598
3598=3a-a
3598=2a
a=1799
so there are 1799 members in art club .
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wich equation is proportional?y=2x-6y=-1/4x
-7t-8=10+2t solve for t
Answer:
t= -2
Step-by-step explanation:
Hope this helps!!
Answer:
t = -2
Step-by-step explanation:
-7t - 8 = 10 + 2t
Subtract 10 from both sides
-7t - 18 = 2t
Add 7t to both sides
-18 = 9t
Divide both sides by 9
-2 = t
Hi, I would like a step by step help on the blanks on how this problem was solved.-5 . (4 . 29) = (___ . ___) . 29= ____ . 29= -580
Recall that the distributive for the product property states that:
[tex]a*(b*c)=(a*b)*c.[/tex]Using the distributive property we get:
[tex]-5*(4*29)=(-5*4)*29.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} (-5*4)*29=-20*29 \\ =-580. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} -5*(4*29)=(-5*4)*29 \\ =-20*29 \\ =-580. \end{gathered}[/tex]
Classify the system (options: consistent, independent consistent, inconsistent)3x + 2y = 73x - 4y = 9
SOLUTION
Let's look at the graphical solution of the pair of simultaneous equations
From the graph, we can see that the equations have at least one solution, which are 2.556, and -0.333. Hence, it is said to be consistent.
Now, since the solutions intersect only at one place, it means that it has exactly one solution. If a consistent equation has exactly one solution, it is said to be independent.
Therefore, the systems of equations are consistent and independent
The area of a playground is 154 yd ^2. The width of the playground is 3 yd longer than its length. FInd the length and width of the playground.
Answer:
The length of the playground = 11 yards
The width of the playground = 14 yards
Explanation:
Let the length of the playground = l yd.
The width of the playground is 3 yd longer than its length.
Therefore, the width of the playground = (l+3) yd
Area of a Rectangle = Length x Width
Substituting the given values, we have:
[tex]154=l(l+3)[/tex]We then solve the equation above for l.
[tex]l^2+3l-154=0[/tex]We factorize:
[tex]\begin{gathered} l^2+14l-11l-154=0 \\ l(l+14)-11(l+14)=0 \\ (l-11)(l+14)=0 \\ l-11=0\text{ or l+14=0} \\ l=11\text{ yards, }l\neq-14 \end{gathered}[/tex]The length of the playground = 11 yards
The width of the playground = 14 yards
Annie purchased a season pass for the new aquarium at a cost of $110. if she uses the pass 10 times this year , what is the unit rate in cost per visit?
If she uses the pass 10 times this year then the unit rate in cost per visit is $11 unit per visit.
In the given question,
Annie purchased a season pass for the new aquarium at a cost of $110.
If she uses the pass 10 times this year then we have to find the unit rate in cost per visit.
We have to find the unit rate.
Unit rate means finding the value of one object, that means we have to find the cost of one visit.
The cost of season pass is $110.
She visit aquarium 10 times.
We find the unit rate cost per visit by dividing the total cost of season pass for the new aquarium by total times she visits in the new aquarium.
10 times = $110 cost
Divide by 10 on both side
10/10 times = $110/10 cost
1 times = $11 cost
Hence, if she uses the pass 10 times this year then the unit rate in cost per visit is $11 unit per visit.
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do 11, 9 ,17 make a triangle
We use the followig property of triangles:
• One side cannot be equal or greater than the sum of the other two sides
The sides of this triangle are: 11, 9 and 17.
The sum of the first two sides is: 11+9=20
The sum of the two sides is greater than the other remaining side (17).
Thus, 11, 9 and 17 do not make a triangle.
MARY BOUGHT A CAR FOR $12,785 IF MARY PAID $2,000 DOWN AND WILL PAY $273.53 FOR 48 MONTHS WHAT IS THE TOTAL FINANCE CHARGE?
First, we will find the amount of money she will pay in 48 months
Since she pays $273.53 for 48 months, then
[tex]273.53x48=13,129.44[/tex]Since she paid a $2000 down payment
Then we will add 2000 to 13,129.44 to find the total amount she paid
[tex]T=13129.44+2000=15,129.44[/tex]Now, we will subtract the price of the car from it to find the finance charge
Since the price of the care is $12,785, then
[tex]\begin{gathered} T.F=15129.44-12785 \\ \\ T.F=2344.44 \end{gathered}[/tex]She will pay $2344.44 for the total finance charge
On a cold day in new york, a street vendor sold 35 cups of hot chocolate and her entire stock of hot cider. if the ratio of cider to hot chocolate is 8:5, how many cups of cider did she sell?
Using the concept of ratio and proportion, the vendor sold 56 cups of hot cider.
How does a ratio operate?The word "proportion" often denotes a portion, share, or sum that is in comparison to a whole. Two ratios are in proportion when they are equal, according to the proportional idea. When an equation or a statement to that effect is used, two ratios or fractions are equal.
Define ratio.A percentage is a mathematical comparison of two numbers. In terms of proportion, two sets of given numbers are said to rise or decrease in the same ratio if they are directly proportionate to one another.
Cider supplied by the street seller for value = x for 35
= x/35
The cider's ratio is 8:5,
x/35 :: 8:5,
x = [35(8)]/ 5
=56.
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F(2-k)=8-5(2-k) evaluating functions
Answer:
f = 5k−2/−k+2
8 As shown in the diagram of rectangle ABCD below, diagonals AC and BD intersect at E. С
From the rectangle given, we see the diagonals of the rectangle bisect each other at E.
From the properties of a rectangle is that;
1) The diagonals are congruent. That is, they are equal. AC = BD
2) The diagonals bisect each other into two equal parts.
These are the two properties we will use in solving the question
[tex]undefined[/tex]given BD and AC bisects each other. prove AB\\ CD
From step #6, AB is congruent to CD by CPCTC or Corresponding Parts of Congruent Triangles are Congruent.
Triangles ABE and CDE are congruent by SAS postulate.
Therefore, angle B and angle D are congruent.
Note that the segment BD is a transversal line that cuts AB and CD, and angle B and angle D are alternate interior angles.
The answer is :
XY || WZ ⇒ AB || CD
with a reason of :
Parallel lines cut by a transversal form congruent alternate interior angles.
Find an equation for the line perpendicular to the line 4x - 9y = - 5 having the same y-intercept as - x - 4y = -2.
Clear y from both equations to find the slope y intercept form of the equations
[tex]\begin{gathered} 4x-9y=-5 \\ -9y=-4x-5 \\ y=\frac{-4x-5}{-9} \\ y=\frac{4}{9}x+\frac{5}{9}\text{ (Eq. 1)} \\ -x-4y=-2 \\ -4y=x-2 \\ y=\frac{x-2}{-4} \\ y=-\frac{x}{4}+\frac{1}{2}\text{ (Eq. 2)} \end{gathered}[/tex]Now, find the equation for the line that is perpendicular to Eq. 1 and has the same y intercept as Eq. 2
[tex]\begin{gathered} m1\cdot m3=-1 \\ m3=-\frac{1}{m1} \\ m3=-\frac{1}{\frac{4}{9}} \\ m3=-\frac{9}{4} \\ y=-\frac{9}{4}x+\frac{1}{2}\text{ (Eq. 3)} \end{gathered}[/tex]Eq. 3 is the equation for the line
Aiden ran a total of 8 miles over the course of 2 track practices. How many track practices would it take for Aiden to run 16 miles? Assume the relationship is directly proportional.
Answer:
4
Step-by-step explanation:
8 miles over 2 practices so double that