What substitution should be used to rewrite 4x12 – 5x6 – 14 = 0 as a quadratic equation? u = x2 u = x3 u = x6 u = x12
Answer: [tex]u=x^6[/tex]
Explanation:
A quadratic equation is an equation written in the form
[tex]au^2 + bu + c=0[/tex] (1)
where a,b,c are coefficients and where u is the variable.
Our original equation is:
[tex]4x^{12} - 5x^6 -14=0[/tex]
If we make the substitution [tex]u=x^6[/tex], we obtain
[tex]4u^2 -5u-14 =0[/tex]
Which corresponds to eq.(1), with coefficients a=4, b=-5, c=-14.
4y-4=16 what is the answer
Vanessa uses the expressions (3x2 + 5x + 10) and (x2 – 3x – 1) to represent the length and width of her patio. Which expression represents the area (lw) of Vanessa’s patio?
Answer:
[tex]3x^{4}-4x^{3}-8x^{2}-35x-10[/tex]
Step-by-step explanation:
We have been given that Vanessa uses the expressions [tex]3x^2+5x+10[/tex] and [tex]x^2-3x-1[/tex] to represent the length and width of her patio.
To find the expression that represents the area of Vanessa's patio we will multiply the length of patio by width of patio as:
[tex](3x^2+5x+10)*(x^2-3x-1)[/tex]
Upon using distributive property [tex]a(b+c)=a*b+a*c[/tex] we will get,
[tex](3x^2*x^2)+(3x^2*-3x)+(3x^2*-1)+(5x*x^2)+(5x*-3x)+(5x*-1)+(10x^2)+(10*-3x)+(10*-1)[/tex]
Using exponent property [tex]a^b*a^c=a^{b+c}[/tex] we will get,
[tex](3x^{2+2})+(-9x^{2+1})+(-3x^2)+(5x^{1+2})+(-15x^{1+1})+(-5x)+(10x^2)+(-30x)+(-10)[/tex]
[tex](3x^{4})+(-9x^{3})+(-3x^2)+(5x^{3})+(-15x^{2})+(-5x)+(10x^2)+(-30x)+(-10)[/tex]
[tex]3x^{4}-9x^{3}-3x^2+5x^{3}-15x^{2}-5x+10x^2-30x-10[/tex]
Now let us combine like terms.
[tex]3x^{4}-9x^{3}+5x^{3}-3x^2-15x^{2}+10x^2-5x-30x-10[/tex]
[tex]3x^{4}-4x^{3}-8x^{2}-35x-10[/tex]
Therefore, the expression [tex]3x^{4}-4x^{3}-8x^{2}-35x-10[/tex] represents the area of Vanessa's patio.
What number is 10 times greater than 5?
Answer:
50
Step-by-step explanation:
IN order to find a number that is "x" times greater than another you have to multiply the number by the times greater, for example if you are trying to find a number that is 2 times greater than 8, you multiply 8 by 2=16 so 16 is 2 times greater than 8.
To find the number that is 10 times greater than 5 you just have to multiply 5*10, as the result will be 50, so that would be the answer.
Bananas are $.59 a pound what is the constant of proportionality?
Really need help!!! will make brainleist Select from the drop-down menu to correctly identify the property shown. (−3.4+(−1.5))+6.2=−(3.4+1.5)+6.2
Answer:
associative property
Step-by-step explanation:
For any integer x, x squared -x will always produce an even value
Answer:
[tex](x^2 - x)[/tex] will always have an even value.
Step-by-step explanation:
We are given an integer x.
Let x be even, then it can be written in the form x = 2n, where n is an integer.
If we evaluate,
[tex](x^2 - x) = (2n)^2 - 2n = 4n^2 - 2n = 2(2n^2 - n)[/tex]
Thus, it have an even value.
If we take x to be an odd integer, then,it can be written in the form x = 2n+1, where n is an integer.
[tex](x^2 - x) = (2n+1)^2 - 2n = 4n^2 + 2n = 2(2n^2 + n)[/tex]
Thus, it have an even value.
Thus,
[tex](x^2 - x)[/tex] will always have an even value.
In 1934 there was an extreme drought in the great plains. In the number 1934, is the value of the 9 in the hundreds place ten times the value of the 3 in the tens place?
What is the recursive formula for this sequence?
14, 18, 22, 26, 30, …
The recursive formula is an = a_(n-1) +4.
The correct option is (D).
what is recursive formula?A recursive formula refers to a formula that defines each term of a sequence using the preceding term(s). The recursive formulas define the following parameters:
The first term of the sequenceThe pattern rule to get any term from its previous termRecursive Formula for Arithmetic SequenceThe recursive formula to find the nth term of an arithmetic sequence is:
an = an-1 + d for n ≥ 2
where
an is the nth term of a A.P.
d is the common difference.
Given:
14, 18, 22, 26, 30, …
a1=14
and, d= 18-14
d=4
a2= a1 + 4
a2 = 14+4= 18
Similarly, going this way
an = a_(n-1) +4
Hence, the recursive formula is an = a_(n-1) +4
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If four points are collinear are they coplanar
Final answer:
Yes, if four points are collinear, they are also coplanar, as they lie on the same straight line and therefore exist in the same plane.
Explanation:
If four points are collinear, this implies that they lie on the same straight line. By definition, a straight line is a one-dimensional figure and hence exists within any given plane. Therefore, four collinear points must also be coplanar, existing on the same plane. In three-dimensional geometry, the concept of coplanarity can be evaluated using a determinant. If this determinant equals zero, it indicates that the four points lie within the same plane.
Moreover, lines and planes in three-dimensional space can be represented by equations, and by combining these into a system of equations, one can ascertain the geometric relationships between the points in question.
the sum of three consecutive numbers is 87. what is the smallest of the 3 numbers?
State the most appropriate metric units to use to measure the width of an eyelash
what's the answer for 41
What is the difference?
9/5-1/6
Divide 28 cans into 2 groups so the ratio is 3 to 4
is 84/45 a irrational repeating decimal or just a irrational one
Stephen lent his friend $100 at a simple annual interest rate of 6%. How much interest will Stephen earn at the end of 3 years?
Use matlab to calculate the probability to get 3 times of '5' in 8 throws of a fair die
The ordered pair (3, –1) is a solution of which system?
To determine the system of equations to which the ordered pair (3, –1) is a solution, we must find equations where substituting 'x' with 3 and 'y' with –1 produces true statements for both equations in the system.
Explanation:The question pertains to finding the system of equations for which the ordered pair (3, –1) is a solution. To determine the correct system, we would need to identify equations that have both 'x' and 'y' variables. An ordered pair is composed of an 'x' coordinate and a 'y' coordinate, following the form (x, y). In this case, the 'x' value is 3, and the 'y' value is –1. If the ordered pair (3, –1) is a solution to a system of linear equations, it must satisfy both equations in the system. This means that when we substitute 'x' with 3 and 'y' with –1 into each equation, the equations should hold true.
For example, if we have a system of equations:
y = 2x - 7y = -x + 2Substituting 'x' with 3 and 'y' with –1 into both equations, we get:
–1 = 2(3) - 7, which simplifies to –1 = 6 - 7 and further to –1 = –1–1 = -3 + 2, which simplifies to –1 = –1Since the ordered pair (3, –1) satisfies both equations, then (3, –1) is a solution to this system. To identify the system of equations the ordered pair belongs to, you would similarly test the pair in the given systems to see which one(s) it satisfies.
Two angry children 450 feet apart are headed straight towards each other—one at 15 feet per second and the other at 6 feet per second. Their mother responds to the crisis by sprinting back and forth between the children, hoping to calm them before they reach each other. Unfortunately, when she reaches each child, she is immediately rejected and rushes back to the other child. If the mother miraculously maintains a constant speed of 20 feet per second the entire time—while racing back and forth between the children—how far will she have run when all three of them collide? She will have run __________ feet. (Round to the nearest foot.)
C= m over 3 π d to the second power , for m
round 141080 to the nearest ten
Two cars leave the same location traveling in opposite directions. One car leaves at 3:00 p.m. traveling at an average rate of 55 miles per hour. The other car leaves at 4:00 p.m. traveling at an average rate of 75 miles per hour. Let x represent the number of hours after the first car leaves. How many hours after the first car leaves will the two cars be 380 miles apart?
15 greater than blank divided by 400
Frederick took out a 20-year loan for $70,000 at an APR of 2.2%, compounded monthly. Approximately how much would he save if he paid it off ...
To calculate Frederick's approximate savings if he paid off the loan early, subtract the total amount he would pay if the loan continued for the full term from the original loan amount. The monthly payment amount can be calculated using the compound interest formula. By multiplying the monthly payment by the number of payments, you can find the total amount paid over 20 years. Subtracting this from the original loan amount gives you the approximate savings.
Explanation:To calculate the approximate amount Frederick would save if he paid off the loan early, we need to find the total amount he would pay if he continued making monthly payments for the full 20 years and subtract the total amount he would pay if he paid off the loan early.
1. First, find the monthly interest rate by dividing the annual interest rate by 12:
i = 0.022 / 12 = 0.00183
2. Next, calculate the monthly payment using the compound interest formula:
P = (r * PV) / (1 - (1 + r)^(-n))
Where P is the monthly payment, r is the monthly interest rate, PV is the loan amount, and n is the number of monthly payments.
3. Substitute the values into the formula:
P = (0.00183 * $70,000) / (1 - (1 + 0.00183)^(-240))
4. Solve for P to find the monthly payment amount:
P ~ $520.63
5. To find the total amount paid over 20 years, multiply the monthly payment by the number of payments:
Total amount paid = $520.63 * 240 = $124,950.98
6. To find the approximate amount saved if the loan is paid off early, subtract the total amount paid from the original loan amount:
Approximate savings = $70,000 - $124,950.98 = -$54,950.98
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Final answer:
Frederick would save approximately $34,692.80 if he paid off the loan early.
Explanation:
To calculate the amount Frederick would save if he paid off the loan early, we need to determine the total cost of the loan and compare it to the amount he would pay if he paid it off in a shorter time period.
First, we need to calculate the monthly payment using the formula:
Monthly Payment = Loan Amount * (Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^(-Total Number of Payments)))
Substituting the values, we have:
Loan Amount = $70,000
Monthly Interest Rate = 2.2% / 12 = 0.1833%
Total Number of Payments = 20 * 12 = 240
Plugging the values into the formula, we get:
Monthly Payment = $70,000 * (0.1833% / (1 - (1 + 0.1833%)^(-240)))
Calculating this equation gives us a monthly payment of approximately $436.22.
Next, we calculate the total cost of the loan by multiplying the monthly payment by the total number of payments:
Total Cost = Monthly Payment * Total Number of Payments
Plugging in the values, we get:
Total Cost = $436.22 * 240
Calculating this equation gives us a total cost of approximately $104,692.80.
If Frederick paid off the loan early, he would save the difference between the total cost and the original loan amount, which is $104,692.80 - $70,000 = $34,692.80.
2 1/2x − 3/4 ( 2x + 5 ) = 38
0.9(x+1.4)−2.3+0.1x=1.6
What is the value of x in both equations.
Expresss 4/3/8 as a decimal correct to 3 significant figure
The three significant figure decimal is 4.38.
What is Decimal?A group of numbers between integers on a number line are known as decimals. They are merely an additional mathematical representation of fractions. Integers, also known as whole numbers, are represented to the left of the decimal point, while decimal fractions are represented to the right of the decimal point.
Given:
4/3/8 as a decimal
Now, divide 3/8 we get
3/8 = 0.375
= 0.38
So, the three significant figure decimal is 4.38.
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May I Please get help?
There are 332,054 people in the city.Of these, 168,278 are under the age of eighteen.Draw a bar diagram and find how many people are eighteen or older
Answer:
The bar diagram is shown below. Number of peoples who are 18 or older is 163,776.
Step-by-step explanation:
Given information:
Total number of peoples in the city = 332,054
Number of peoples who are under 18 = 168,278
Number of peoples who are 18 or older is
[tex]332,054-168,278=163,776[/tex]
We need to draw a bar diagram.
In the bar diagram x axis represents the age and y-axis represents the number of peoples.
First bar represents the number of peoples who are under 18 i.e., 168,278.
Second bar represents the number of peoples who are 18 or older i.e., 163,776.
Evaluate 4g - 12 when g = 5
Given expression is:
[tex]4g-12[/tex][tex]g = 5[/tex]By substituting the value of "g" in the given expression, we get
→ [tex]4g-12[/tex]
→ [tex]4(5) -12[/tex]
→ [tex]20-12[/tex]
→ [tex]8[/tex]
Thus the above answer is correct.
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