Answer:
b. better; high
Step-by-step explanation:
FACTORING PUZZLE
Use the digits 0-9 to fill in the squares. Each digit can be used only once.
x² - x -
x² - 1
X² +
Keira
X²
1 = (x + 2)(x-
x +
-
= (x-2)(x -
x + 1
= (x +
x - 24 = (x-6)(x +
=
(x + 2)
Source: Public Schools of North Carolina Resources for Algebra
Using the digits 0-9, the puzzle becomes:
x² - x - 2 = (x + 2)(x - 1)x² - 1x + 1 = (x - 2)(x - 1)x² + 3x + 2 = (x + 1)(x + 2)x² - 18x - 24 = (x - 6)(x - 4)How to solve the puzzle?To solve this puzzle, use the factoring pattern (a-b)(a+b) = a² - b² for the second equation.
First, the first blank in equation 1 must be either 1 or 3, since the two factors must have a difference of 1. Therefore, the first blank in equation 1 must be 1, and the second blank must be 2.
Next, use the factoring pattern in equation 2 to get:
x² - 1x + 1 = (x - 2)(x - 1)
This means that the missing number in the second set of blanks is 1, since the two factors have a difference of 1.
In equation 3, the second blank must be -3, since the two factors must have a difference of 5. Therefore, the first blank must be -1.
Finally, in equation 4, the missing number in the second set of blanks must be -4, since the two factors must have a difference of 2. Therefore, the missing number in the first set of blanks is 18.
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Solve the absolute value equation. [2x] +1=3
Answer:
x=1
Step-by-step explanation:
Answer:
x = -1x =1Step-by-step explanation:
\(\left|2x\right|+1=3\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\\\\left|2x\right|+1-1=3-1\\\\Simplify\\\left|2x\right|=2\\\\\mathrm{Apply\:absolute\:rule}:\\\quad \mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a\\\\2x=-2\quad \mathrm{or}\quad \:2x=2\\\\2x=-2\quad :\quad x=-1\\2x=2\quad :\quad x=1\\\\\mathrm{Combine\:Solutions:}\\\\x=-1\quad \mathrm{or}\quad \:x=1\)
HELP due in 4 minutes
if f(x)=-2x+4 find 3[f(1)]+3
to what is 9% increased to get 79.57
Please help :(
Answer:
Step-by-step explanation:
6.57
The numbers x, y and z are successive terms of the arithmetic sequence with a common difference of d=4. What is the sum of these numbers, if the numbers x, y and z+8 are successive terms of the geometric sequence?
Answer: The sum of the numbers is 3x + 12
Step-by-step explanation: A brief explanation of an arithmetic progression would be useful for a start.
An arithmetic progression (also known as arithmetic sequence) is series of consecutive numbers in which every term in the entire series is determined by adding a common difference to the previous term. In other words, if x and y are two successive numbers in an arithmetic term, y can be determined by adding the common difference to x. Similarly, the term that comes after y is determined by adding the same common difference to y.
As stated in the question, the numbers x, y and z are successive terms of an arithmetic progression, and the common difference is given as 4. This simply means;
y = x + 4
z = y + 4
z = (x + 4) + 4
z = x + 8
The terms x, y and z can now be re-written as follows,
x, x + 4, and x + 8
The sum of these numbers therefore is derived as,
Sum = x + x + 4 + x + 8
Sum = 3x + 12
Lily wants to open an investment account to save for a down payment on a house. The growth of the account that her banker recommends (account A) can be modeled by the function A(t) = 3,000(1.024)^4t, where t is the number of years that the account is open.
Consider the account that Lily’s banker recommends (account A) to complete the statement.
Select the correct answer from each drop-down menu.
If Lily chooses account A, the balance of her account would increase by a rate of __
on a __ basis.
1. .024%
0.24%
2.4%
3%
4%
1.024%
2. monthly
yearly
quarterly
weekly
semi-annual
If Lily chooses account A, the balance of her account would increase by a rate of 2.4% on a quarterly basis
The EquationThe equation of the function is given as:
\(A(t) = 3000(1.024)^{4t\)
Exponential functionAn exponential function is represented as:
\(y = a(1 + r)^x\)
Where:
a represents the initial valuer represents the rateSo. by comparison:
\(1 + r=1.024\)
Subtract 1 from both sides
\(r=.024\)
Express as percentage
\(r=2.4\%\)
From the function, the exponent of the rate is 4t.
This means that, the balance increases four times in a year.
So, her balance would increase quarterly
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a key requirement for the process of testing hypotheses in the scientific method is
A key requirement for the process of testing hypotheses in the scientific method is experimentation. A hypothesis is an idea or explanation for a phenomenon that is grounded in existing knowledge or observations, and the scientific method involves testing those hypotheses through experimentation.
The process of testing hypotheses requires the development of a testable hypothesis, the design of experiments to test the hypothesis, and the collection and analysis of data from those experiments to evaluate the hypothesis. The experiments must be designed carefully, with appropriate controls and variables to ensure that the results are reliable and valid. Scientists also need to communicate their findings to the scientific community, which involves publishing their results in scientific journals and presenting their work at conferences.
This helps to ensure that other scientists can replicate their experiments and validate their findings, which is a critical part of the scientific process. Ultimately, the process of testing hypotheses is essential for advancing scientific knowledge and understanding how the world works.
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
xº
23°
Please help m
The measure of the angle x in the right triangle is 67 degrees.
How to find the angle of a right triangle?A right angle triangle has one of its angles as 90 degrees.
The sum of angle in a triangle is 180 degrees.
Therefore,
x + 90 + 23 = 180
x + 113 = 180
x + 113 - 113 = 180 - 113
x = 67°
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if the price of bananas is $2 a pound, how many pounds of bananas will suppliers supply? 10 1 10,000 0
If the demand for bananas at $2 per pound is 10 pounds, then the suppliers will supply 10 pounds of bananas.
The question is about determining the number of pounds of bananas suppliers will supply at a given price of $2 a pound.
To determine the number of pounds of bananas suppliers will supply, we need more information than just the price of bananas.
Supply is affected by many factors like cost of production, demand, and the price of substitutes.
Suppliers will supply bananas to the market until the price they get equals the cost of production plus a margin.
If the price is higher than the cost of production plus a margin, then they will continue to supply to maximize their profits.
In the given question, we don't have enough information about the cost of production, demand, and substitutes. Therefore, we cannot accurately predict the amount of pounds of bananas that will be supplied.
However, if we assume that the cost of production is constant and there are no substitutes, then the suppliers will supply bananas at a price of $2 per pound until the market reaches equilibrium.
At equilibrium, the quantity supplied equals the quantity demanded.
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a) how many license plates are possible if each plate must have three letters followed by three numbers?
The permutation combination of license plate is 35152000.
Numbers can be 10 digits (0, 1, 2, …, 9) and 26 letters (A, B, C, ..., Z).
Repetition is allowed, leaving 26 next choices for each letter used and 10 next choices for each digit used.
Therefore, according to the multiplication principle, the total number of different letter permutations.
26× 26 × 26 = 17576
and the total number of digit permutation: 10 × 10 × 10 = 1000
now, they can be in any order:
⁶C₃ = 6!/(6−3)!3!
We have to consider 20 different combinations of positions.
So the total number of different license plates possible by the multiplication principle is
17576 × 1000 × 20 = 351520000
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What is the equation of a line, in general form, with a point (-3, 0) and an undefined slope? x - 3 = 0 y + 3 = 0 y - 3 = 0 x + 3 = 0.
Answer: x+3=0
Step-by-step explanation:
Answer: x+3=0
Step-by-step explanation: make me brainliest please
\( \frac{5}{7} \times 6\)
what is 5/7 x 6
Answer:
\(\frac{30}{7}\)
Step-by-step explanation:
to multiply a number by a fraction, just multiply straight across
you just do 5 * 6 to get 30 and since there isn't anything under the 6, you put an imaginary 1 to get you 7 so your answer will be 30/7
The bar chart below shows the monthly energy bill for Wally's tackle shop. Which of the listed months had bills between $40 and $50? Scroll down to see all six answer options and check all that apply Emers bill is Months
A. May
B. April
C. March
D. November
E. October
F. June
Answer:
there is no bills listed
Step-by-step explanation:
there is no picture
send it again please
An entrepreneur sold a damage bedspread for $130.50, there by making a loss of 13% on the cost price. Determine the cost price of the bedspread.
Answer:
130.50 X 13% = $16.97
130.50 - 16.97 = 113.53
Answer 113.53
Step-by-step explanation:
Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use the order of operations to find the value of the expression.
5 x 2 + 6 - 5
I will be giving brainliest and 15 points so if you get this correct then you have a suprise coming! Thank you to whoever answers this question as well.
Answer:
11
Step-by-step explanation:
5 x 2 = 10
10 + 6 = 16
16 - 5 = 11
there u go!
suppose the true proportion of voters in the county who support a restaurant tax is 0.55. consider the sampling distribution for the proportion of supporters with sample size n
The mean of this distribution is 0.55
The standard error of this distribution is 0.0384
We have the following:
p=0.55
sample size, n=168
Mean of distribution:
Mean=true proportion of voters who support a restaurant
Mean=p=0.55
Hence, the mean of distribution is 0.55
Standard error of the distribution:
\(=\sqrt{\frac{p(1-p)}{n} }\)
\(=\sqrt{\frac{0.55(1-0.55)}{168} }\)
=0.0384
Hence, the standard error is 0.0384
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The questions was incomplete, the complete question is given below:
Suppose the true proportion of voters in the county who support a restaurant tax is 0.55. Consider the sampling distribution for the proportion of supporters with sample size n = 168.
What is the mean of this distribution?
What is the standard error of this distribution?
What is the rate of change for y= 0.75-2?
Answer:
The slope is 0.75.
The equation is y=0.75x-2
Step-by-step explanation:
A bus traveled on a straight road for 3 h at an average speed that was 12 mph faster than its average speed on a winding road. The time spent on the winding road was 3 h. Find the average speed on the winding road if the total trip was 210 mi.
The average speed on the winding road was 45 mph.
The bus traveled for 3 hours on the winding road, so the distance covered can be calculated using the formula: Distance = Speed × Time. Let's assume the average speed on the winding road as 'x' mph. Therefore, the distance covered on the winding road is 3x miles.
On the straight road, the bus traveled for 3 hours at an average speed that was 12 mph faster than its average speed on the winding road. So the average speed on the straight road can be expressed as 'x + 12' mph. The distance covered on the straight road can be calculated as 3(x + 12) miles.
The total distance covered in the entire trip is given as 210 miles. Therefore, we can write the equation:
3x + 3(x + 12) = 210
Simplifying the equation:
3x + 3x + 36 = 210
6x + 36 = 210
6x = 174
x = 29
So the average speed on the winding road was 29 mph.
The problem states that the bus traveled for 3 hours on both the winding road and the straight road. Let's assume the average speed on the winding road as 'x' mph. Since the bus traveled for 3 hours on the winding road, the distance covered can be calculated as 3x miles.
On the straight road, the average speed was 12 mph faster than on the winding road. Therefore, the average speed on the straight road can be expressed as 'x + 12' mph. The distance covered on the straight road can be calculated as 3(x + 12) miles.
The total distance covered in the entire trip is given as 210 miles. This allows us to set up the equation 3x + 3(x + 12) = 210 to solve for 'x'. Simplifying the equation leads to 6x + 36 = 210. Solving for 'x', we find that the average speed on the winding road was 29 mph.
In summary, the average speed on the winding road was 29 mph.
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The future amount due on a compound interest loan of $12,000 at 7% compounded semiannually for four years is approximately ____. If the compounding period is increased to monthly, the amount due on the loan would be approximately ____
Part a: Future amount due on a compound interest loan is $12271.78.
Part b: The amount due on the loan would be $12033.64, if the compounding period is increased to monthly.
Explain the term compounding?Compounding is the method through which interest is added to both the principle balance already in place and the interest that has already been paid. Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."The formula for compounding is:
A = P(1 + r/100n)∧nt
P = $12,000
r = 0.07
Part a: compounded semiannually.
t = 4 years.
n = 2
A = 12000(1 + 0.07/100*2)∧2*4
A = 12000*1.00280
A = 12271.78
Thus, future amount due on a compound interest loan is $12271.78.
Part b:
t = 4 years.
n = 12
A = 12000(1 + 0.07/100*12)∧12*4
A = 12000*1.0028038
A = 12033.64
Thus, if the compounding period is increased to monthly, the amount due on the loan would be $12033.64.
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Answer: $15,802
$15,865
Step-by-step explanation:
Claire jogs no more than 20 miles per week. Which inequality represents the number of miles she runs each week? A.x > 20 B.x < 20 C. x ≥ 20 D.x ≤ 20
Answer: I’m pretty sure its D
Step-by-step explanation:I will tell you once i finish my test.....
Yes, the correct answer is D. I just finished my test and received a 100.
Maya’s watch shows a time of 1:30pm. At. 5:30pm, her watch shows the time as
5:42pm. How many minutes did her watch gain every hour after 1:30pm?
Answer:
3 min/hr gain from 1:30 p.m. to 5:30 (nominal)
Step-by-step explanation:
Subtract 5:30 from 5:42; the result is 0:12. The watch gained a total of 12 minutes over the four-hour period from 1:30 p.m. to 5:30 p.m., or 3 min/hr:
1:30-2:30: 3 MIN
2:30-3:30: 3 MIN
3:30-4:30: 3 min
4:30-5:30: 3 min Summing up 3 min plus 3 min plus 3 min plus 3 min gives us 12 min.
Identify the period and describe two asymptotes for each function.
y=tanπθ
The horizontal asymptote occurs at y = 0. The absolute value of θ becomes large, the value of the tangent function approaches zero.
The function y = tan(πθ) belongs to the period π, which means that it repeats every π units along the x-axis.
For this function, there are two asymptotes: a vertical asymptote and a horizontal asymptote.
The vertical asymptotes occur at θ = -π/2, π/2, 3π/2, etc.
These values make the denominator of the tangent function equal to zero, resulting in an undefined value.
The horizontal asymptote occurs at y = 0.
As the absolute value of θ becomes large, the value of the tangent function approaches zero.
This means that the graph of y = tan(πθ) gets closer and closer to the x-axis but never touches it.
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4) Find the values of k for which the line y = 3x + 1 cuts the curve y = x² + kx + 2 in two distinct
points.
Answer:
\(k<1, k>5\)
Step-by-step explanation:
\(3x+1=x^2+kx+2 \\ \\ x^2+x(k-3)+1=0 \\ \\ \Delta>0 \implies (k-3)^2-4(1)(1)>0 \\ \\ (k-3)^2-2^2>0 \\ \\ (k-1)(k-5)>0 \\ \\ k<1, k>5\)
Mental processes or behavior patterns that cause emotional distress or substantial impairment in functioning are considered _____ A. conditions of worth. B. psychological disorders. C. trait theories. D. cognitive distortions.
Answer: b) psychological disorders
Step-by-step explanation:
Consider the parametric curve x = 4t 3 − 3t, y = t 5 − 5t, t ∈ R. (a) Find the points where the tangent line is horizontal or vertical. (b) Determine the intervals where the slope of the tangent line to the curve is positive or negative. (c) Determine the intervals where the curve is concave upward or downward. (d) Sketch the curve.
The points where the tangent line is vertical are (13/16, -5/16) and (-13/16, 5/16) and The slope of the tangent line is positive on the intervals t < -1 and t > 1, and negative on the interval -1 < t < 1.
How can we analyzing the properties of a parametric curve?(a) To find where the tangent line is horizontal, we need to find values of t where the derivative of y with respect to x (dy/dx) is equal to 0.
We have:
dy/dx = (dy/dt)/(dx/dt) = (5t^4 - 5)/(12t^2 - 3)
Setting dy/dx = 0, we get:
5t^4 - 5 = 0
t^4 = 1
t = ±1 or t = ±i
Substituting t = 1 into the parametric equations gives us the point (1,-4). Substituting t = -1 gives us the point (-1,4). Substituting t = i or t = -i gives us points on the imaginary axis, which are not part of the real plane.
Therefore, the points where the tangent line is horizontal are (1,-4) and (-1,4).
To find where the tangent line is vertical, we need to find values of t where dx/dt is equal to 0.
We have:
dx/dt = 12t^2 - 3
Setting dx/dt = 0, we get:
t^2 = 1/4
t = ±1/2
Substituting t = 1/2 into the parametric equations gives us the point (13/16, -5/16). Substituting t = -1/2 gives us the point (-13/16, 5/16).
Therefore, the points where the tangent line is vertical are (13/16, -5/16) and (-13/16, 5/16).
(b) To determine the intervals where the slope of the tangent line is positive or negative, we need to examine the sign of the derivative dy/dx.
From part (a), we know that dy/dx is equal to:
dy/dx = (5t^4 - 5)/(12t^2 - 3)
The denominator is always positive, so the sign of dy/dx is determined by the numerator.
For t < -1, we have 5t^4 - 5 > 0, so dy/dx > 0.
For -1 < t < 1, we have 5t^4 - 5 < 0, so dy/dx < 0.
For t > 1, we have 5t^4 - 5 > 0, so dy/dx > 0.
Therefore, the slope of the tangent line is positive on the intervals t < -1 and t > 1, and negative on the interval -1 < t < 1.
(c) To determine the intervals where the curve is concave upward or downward, we need to examine the sign of the second derivative d^2y/dx^2.
We have:
d^2y/dx^2 = ((d^2y/dt^2)(dx/dt) - (dy/dt)(d^2x/dt^2)) / (dx/dt)^3
Calculating the second derivatives, we get:
d^2y/dt^2 = 20t^3
d^2x/dt^2 = 24t
Substituting these into the expression for d^2y/dx^2, we get:
d^2y/dx^2 = (20t^3)(12t^2 - 3) - (5t^4 - 5)(24t) / (12t^2 - 3)^3
Simplifying this expression, we get:
d^2
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Help please -?
An answer and an explanation to understand would be helpful
Answer:
A c b
Step-by-step explanation:
A
can someone pls pls help me ?
9514 1404 393
Answer:
a = 9 meters
Step-by-step explanation:
The perimeter is the sum of the side lengths:
28 m = a + 2m + a + 8m
18 m = 2a . . . . . . . . . . . . . . . . subtract 10m, collect terms
9 m = a . . . . . . . . . . . . . . . divide by 2
The value of a is 9 meters.
Solve please I don’t know how to do this.
Answer:
n=40
Step-by-step explanation:
Answer:
Step-by-step explanation:
15 = 3/8 n
n = 8/3 * 15
n = 40
Where is point A located on the coordinate grid below?У4A2-41-2O24-2-4O Quadrant 11Quadrant IIIQuadrant !
Answer
Quadrant I
Step-by-step explanation
Hence, point A is located on the Quadrant I
Expression that is equivalent to (6)(6)(6)
Answer:
36×6
Step-by-step explanation:
(6)(6)(6)
6×6×6
36×6
216
The answer is: " 6³ " .
__________
Step-by-step explanation:
Note: " (6)(6)(6) " ; is the value of the
[number "6" ; multiplied by that same number, "6" —two additional times;
→ so the same number, "6" ; being multiplied: "3 (three) times'
= 6 * 6 * 6 = 6³ ; that is: the number "6", raised to the third power (as an exponent);
→ since: there are 3 (three) of the same numbers being multiplied;
⇒ hence the exponent, "3" .
__________
The answer is: " 6³ " .
__________
Hope this helps!