Answer:
A) 3%
B) Product A
Step-by-step explanation:
Exponential Function
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
Part A
Product A
Assuming the function for Product A is exponential:
[tex]f(x) = 0.69(1.03)^x[/tex]
The base (b) is 1.03. As b > 1 then it is an increasing function.
To calculate the percentage increase/decrease, subtract 1 from the base:
⇒ 1.03 - 1 = 0.03 = 3%
Therefore, product A is increasing by 3% each year.
Part B
[tex]\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100[/tex]
To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:
[tex]\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%[/tex]
Check using different two consecutive values of f(t):
[tex]\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%[/tex]
Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.
Although the question has not asked, we can use the given information to easily create an exponential function for Product B.
Given:
a = 10,100b = 1.01n = t - 1 (as the initial value is for t = 1 not t = 0)[tex]\implies f(t) = 10100(1.01)^{t-1}[/tex]
To check this, substitute the values of t for 1 through 4 into the found function:
[tex]\implies f(1) = 10100(1.01)^{1-1}=10100[/tex]
[tex]\implies f(2) = 10100(1.01)^{2-1}=10201[/tex]
[tex]\implies f(3) = 10100(1.01)^{3-1}=10303.01[/tex]
[tex]\implies f(4) = 10100(1.01)^{4-1}=10406.04[/tex]
As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.
Help with Pre Calculus
Answer:
The first option
Step-by-step explanation:
The domain of a rational function should be all real numbers except for when the denominator is equal to 0. To find when the denominator is equal to 0 you simply need to find the zeroes of the denominator... but in this case you can do that through factoring and using the quadratic equation.
So first step is going to be to factor out the GCF, which in this case is x. This gives you the equation. [tex]x(2x^2-x-15)[/tex]. So one of the zeroes is when x=0. Now to find the other two zeroes you can use the quadratic equation which is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\[/tex]. So to find the other zeroes you simply plug the values in. a=2, b=-1, c=-15
[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(2)(-15)}}{2(2)}\\\\x=\frac{1\pm\sqrt{1-4(2)(-15)}}{4}\\\\x=\frac{1\pm\sqrt{121)}}{4}\\\\x=\frac{1\pm11}{4}\\\\x=\frac{12}{4}\\x=3\\\\x=\frac{-10}{4}\\x=-\frac{5}{2}[/tex]
can someone help meeee
Answer:
1. 0
2. undefined
3. -3/2
Step-by-step explanation:
y=-3/2. This value is constant and the x does not change the value at all. so the coordinate are going to be (x, -3/2) so if we take any 2 values you're going to get (-3/2 - (-3/2)) / (x2 - x1) = (-3/2 + 3/2) / (x2 - x1) = (0) / (x2 - x1) which is always going to be 0.
x=-3/2. This value is also constant except the x-value does not vary at all so x2 and x1 are always going to be equal which will result in a 0 as the denominator thus making the slope undefined
y=-3/2x. it's just -3/2 given the slope-intercept form y=mx+b where m is the slope
Answer:
0 underfined 3
—
2
Step-by-step explanation:
SOLVING STEP.
the line y= 3 is parallel to the x-axis,
—
— 2
so the slope is 0
the line x= 3 is perpendicular to the x-axis,
—
— 2
so the slope is underfined
the slope of the line y= 3 x 3
—
— — 2.
2
thank me later
can someone pleasee
what is b when the slope is 7/6 and the points are (10, -9)
Answer:
y = 7/6x - 62/3
Step-by-step explanation:
The equation for slope:
y = mx + b
m is the slope and b is the y-intercept
y = 7/6x + b
-9 = 7/6(10) + b
-9 = 35/3 + b
-62/3 = b
what is equivalent to the given equation -8(x+13)=2(x-7)+4x
(-8x-104=6x-14) is equivalent to the given equation (-8(x+13)=2(x-7)+4x).Option C is correct.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Given equation;
⇒-8(x+13)=2(x-7)+4x
⇒-8x-13×8 = 2x-2×7+4x
⇒-8x-104=2x-14+4x
⇒-8x-104=6x-14
(-8x-104=6x-14) is equivalent to the given equation (-8(x+13)=2(x-7)+4x).
Hence, option C is correct.
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write the equation of the line in fully simplified slope-intercept form
Answer:
y=-x+4
Step-by-step explanation:
First use slope formula using 2 points.
(0,3) and (1,2)
[tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{2-3}{1-0}=\frac{-1}{1} =-1[/tex]
Slope is -1.
Now, use point-slope formula.
y-y1=m(x-x1)
Plug in the information that we have.
y-3=-1(x-0)
Use distributive property.
y-3=-x+1
Add 3 to both sides.
y=-x+4
It is now in slope-intercept form.
Hope this helps!
If not, I am sorry.
Given: ∠T ≅ ∠V; ST || UV
Prove: TU || VW
4 connected lines are shown. A line from point S goes slightly down and to the left to point T to form S T. A line from point T goes slightly down and to the right to point U to form T U. A line from point U goes slightly down and to the left to point V to form U T. A line goes slightly down and to the right to point W to form point W.
Complete the two-column proof.
edge 2022 pls helpppppp
We have proven that line TU is parallel to line VW as shown below. That is, TU || VW
Proof of anglesFrom the question, we are to prove that TU || VW
In the given image,
Statements Reasons
1. ST || UV Given
2. ∠T ≅ ∠U Alternate angles
3. ∠T ≅ ∠V Given
4. ∠U≅ ∠V Substitution property
5. TU || VW Alternate interior angles theorem
NOTE: If the alternate interior angles formed by a transversal of two lines are equal, then the lines are parallel
Hence, we have proven that line TU is parallel to line VW. That is, TU || VW
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Answer:
a c c
Step-by-step explanation:
the terminal side of an angle, Theta, whose sine value is One-half
Theta has a reference angle of 30° and is in Quadrant I or II.
Sin(theta) = ½
Basic angle: 30
What is the reference angle?
The acute angle between the terminal arm/terminal side and the x-axis. The reference angle is always positive. In other words, the reference angle is an angle sandwiched between the terminal side and the x-axis.
Angles: 30,
180-30 = 150
Because sin is positive in quadrants 1 and 2.
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(-4^0) + 1 equals to ?
Answer:
zero (0)
Step-by-step explanation:
-4^0=-1
-1+1=0
x(x+3)-2(-5x+1)x=x^2-3(4-2x)
The answer is no solution
Explanation:
it depends on how you interpret what's written. The way I initially interpreted it*, I was able to use the quadratic formula to find :
[tex]x=\frac{1}{4}-i\frac{\sqrt{455}}{20},\:x=\frac{1}{4}+i\frac{\sqrt{455}}{20}[/tex]
*I interpreted it as: [tex]x\left(x+3\right)-2\left(-5x+1\right)x=x^2-3\left(4-2x\right)[/tex]
but I don't want to say that this is your correct answer, because there are multiple interpretations (like a lot of interpretations)
{this is mostly in response to other answers}
What is the gradient of the line y = -7x + 13?
Answer:
y = 7 x - 13. y=7x−13. Swap sides so that all variable terms are on the left hand side. Swap sides so that all variable terms are on the left hand side.7x-13=y. 7x−13=y. Add 13 to both sides. ... 7x=y+13. 7x=y+13. Divide both sides by 7. ... \frac{7x}{7}=\frac{y+13}{7} 77x=7y+13 Dividing by 7 undoes the multiplication by 7.
Step-by-step explanation: hope this helps
Answer:
-7
Step-by-step explanation:
Simplify the following expressions
if someone could do all and or tell me how to do it that would be great if someone dose them all they'll get brainliest
Answer:
See below.
Step-by-Step Explanation:
5) 8x+9-6x-7
8x + 2 - 6x (Subtract the numbers)
2x + 2 (Combine like terms)
2 (x + 1) (Common factor - Factor by grouping twice)
6) 2y-6+5y+9
2y + 3 + 5y (Add the numbers)
7y + 3 (Combine like terms)
7) 3x+8+4x-9
3x - 1 + 4x (Subtract the numbers)
7x - 1 (Combine like terms)
8) 9y+16-12y+24
9y + 40 - 12y (Add the numbers)
-3y + 40 (Combine like terms)
9) 7g-5-8g+12
7g + 7 - 8g (Add the numbers)
-g + 7 (Combine like terms)
10) 11c-8+5c-8
11c - 16 + 5c (Subtract the numbers)
16c - 16 (Combine like terms)
16 (c - 1) (Common factor - Factor by grouping twice)
11) 5(2x + 3) (This one was a bit blurry, I am assuming that's a addition sign.)
10x + 15 (Distribute)
12) 5(-2x+3)
-10x + 15 (Distribute)
Hope this helps!
Answer: those are the answers its a long time.
Question 5 Answer: 2(x+1)
8x+9−6x−7
Multiply and combine like terms.
2x+2
Factor out 2.
2(x+1)
Questio 6 Answer : 7y + 3
2y−6+5y+9
Combine 2y and 5y to get 7y.
7y−6+9
Add −6 and 9 to get 3.
7y+3
Question 7 Answer: 3x+8+4x−9
Combine 3x and 4x to get 7x.
7x+8−9
Subtract 9 from 8 to get −1.
7x−1
Question 8 Answer: - 3y + 40
9y+16−12y+24
Combine 9y and −12y to get −3y.
−3y+16+24
Add 16 and 24 to get 40.
−3y+40
Question 9 Answer: -g + 7
7g−5−8g+12
Combine 7g and −8g to get −g.
−g−5+12
Add −5 and 12 to get 7.
−g + 7
Question 10 Answer: 16 ( c - 1 )
11c−8+5c−8
Combine 11c and 5c to get 16c.
16c−8−8
Subtract 8 from −8 to get −16.
16c - 16
Question 11 Answer: 10x +15
5(2x+3)
Use the distributive property to multiply 5 by 2x+3.
10x+15
Question 12 Answer: 15 - 10x
5(−2x+3)
Use the distributive property to multiply 5 by −2x+3.
−10x+15
Which phrase best describes the relationship indicated by the scatter plot?
OA constant correlation
B. negative correlation
C. positive correlation
D. no correlation
Phrase D best describes the relationship indicated by the scatter plot. There is no correlation.
What is a scatter plot?In an effort to demonstrate how much one variable is influenced by another, scatter plots are used to depict data points on a horizontal and vertical axis.
When there is no connection between two variables, it is called a zero correlation. For instance, there is no correlation between IQ level and the quantity of tea consumed.
Phrase D best describes the relationship indicated by the scatter plot. There is no correlation.
Hence option D is correct.
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Answer:
no correlation
Step-by-step explanation:
A game requires players to throw a ball into a target. The table below shows values from the function that represents one path of a thrown ball, where x represents the horizontal distance the ball travels in feet and f(x) represents the height of the ball in feet.
If the ball enters the target at the highest point in its path, based on the table, what is the height of the target?
1.5 feet
4 feet
28 feet
29 feet
The height of the target is 29 feet.
The correct option is (D)
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The given table path of the thrown ball,
where x represents the horizontal distance and f(x) represents the height of the ball.
Now,
when x = 1.25 feet horizontally, the height will be maximum.
also, the height of the ball at distance x = 1.25 feet is
f(1.25) = 29 feet.
Hence, height of the target is 29 feet.
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Answer:
D. 29 feet
Step-by-step explanation:
Find a the shortest distance from d to b
79=11x+13
Solve each equation by using the properties of equality and justify each step
Solution: X=6
Detailed explanation:
In this problem we're asked to find "x" or the unknown.
The first step is to subtract 11x from both sides.
[tex]---\mapsto\boldsymbol{-11x+79=13}[/tex]
Next, subtract 79 from both sides.
[tex]---\mapsto\boldsymbol{-11x=-66}[/tex]
To finish this off, divide both sides by -11.
[tex]---\mapsto\boldsymbol{x=6}[/tex]
Voila! There's our answer!
Cheers!! ^-^___________________
Hope I helped. Best wishes.
Reach far. Aim high. Dream big.
___________________
[tex]\large\green\longrightarrow \tt \large \:79 \: = \: 11x \: + \: 13[/tex]
[tex]\large\green\longrightarrow \tt \large \:79 \: - \: 13 \: = \: 11x[/tex]
[tex]\large\green\longrightarrow \tt \large \:66 \: = \: 11x[/tex]
[tex]\large\green\longrightarrow \tt \large \: \frac{ \cancel{66} \: \: ^{ \pink6} }{ \cancel{11}} \: = \: x \\ [/tex]
[tex]\large\green\longrightarrow \tt \large \:6 \: = \: x[/tex]
Hence , the value of x is 6
Given parallelograms ABCD, AC=22, and AE=2x-5, find the value of x.
Answer:
D
Step-by-step explanation:
the diagonals of a parallelogram bisect each other , then
2 AE = AC ( substitute values )
2(2x - 5) = 22 ( divide both sides by 2 )
2x - 5 = 11 ( add 5 to both sides )
2x = 16 ( divide both sides by 2 )
x = 8
Which is an example of a statistical question? Questions Question 1 How many pets does Alisha have at home? Question 2 How old were you when you got your first pet? Do you like having a pet? Question 3 Question 4 What is Alisha's pet's name? question 1 O question 2 O question 3 O question 4
Answer:
Do you like having a pet? - statistcal question
Step-by-step explanation:
^^^^
What is the area of a regular octagon
having an apothem of 6 meters and a
side length of 7 meters?
The area of the octagon having an apothem of 6 meters and a side length of 7 meters is 168 meter square
How to the area of an octagonUsing the formula:
Area of an octagon = perimeter * apothem / 2
Note that perimeter of an octagon = 8 a
where a is the length of it's side
Perimeter = 8 * 7
Perimeter = 56 meters
Apothem = 6 meters
Substitute into the formula
Area = 56 * 6/ 2
Area = 336 / 2
Area = 168 meter square
Thus, the area of the octagon is 168 meter square
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What is the range of the function on the graph?
Answer:
the answer is [1, infinity)
24. Factorise completely the expression: 7x-21+ 2xy - 6y
Answer:
below
Step-by-step explanation:
7(x-3)+2(xy-3y)
I'm positive it's the correct answer
Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($) 2
4 6 8 10
Probability 0.5 0.2 0.15 0.1 0.05
Expected Value = [?]
Round to the nearest hundredth.
Enter
The expected value of the winnings from the game is $4
How to determine the expected value?The payout probability distribution is given as:
Payout ($) 2 4 6 8 10
Probability 0.5 0.2 0.15 0.1 0.05
The expected value is then calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
This gives
E(x) = 2 * 0.5 + 4 * 0.2 + 6 * 0.15 + 8 * 0.1 + 10 * 0.05
Evaluate the expression
E(x) = 4
Hence, the expected value of the winnings from the game is $4
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Where is the error in the proof? select all that aply
The correct answer is option D the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB
What is the Linear pair theorem?The linear pair postulate or linear pair theorem in mathematics states the same thing mathematically. The sum of the measurements of two angles that make up a linear pair is 180°.
In the proof of the given question, it is given that the ∠AOP and ∠POB are complementary angles by linear pair of theorem but the linear pair of the theorem is applied to the angles with the sum of 180.
Therefore the correct answer is option D the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB
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This is a sketch of the curve with equation y = f(x).
The curve has a minimum point at M(-1, -3).
Write down the coordinates of the minimum point
of the curve with equation
y = f(x) - 2
Answer:
(-1, -5)
Step-by-step explanation:
Each point on a graph is the ordered pair (x, f(x)). Then the point M(-1 -3) is the ordered pair (-1, f(-1)) where f(-1) = -3.
A point on the shifted graph will be ...
(x, f(x) -2)
Then for x = -1, the point is ...
(-1, f(-1) -2) = (-1, -3 -2) = (-1, -5)
The minimum on the shifted curve is M'(-1, -5).
_____
Additional comment
f(x) is the y-coordinate of a point on a graph. Then f(x) -2 is the y-coordinate shifted down 2 units.
Solve for x. Round to the nearest hundredth sin x ≈ 0.965926
how do u do a problem like this?
In the given equation, the value of x is approximately 75°
TrigonometryFrom the question, we are to determine the value of x
The given equation is
sin x ≈ 0.965926
If sin x ≈ 0.965926
Then,
x ≈ sin⁻¹(0.965926)
∴ x ≈ 75.0°
Hence, the value of x is approximately 75°
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If pound of cheese costs $3.43, what is the cost per pound?
PLS HELP
Answer:
$3.43
Step-by-step explanation:
Cost per pound means how much you are paying for one pound of the item. In this question it says a pound of cheese costs 3.43, therefore each pound of cheese costs 3.43. We can also use the equation 3.43x where x represents the amount of pounds you are purchasing. Just multiply the two and you will get a cost for any amount (pounds) of cheese.
13x13x13=????
I too lazy to calculate
Answer:
13×13×13=2197 that is the answer
The lines below are parallel. If the slope of the green line is -3, what is the
slope of the red line?
m =
Answer:
m=-3
Step-by-step explanation:
Since the lines are parallel to each other, their gradients are equal.
∴ gradient of green line = gradient of red line
∴ m = -3
Solution: slope=-3
Detailed explanation:
This little problem asks us to find the slope of the line. Let's do this!
[tex]\searrow[/tex]
This is what parallel lines look like:
<------------------------------------------------------------------------------------------------------->
<------------------------------------------------------------------------------------------------------->
The two lines above will never intercept each other.
And that's what parallel lines are - they are lines that never intercept.
They can be vertical, horizontal, or diagonal, it doesn't matter. As long as both of them have the same slope and never intercept each other.
So, since parallel lines have identical slopes, the slope of the red line = slope of the green line (the problem provides us that both lines are parallel)
Slope of the red line = -3
Voila! There's our answer!
Cheers! ^-^__________________________
Hope I helped! Best wishes!
Reach far. Aim high. Dream big.
"reflection"
__________________________
The lengths of three sides of a trapezoid are shown below:
Side 1: 11z2 − 4z + 2
Side 2: −2z + 3 + 12z2
Side 3: 3 − 3z + 13z2
The perimeter of the trapezoid is 5z3 + 40z2 + 7z − 15.
Part A: What is the total length of sides 1, 2, and 3, of the trapezoid? (4 points)
Part B: What is the length of the fourth side of the trapezoid? (3 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (3 points)
Answer:
Part A = 36z² - 9z + 8
Part B = 5z³ + 4z² + 16z - 23
Part c = Yes.
Step-by-step explanation:
Polynomials : Polynomials are algebraic expressions that consist of variables and coefficients.
Trapezium: A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other.
Given the length of sides :
Side 1: 11z² - 4z + 2
Side 2: -2z + 3 + 12z²
Side 3: 3 - 3z + 13z²
and The perimeter of the trapezoid is 5z³ + 40z² + 7z - 15.
PART A:
The total length of sides 1, 2, and 3 of the trapezoid is obtained by the sum of the trapezoid :
11z² - 4z + 2 + (-2z + 3 + 12z²) + 3 - 3z + 13z²
11z² - 4z + 2 - 2z + 3 + 12z² + 3 - 3z + 13z²
36z² - 9z + 8
PART B:
The length of the fourth side of the trapezoid is given by the difference between the perimeter of the trapezoid and the sum of length of sides 1, 2, and 3.
5z³ + 40z² + 7z - 15 - 36z² + 9z - 8
5z³ + 4z² + 16z - 23
PART C:
From part A, we can see that the addition of polynomials results in a polynomial.
Likewise, the subtraction of polynomials results in a polynomial.
Therefore, we can say that the polynomials are closed under addition and subtraction.
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Give the fact that connects the look below there is image two angles labelled below.
Use this fact to find the value of c in degrees ().
C
74°
Not to scale
Assuming that both lines are parallel, we conclude that C = 74°.
How to find angle C?
Here we can see that both of the lines that go upwards are parallel lines. This means that C and the 74° angles are opposite angles.
Then if we say that x is the angle at the right of the 74°, we must have that:
x + 74° = 180°
x = 180° - 74° = 106°
And we also must have that:
x + C = 106° + C = 180°
Solving for C:
C = 180° - 106° = 74°
C = 74°.
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