Answer:
Rate = 0.11%
Step-by-step explanation:
Using I = PRT
Where,
P = Principal = $1200R = Rate = ✘T = Time in years = 0.75 yearsI = Interest = $99⟼ I = PRT
Substitute values
⟼ 99 = 1200 × 0.75 × ✘
Multiply
⟼ 99 = 900✘
Divide both sides by the coefficient of ✘
⟼ 99/900 = ✘
⟼ ✘ = 0.11
Therefore, Rate is 0.11%
A candy bar that originally sold for $.60 undergoes a 3% price increase each year.
Both calculations from part (1) and part (2) yield the same result of $0.86 for the new cost of the candy bar after 11 years.
Part 1 of 2:
The new cost of the candy bar after 11 years can be calculated by applying a 3% price increase each year to the original cost of $0.60.
To calculate the new cost after 11 years, we can use the formula:
New Cost = Original Cost * (1 + Percentage Increase)^Number of Years
Plugging in the values:
New Cost = $0.60 * (1 + 3%)^11
≈ $0.60 * (1 + 0.03)^11
≈ $0.60 * (1.03)^11
≈ $0.60 * 1.432364654
Rounding to the nearest cent, the new cost of the candy bar after 11 years is $0.86.
Part 2 of 2:
If the cost of the candy bar increased by 3% of the original cost each year for 11 years, we can calculate the final cost by multiplying the original cost by (1 + 3%) for each year.
Using the formula:
Final Cost = Original Cost * (1 + Percentage Increase)^Number of Years
Plugging in the values:
Final Cost = $0.60 * (1 + 3%)^11
≈ $0.60 * (1 + 0.03)^11
≈ $0.60 * (1.03)^11
≈ $0.60 * 1.432364654
Rounding to the nearest cent, the final cost would also be $0.86.
For more such questions on cost
https://brainly.com/question/25109150
#SPJ8
Note: The complete question is - What will be the cost of the candy bar after a specific number of years if it originally sold for $.60 and undergoes a 3% price increase each year?
Solve for x.
OA. 9
OB. 1
OC. 4
OD.7
The value x in the secant line using the Intersecting theorem is 4.
What is the value of x?Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.
From the figure:
First sectant line segment = ( x - 1 ) + 5
External line segment of the first secant line = 5
Second sectant line segment = ( x + 2 ) + 4
External line segment of the second secant line = 4
Using the Intersecting secants theorem:
5( ( x - 1 ) + 5 ) = 4( ( x + 2 ) + 4 )
Solve for x:
5( x - 1 + 5 ) = 4( x + 2 + 4 )
5( x + 4 ) = 4( x + 6 )
5x + 20 = 4x + 24
5x - 4x = 24 - 20
x = 4
Therefore, the value of x is 4.
Option C) 4 is the correct answer.
Learn more about Intersecting secants theorem here: brainly.com/question/30242636
#SPJ1
Ted's debt is 13 less than 1/2 of mike's debt. If we let y represent mike's debt, write an algebraic expression for Ted's debt
Answer:
x = y - 13
Step-by-step explanation:
y = 1/2 of mike's debt
x = Ted's debt
x = y - 13
. Bert has a well-shuffled standard deck of 52 cards, from which he draws one card; Ernie has a 12-sided die, which he rolls at the same time Bert draws a card. Compute the probability that:
a. Bert gets a Jack and Ernie rolls a five.
b. Bert gets a heart and Ernie rolls a number less than six.
c. Bert gets a face card (Jack, Queen or King) and Ernie rolls an even number.
d. Bert gets a red card and Ernie rolls a fifteen.
e. Bert gets a card that is not a Jack and Ernie rolls a number that is not twelve.
Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.
What is probability, exactly?The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.
Here,
a.
P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)
= (4/52) * (1/12)
= 1/78
b.
P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)
= (13/52) * (5/12)
= 65/624
c.
P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)
= (12/52) * (6/12)
= 1/4
d.
P(Bert gets a red card and Ernie rolls a fifteen) = 0
e.
Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:
A regular 52-card deck contains 48 cards that are not Jacks,
so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.
On a 12-sided dice with 11 possible outcomes,
Ernie rolls a non-12th-number (1, 2, 3, etc.).
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
calculate the average power radiated by each square meter of the sun's surface. (hint: the formula for the surface area of a sphere is a
The average power radiated by each square meter of the sun's surface is approximately 386 W/m². This value is calculated by dividing the total power radiated by the sun (approx. 386 billion Megawatts) by its surface area (approx. 6.08 x 10¹⁸ square meters). The formula for the surface area of a sphere is 4πr².
Sun Power Output CalculationThe average power radiated by each square meter of the sun's surface can be calculated as follows:
Calculate the total power radiated by the sun:The total power radiated by the sun is approximately 386 billion
Megawatts (3.86 x 10³³ erg/s).
Calculate the surface area of the sun:The surface area of the sun can be calculated using the formula for
the surface area of a sphere:
A = 4πr², where r is the radius of the sun (approx. 6.96 x 10⁸
meters).
Plugging in the values, we get:
A = 4π (6.96 x 10⁸)² = 6.08 x 10¹⁸ square meters.
Divide the total power by the surface area:Finally, divide the total power by the surface area to get the
average power radiated by each square meter of the sun's surface:
P = 3.86 x 10³³ erg/s / 6.08 x 10¹⁸ m² = 386 W/m².
Learn more about Sun Power Output Calculation here:
https://brainly.com/question/30174924
#SPJ4
what is the solution to the equation:
5(n - 1/10) = 1/2
a. n= 13/5
b. n= 3/25
c. n= 0
d. n= 1/5
\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)
\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)
\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)
\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)
\( \sf \longrightarrow \: \: 100n =20\\ \)
\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)
\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)
Answer:-
Answer:- D) n = ⅕ ✅To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:
Step 1: Distribute the 5 on the left side:
\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)
Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:
\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)
\(\sf 5n = 1 \\\)
Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):
\(\sf \frac{5n}{5} = \frac{1}{5} \\\)
\(\sf n = \frac{1}{5} \\\)
Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
I need your help to buy a door for my house. I have a scale drawing for the door I want but I am not sure of the true size. In the scale drawing the length is 4 in and the width as 7in. The scale for the door is 1 in = 1.5 ft. What are the actual measurements of the door?
Answer:
According to the scale, 1 inch on the drawing represents 1.5 feet in real life. So, to find the actual length of the door, we need to multiply the length on the drawing by the scale factor:
4 inches x 1.5 feet/inch = 6 feet
Similarly, to find the actual width of the door, we need to multiply the width on the drawing by the scale factor:
7 inches x 1.5 feet/inch = 10.5 feet
Therefore, the actual measurements of the door are 6 feet by 10.5 feet.
sin^22x - 2cos2x + 2=0
Answer:
x=πn, n∈Z
Step-by-step explanation:
if sin²2x=1-cos²2x, then
1-cos²2x-2cos2x+2=0; ⇒ cos²2x+2cos2x-3=0; ⇔ (cos2x+3)(cos2x-1)=0;
\(\left[\begin{array}{cc}cos2x+3=0\\cos2x-1=0\\\end{array} \ <=> \ \left[\begin{array}{cc}x \ 'does-not-exist'\\cos2x=1\\\end{array} \ <=> \ 2x=2\pi n, n=Z \ <=> x=\pi n, n=Z\)
Draw the image of AABC under a translation by 3 units to the left and 3 units down
Answer:so basicaly on this one bring the line down 3 units and 3 unit to the left it is really easy
Step-by-step explanation:
The image of triangle ABC under a translation by 3 units to the left and 3 units down is triangle A'B'C' with vertices A'(-7, 0), B'(-5, 1), and C'(3, -7).
To draw the image of triangle ABC under a translation by 3 units to the left and 3 units down, we need to apply the same translation to each of the three vertices of the triangle.
Original triangle ABC with vertices:
A(-4, 3)
B(-2, 4)
C(6, -4)
To translate each point 3 units to the left and 3 units down, we subtract 3 from the x-coordinate and subtract 3 from the y-coordinate of each vertex:
Translated triangle A'B'C' with vertices:
A'(-4 - 3, 3 - 3) => A'(-7, 0)
B'(-2 - 3, 4 - 3) => B'(-5, 1)
C'(6 - 3, -4 - 3) => C'(3, -7)
Now, let's plot the original and translated triangles on a coordinate plane:
Original Triangle ABC (in blue):
A(-4, 3)
B(-2, 4)
C(6, -4)
Translated Triangle A'B'C' (in red):
A'(-7, 0)
B'(-5, 1)
C'(3, -7)
In the above diagram, the original triangle ABC is shown in blue, and the translated triangle A'B'C' is shown in red. The red triangle is the image of the blue triangle after the translation by 3 units to the left and 3 units down.
To know more about triangle, refer here:
https://brainly.com/question/28967854
#SPJ2
At 8% sales tax, the total price of a color TV whose marked price is $425 is
A)$451
B)$459
C)$465.25
D)$425.75
Answer:
B 459
Step-by-step explanation:
After adding the sales tax of 8% to the marked price of the TV, the price of the TV will be equal to $459. Hence, option B is correct.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages.
In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the given data in the question,
Sales tax on TV = 8%
Marked price of TV = $425
The total price of the TV, T = Tax + Marked Price
T = 8% × $425 + $425
T = $34 + $425
T = $459
Hence, the total price is $459.
To know more about Percentage:
https://brainly.com/question/29306119
#SPJ2
An ant walks 9 3/4 feet in 3/4 minute. The distance in feet the ant walks is directly proportional to the time in minutes the ant walks. What is the constant of proportionality that relates the distance in feet the ant walks to the time in minutes it takes the ant to walk that distance?
Answer:
\(7\frac{5}{16}\) ANSWER (C.
Step-by-step explanation:
Multiply \(9\frac{3}{4}\) by \(\frac{3}{4}\) to get \(\frac{117}{16}\)
-
\(7\frac{5}{16} = \frac{117}{16}\)
because 7 multiply by 16 plus 5 = 117
So 117 over 16
is the same as \(7\frac{5}{16}\) .
3 c ≈ how many mL? Round to the nearest hundredth if necessary.
Answer: It is not possible to convert 3 c to mL without a conversion factor. There are several different units of measurement for volume, including cubic centimeters (cc), milliliters (mL), and cubic meters (m^3). To convert from one unit to another, you need to know the conversion factor.
The conversion factor between cubic centimeters (cc) and milliliters (mL) is 1:1, meaning they are equivalent units of measurement. So, 3 cc is equal to 3 mL.
Step-by-step explanation:
Time-series models rely on judgment in an attempt to incorporate qualitative or subjective factors into the forecasting model. (Points : 1)
True
False
False. Time-series models do not rely on judgment in an attempt to incorporate qualitative or subjective factors into the forecasting model.
One of the most often used methods of data science in business, finance, supply chain management, production, and inventory planning is time series forecasting. A time component is often present in prediction difficulties, necessitating the extension of time series data or time series forecasting. Another crucial field of machine learning (ML) is time series forecasting, which may be viewed as a supervised learning issue.
Time series models are utilized to forecast events. Moving average, smooth-based, and ARIMA are common example types. It's important to choose the model that works best depending on the unique time series because not all models will produce similar outcomes for the comparable dataset.
Trend analysis, regression analysis, and time series models are the three categories of forecasting models. To determine whether the data exhibits a long-term trend, trend analysis is utilized.
For more information on Time-series models , visit :
https://brainly.com/question/15542776
#SPJ4
3x2 + 6x + 3
Factor out the GCF
Answer:
\(3( {x}^{2} + 2x + 1)\)
Hope this helps!
Consider the right triangle below:
The length of the missing leg, AC= meters
Round your answer to the nearest tenth.
Note: Figure not drawn to scale and all the measurements are in meters.
What is the perimeter of triangle ABC
Sinx-sin3x /sin^2x -cos^2x
The answer is (sin x - 2 sin 3x cos x) / (1 - 2 cos² x). To simplify the given expression, we can use the identity sin 2x = 2sin x cos x.
Substitute the numerator with sin x - sin 3x. Substitute the denominator with sin² x - cos² x to get a common factor.
Substitute sin² x with (1 - cos² x) to get sin x - sin 3x / (1 - cos² x - cos² x).Then substitute sin² x with (1 - cos² x) to get sin x - sin 3x / (1 - 2 cos² x).
Now, use the identity sin 2x = 2sin x cos x to simplify the numerator. sin x - sin 3x can be written as sin x - sin (x + 2x) which equals sin x - [sin x cos 2x + cos x sin 2x].
Now, simplify the expression: sin x (1 - cos² x - cos² x) - sin x cos 2x - cos x sin 2x. We will simplify this expression further, leading us to get sin x (1 - 2 cos² x) - sin 2x cos x.
Finally, the expression becomes sin x (1 - 2 cos² x) - sin 2x cos x / (1 - 2 cos² x). Therefore, the answer is (sin x - 2 sin 3x cos x) / (1 - 2 cos² x).
For more question on expression
https://brainly.com/question/1859113
#SPJ8
Need help quick please
Answer:-1/6
Step-by-step explanation:
Draw a line out in the 2nd quadrant.
Your y=\(\sqrt{35}\) hypotenuse=6 use pythagorean theorem to solve for x
6² = 35 + x²
x=1
so
cosΘ = -1/6
Please help me in this math problem
Answer:
Step-by-step explanation: well, you will more than likely get it at least 60%-80% of the time! If this doesn't help i can try to explain in a lot more detail unless someone does for me!
The points J (9,7), K (2,1), L(0,−8) and M (7,−2) form quadrilateral JKLM.
Plot the points
slope of JK =
length of JK =
slope of KL =
length of KL =
slope of LM =
length of LM =
slope of MJ =
length of MJ =
Quadrilateral JKLM can BEST be described as
Quadrilateral JKLM has sides with equal lengths (√85), and the slopes of opposite sides are equal. However, it is not a special type of quadrilateral like a rectangle or a square.
To describe quadrilateral JKLM, let's first plot the given points J(9, 7), K(2, 1), L(0, -8), and M(7, -2) on a coordinate plane:
J(9, 7) K(2, 1)
L(0, -8) M(7, -2)
To find the slopes and lengths of each side of the quadrilateral, we can use the distance formula and the slope formula.
Slope of JK:
Slope (m) = (change in y) / (change in x)
m(JK) = (7 - 1) / (9 - 2) = 6/7
Length of JK:
Length (d) = √[(x2 - x1)^2 + (y2 - y1)^2]
d(JK) = √[(9 - 2)^2 + (7 - 1)^2] = √(49 + 36) = √85
Slope of KL:
m(KL) = (-8 - 1) / (0 - 2) = -9/2
Length of KL:
d(KL) = √[(0 - 2)^2 + (-8 - 1)^2] = √(4 + 81) = √85
Slope of LM:
m(LM) = (-2 - (-8)) / (7 - 0) = 6/7 (same as slope of JK)
Length of LM:
d(LM) = √[(7 - 0)^2 + (-2 - (-8))^2] = √(49 + 36) = √85
Slope of MJ:
m(MJ) = (7 - (-2)) / (9 - 7) = 9
Length of MJ:
d(MJ) = √[(7 - 9)^2 + (-2 - (-8))^2] = √(4 + 36) = √40
Based on the calculations, we can describe quadrilateral JKLM as follows:
The slope of JK and LM is 6/7.
The slope of KL is -9/2.
The slope of MJ is 9.
The length of each side (JK, KL, LM, MJ) is √85.
The quadrilateral is not a rectangle or a square since the slopes of opposite sides (JK and LM) are not perpendicular.
For more such question on Quadrilateral. visit :
https://brainly.com/question/23935806
#SPJ8
According to Greg, the perfect cherry pies have a ratio of 240 cherries to 3 pies. How many cherries does Greg need to make 9 perfect cherry pies?
Answer:
720 cherries
Step-by-step explanation:
3 pies need 240 cherries so the equation would be:
3c = 240
so, c = 80
But, he needs to make 9 "perfect" pies so you make the equation:
9c = 80*9
9c = 720
So Greg needs 720 cherries to make 9 perfect cherry pies.
the question is below
Answer:
use sin to find the angle x
Answer:
We can use the triginotemtric ratio inverse cos to solve this problem.
Cos=adjacent side/hypotenuse
cos(h)=21/69
\(cos^-1(21/69)=x\\cos^-1(0.30434782608) \\x=72\)
Step-by-step explanation:
Santo paid $16.25 to buy 5 children tickets and 1 adult ticket. Hulda paid $24.00 to buy 4 children tickets and 3 adult tickets. If both people paid the same price per ticket what was the price of an adult ticket
Answer:
The price of an adult ticket it $5
Step-by-step explanation:
To solve this, we would find the system of equations. We would set up two equations that will represent the situation.
Let c = price per children ticket
Let a = price per adult ticket
Santo:
5c + 1a = 16.25
Hulda:
4c + 3a = 24
5c + 1a = 16.25 -> a = 16.25 - 5c
4c + 3a = 24
4c + 3(16.25 - 5c) = 24
4c + 48.75 - 15c = 24
-11c + 48.75 = 24
-48.75 -48.75
-11c = -24.75
/-11 /-11
c = 2.25
5c + a = 16.25
5(2.25) + a = 16.25
11.25 + a = 16.25
-11.25 -11.25
a = 5
a = $5 , c = $2.25
Mofor has homework assignments in five subjects. He only has time to do two of
them.
The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.
If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:
1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.
2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.
3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.
The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.
For more such questions on homework
https://brainly.com/question/28521601
#SPJ8
May I please get a little help with this question? Thank you so much.
The y-intercept of the function is (0, c)
The coefficients b determine the horizontal shift of the parabola compared to the parent function
If a is negative, the parabola opens downward
The y-intercept of the function is (0, c).
This means that when x = 0, the y-value is equal to c.
The constant term c represents the y-coordinate of the point where the parabola intersects the y-axis.
The coefficient b determines the horizontal shift of the parabola compared to the parent function.
The value of b affects the position of the vertex and determines if the parabola is shifted to the left or right.
A positive value of b shifts the parabola to the left, while a negative value of b shifts it to the right.
If a is negative, the parabola opens downward.
The coefficient a determines the shape of the parabola.
If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The sign of a determines the direction in which the parabola faces.
To learn more on Parabola click:
https://brainly.com/question/29267743
#SPJ1
Cómo se hace y cómo es el proceso ayuda porfaaaaa
Answer:
30: 100
31: -13
32: -45
33: 14
34: -32
35: -22
36: 17
The quadrilateral KLMN is dilated with the center of dilation located at point M. Which statement is accurate?
1. The scale factor is 3, which means the length of the image of segment KL will be 1/3 times as long.
2. The scale factor is 1/3, which means the length of the image of segment KL will be 1/3 times as long.
3. The scale factor is 3, which means the length of the image of segment KL will be 3 times as long.
4. The scale factor is 1/3, which means the length of the image of segment KL will be 3 times as long.
Answer:
3. The scale factor is 3, which means the length of the image of segment KL will be 3 times as long.
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure. If a point A(x, y) is dilated about the center of dilation located at O(a, b), the new point is at A'[k(x - a) + a, k(y - b) + b].
Quadrilateral KLMN has vertices at K(2, 1), L(-1, -5), M(6, -5) and N(6, 1). If it is dilated by 3, about the center M(6, -5), the new points are:
K' = (3(2 - 6) + 6, 3(1 - (-5)) + (-5)) = (-6, 13)
L' = (3(-1 - 6) + 6, 3(-5 - (-5)) + (-5)) = (-15, -5)
M' = (3(6 - 6) + 6, 3(-5 - (-5)) + (-5)) = (6, -5)
N' = (3(6 - 6) + 6, 3(1 - (-5)) + (-5)) = (6, 13)
Therefore the image of segment KL will be 3 times long.
I need to know where to put it on the number line! Please help
Answer:
Graph uploaded!
Step-by-step explanation:
First, let's simplify the inequality before graphing it on the line.
2x + 4 < 8=> 2x < 8 - 4=> 2x < 4=> x < 2Now, let's graph it on the line. Please consider looking at my graph.
Hoped this helped!
On the number line above, the numbers a and b are the same distance from O.Part AWhat is a + b?Answer:Part BExplain what you did to solve this problem.
(b) We know that a and b are both the same distance away from zero. However, we can see from the preceding number line that a and b are on opposite sides of zero.
If we start at zero and move units to the right, and then move the same number of units to the left, we will be back at 0.
This can also be expressed symbolically. We know they are opposites because a and b are the same distance from zero but on opposite sides of zero, therefore b=-a. A number's sum and its inverse are always zero.
Write x^2 - 8x + 10 in the form
(x + a)^2 + B
\(x^2-8x+10=x^2-8x+16-6=(x-4)^2-6\)
Calculate the distance between the points (4,-2) and (7,-9)
The Distance between the points (4, -2) and (7, -9) is sqrt(58) or approximately 7.62 units.
The distance between two points in a coordinate plane. The distance formula is based on the Pythagorean theorem and calculates the straight-line distance between two points.
The coordinates of the first point as (x1, y1) = (4, -2) and the coordinates of the second point as (x2, y2) = (7, -9).
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values:
d = sqrt((7 - 4)^2 + (-9 - (-2))^2)
d = sqrt((3)^2 + (-7)^2)
d = sqrt(9 + 49)
d = sqrt(58)
Hence, the distance between the points (4, -2) and (7, -9) is sqrt(58) or approximately 7.62 units.
To know more about Distance .
https://brainly.com/question/23848540
#SPJ11