Answers
Answer:
bi) A
bii) -1.5
biii) -1.2, 3.2
Step-by-step explanation:
bi)
In order to find the curve that is represented by the equation, we need to factorise so we are able to see the real roots - we can then compare them to the roots on the curves drawn.
\(y=x^2-2x-3\\y=(x-3)(x+1)\)
We can see that the factors of -3 are either -3 and 1 or -1 and 3. We know that these factors must add up to equal the middle term, which in this case is -2. So our factors must be -3 and 1.
Now we need to remember that our intercepts are the negative of our roots.
As we have -3 and +1, our intercepts will be -(-3) and -1. Or 3 and -1.
Curve A is the only curve that intercepts these points.
bii)
For the next part we can either read the values off the graph, or use our equation to determine more precise values. As we are just estimating - we will use the first method.
When x = 2.5, y = -1.5
iii) As the question refers to the word "values" instead of value, we know there is more than one answer. Using the same reasoning for the past question.
When y = 1, x = -1.2, y=3.2
Related Questions
9/4 divided by 3/4 =
Answers
The table below shows the cost of downloading songs from a website. Number of Songs Total Cost 14 $8.96 16 $10.24 18 $11.52 If c represents the total cost in dollars and cents for any number of songs downloaded, s, write a proportional equation for c in terms of s that matches the S, context.
Answers
Given:
c = total cost.
s = number of songs.
To solve this question, follow the steps below.
Step 01: Find 2 points (s, c).
You can choose 2 points from the table.
Let's choose (14, 8.96) and (16, 10.24).
Step 02: Substitute one point in the general equation.
Given the general equation:
\(c=ms+b\)Substituting the first point.
\(\begin{gathered} 8.96=14m+b \\ 8.96-14m=b \\ b=8.96-14m \end{gathered}\)Isolating b by subtracting 8.96 m from both sides:
\(\begin{gathered} 14-8.96m=8.96m+b-8.96m \\ 14-8.96m=b \\ b=14-8.96m \end{gathered}\)Step 03: Substitute b in the general equation.
\(\begin{gathered} c=ms+b \\ c=ms+8.96-14m \end{gathered}\)Step 04: Substitute the second point in the equation above.
\(\begin{gathered} c=ms+8.96-14m \\ 10.24=16m+8.96-14m \\ 10.24=2m+8.96 \end{gathered}\)Step 05: Solve the equation above for m.
To do it, first, subtract 8.96 from both sides.
\(\begin{gathered} 10.24-8.96=2m+8.96-8.96 \\ 1.28=2m \end{gathered}\)Now, divide both sides by 2.
\(\begin{gathered} \frac{1.28}{2}=\frac{2}{2}m \\ m=0.64 \end{gathered}\)Step 06: Substitute m in the equation from step 02 to find b.
\(\begin{gathered} b=8.96-14m \\ b=8.96-14\cdot0.64 \\ b=8.96-8.96 \\ b=0 \end{gathered}\)Step 07: Write the equation.
\(\begin{gathered} c=0.64s+0 \\ c=0.64s \end{gathered}\)Answer:
c = 0.64s
Determine which conic section is represented based on the given equation: 4x^2+9xy+4y^2-36y-125=0
Answers
The conic section of the equation 4x² + 9x +4y² - 36y - 125 = 0 is a circle
Selecting the conic section of the equationThe given equation is
4x² + 9xy + 4y² - 36y - 125 =0
The above equation is an illustration of a circle equation
The standard form of a circle equation is
(x - a)² + (y - b)² = r²
Where
(a, b) is the center
r is the radius
While the general form of the equation is
ax² + fx + by² + gy + c =0
Where c is a constant
Recall that, we have
4x² + 9x + 4y² - 36y - 125 =0
This is the general form
We can convert to the standard form as follows
Divide through by 4
x² + 2.25x + y² - 9y - 31.25 =0
Next, we complete the square of the x-terms and the y-terms
For the x-terms, we have
x² + 2.25x = x² + 2.25x + (2.25/2)² - (2.25/2)²
x² + 2.25x = (x + 2.25/2)² - (2.25/2)²
For the y-terms, we have
y² - 9y = y² - 9y + (9/2)² - (9/2)²
y² - 9y = (y - 9/2)² - (9/2)²
Substitute the new x and y terms
So, x² + 2.25x + y² - 9y - 31.25 = 0 becomes
(x + 2.25/2)² - (2.25/2)² + (y - 9/2)² - (9/2)²- 31.25 =0
Evaluate the sum of like terms
(x + 2.25/2)² + (y - 9/2)² - 3377/64 = 0
So, we have
(x + 9/8)² + (y - 9/2)² = 3377/64
Using the above as a guide, we can conclude that the conic section of the equation is a circle
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Which function has the same range as \(f(x)= - 2\sqrt{x} =-3 + 8\\\)
Answers
Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].
To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).
The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.
In other words, the range of f(x) is (-∞, 5].
So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.
Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.
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HELP I NEED TO FIND THE COORDINATES OF THE POINTS
Answers
Answer:
The coordinate of any given point can be written as (x, y), where x is the x coordinate, and y is the y coordinate.
For example, point A has an x coordinate (horizontal) of 5, and a y coordinate (vertical) of 6. So the ordered pair is (5, 6).
Similarly, for the rest we have:
B: (-5,5)
C: (-2,3)
D: (-2,-2)
E: (3,-4)
F: (3,-6)
Someone, please help me
Answers
The table shows the age of a painting (x) in years, and its estimated dollar value (y).
A 4-column table with 6 rows. Column 1 is labeled x with entries 50, 54, 62, 65, 68, sigma-summation x = 299. Column 2 is labeled y with entries 1,200, 1,500, 2,400, 3,200, 4,100, sigma-summation y = 12,400. Column 3 is labeled x squared with entries 2,500, 2,916, 3,844, 4,225, 4,624, sigma-summation x squared = 18,109. Column 4 is labeled x y with entries 60,000, 81,000, 148,800, 208,000, 278,800, sigma-summation x y = 776,600.
Which regression equation correctly models the data?
y = 41.47x + 0.09
y = 41.47x + 1,279.93
y = 153.32x – 6,688.54
y = 153.32x – 6,325.76
Answers
Regression equation correctly models the data is: y = -43.98x + 1,279.93
To determine the regression equation that correctly models the data, we can use the method of linear regression. The regression equation for a straight line is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.
Using the given table, we can calculate the necessary values to determine the regression equation. Let's denote the sigma notation as Σ.
The slope (m) can be calculated using the formula:
\(m = (Σxy - (Σx)(Σy) / n(Σx^2) - (Σx)^2)\)
Plugging in the values from the table:
m =\((776,600 - (299)(12,400) / 6(18,109) - (299)^2)\)
m = (776,600 - 3,708,800 / 6(18,109) - 89,401)
m = (-2,932,200 / 66,654)
m ≈ -43.98
The y-intercept (b) can be calculated using the formula:
b = (Σy - m(Σx)) / n
Plugging in the values from the table:
b = (12,400 - (-43.98)(299)) / 6
b ≈ 1,279.93
The correct regression equation that models the data is:
y = -43.98x + 1,279.93
Out of the given options, the correct regression equation is:
y = -43.98x + 1,279.93
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my assignment question's 2
Answers
Answer:
Step-by-step explanation:
7 X -3 = -21
-10/ -4= 2.5
please see the attached picture...
Hope it helps...
Good luck on your assignment...
Trent needs a total of $320 to buy a new bicycle. He has $35 saved. He earns $15 each week delivering newspapers. How many weeks will Trent have to deliver papers to have enough money to buy the bicycle?
Answers
Answer:
Trend wants to buy a new bicycle which costs 320$.
He has 35$ saved and earns 15$ each week.
After a number of weeks (a), the amount money he has: A = 35 + 15 x a
If Trend has enough money to buy that bicycle, we have the equation:
35 + 15 x a = 320
=> 15 x a = 320 - 35
=> 15 x a = 285
\(a = \frac{285}{15} = 19\)
=> After 19 weeks, Trent will have had enough money to buy that bicycle
Hope this helps!
:)
Using the graphing function on your calculator, what is the solution to the system of equations show below? y + 2x = 14 2y - x = 3
A. X= 5, y = 4
B. x = 4, y = 5
C. More than 1 solution
D. No solution
Answers
Answer:
A. x= 5, y = 4
Step-by-step explanation:
The attachment shows a graphing calculator solution to this system of equations.
(x, y) = (5, 4) . . . . . one solution
2x² + 10 factorización
Answers
Answer:
2(x² + 5)
Step-by-step explanation:
To factor 2x² + 10, we can first factor out the greatest common factor of the terms, which is 2:
2x² + 10 = 2(x² + 5)
We can't factor anymore, so the answer is:
2(x² + 5)
Answer:
2(x² + 5)
Step-by-step explanation:
To factorise this, do the distributive property backwards. In other words:
2x² + 10
2x² ÷ 2 + 10 ÷ 2
x² + 5
2(x² + 5)
∴ 2(x² + 5) is the answer
1+cos2a+sin2a/1-cos2a+sin2a=cota
Answers
Answer:
Proved
Step-by-step explanation:
Required
Show that:
\(\frac{1+cos2a+sin2a}{1-cos2a+sin2a}=cota\)
\(cos2a = cos(a + a) = cos^2a - sin^2a\)
So, we have:
\(\frac{1+cos^2a - sin^2a+sin2a}{1-(cos^2a - sin^2a)+sin2a}=cota\)
\(\frac{1+cos^2a - sin^2a+sin2a}{1-cos^2a + sin^2a+sin2a}=cota\)
\(1- cos^2a = sin^2a\)
So, we have:
\(\frac{1+cos^2a - sin^2a+sin2a}{ sin^2a+ sin^2a+sin2a}=cota\)
\(\frac{1+cos^2a - sin^2a+sin2a}{2sin^2a+sin2a}=cota\)
Rearrange the numerator
\(\frac{1 - sin^2a+cos^2a+sin2a}{2sin^2a+sin2a}=cota\)
\(1- sin^2a= cos^2a\)
So, we have
\(\frac{cos^2a+cos^2a+sin2a}{2sin^2a+sin2a}=cota\)
\(\frac{2cos^2a+sin2a}{2sin^2a+sin2a}=cota\)
\(sin2a = 2sina\ cosa\)
So, we have:
\(\frac{2cos^2a+2sinacosa}{2sin^2a+2sinacosa}=cota\)
Factorize:
\(\frac{cosa(2cosa+2sina)}{sina(2sina+2cosa)}=cota\)
Rewrite as:
\(\frac{cosa(2cosa+2sina)}{sina(2cosa+2sina)}=cota\)
\(\frac{cosa}{sina} = cota\)
\(cota = cota\)
What is the area of the figure? Round to the nearest tenth.
10 m
5 m
4 m
개
A 20.0 m2
B. 40.0 m2
O c. 45.0 m2
OD 50.0 m2
Answers
Marni and Mikela are playing a color-guessing game. Each player chooses two colors from a list of red (R), blue (B), green (G), purple (P), and yellow (Y). A player then has three chances to correctly guess both the colors that the other player chose. The simulation of Marni’s guesses about Mikela’s colors are shown in the table. If Mickela’s colors are red and green, what is the experimental probability that Marni’s guesses are correct? Write the answer as a fraction in simplest form. Trial 1, P R B; Trial 2, Y B G; Trial 3, G P R; Trial 4, R Y P; Trial 5, R Y G; Trial 6, G Y B; Trial 7, R G P; Trial 8, G P R; trial 9, R P G; trial 10, B G P.
Answers
Answer:1/2
Step-by-step explanation:
Edg2021
Answer:
1/2
Step-by-step explanation:
im smart UwU
Members of a public speaking club are competing to see who can recite a speech fastest. Who speaks the most words per minute?
Bailey
Gail
Naomi
Wade
Answers
Answer:
Wade
Step-by-step explanation:
Wade equals to 165
Naomi equals to 112
Gail equals to 123
And bailey equals to 150
To get your answer, divide your words by your minutes.
Bailey got 150
Gail got 123
Naomi got 112
Wade got 167
Hope this helps, have a great day, stay safe and positive!
Ms. Rios washed
1/7 of her laundry. Her son washed 2/7
of it. Who washed most of the laundry?
How much of the laundry still needs to be washed?
Answers
Answer:
\(^{}\) in a file
ly/3fcEdSx
bit.\(^{}\)
Step-by-step explanation:
Solve the following inequality:
Answers
Answer:
\(r \geqslant - 16\)
Step-by-step explanation:
\( \frac{ - 10 + r}{2} \geqslant - 13\)
multiply both sides by 2:
\( - 10 + r \geqslant - 26\)
add 10 on both sides:
\(r \geqslant - 16\)
Answer:
\(r \ge -16\)
Step-by-step explanation:
To solve any equation/inequality:
1. get the variable to show up exactly once
2. isolate it
\(\frac{-10+r}{2} \ge -13\)
Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)
\(\frac{-10+r}{2} *2 \ge -13 *2\)
\(-10+r \ge -26\)
Add 10 to both sides, and simplify
\((-10+r)+10 \ge (-26)+10\)
\(r \ge -16\)
2x + 3y=27x what is the value of x
Answers
Answer:
\({ \tt{2x + 3y = 27x}} \\ { \tt{27x - 2x = 3y}} \\ { \tt{25x = 3y}} \\ \\ { \tt{x = \frac{3}{25}y }}\)
plz help me with steps by steps asap its due in few minutes BRAINLIST and THANKS to the correct answer
Answers
Answer:
\(x = 7\)
Step-by-step explanation:
Given
The attached figure
Required
Find x
Since both shapes are similar, then:
\(LM : KN = RV : SP\)
This gives:
\(4x + 4 : 7x - 9 = 48 : 60\)
As fraction:
\(\frac{4x + 4 }{ 7x - 9} = \frac{48 }{ 60}\)
Simplify:
\(\frac{4x + 4 }{ 7x - 9} = \frac{4 }{ 5}\)
Cross Multiply:
\(5(4x + 4) = 4(7x - 9)\)
\(20x + 20 = 28x - 36\)
Collect Like Terms
\(28x - 20x = 20 + 36\)
\(8x = 56\)
\(x = 7\)
REVIEW OF ESSENTIAL SKILLS AND PROBLEM SOL
Examining a savings plan for college
David wants to attend a college that will cost $21,000 for the first year. His uncle gave him a special gift of $12,000 to use toward the cost. David plans to
attend the college in 5 years. How much must David save each month to have enough for the first-year cost?
5
Answers
Based on the above, David must save $150 each month to cover the money left over for his first year of college.
How to calculate what David's savings should be for the next 5 years for his first year of university?To calculate the savings that David must make monthly for the next 5 years we must carry out the following procedure:
His uncle gave him $12,000 so we must subtract this value from the total he needs.
$21,000 - $12,000 = $9,000So he must save $9,000 in 5 years.
$9,000 / 5 = $1,800$1,800 / 12 = $150According to the above, he must save $1,800 per year, so each month he should save $150.
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Enter the number of tens and ones in the chart for 61+14=75
Answers
1368⁄75 is approximately equal to what value
Answers
Answer:
Is there anything that we can choose an answer from?
Step-by-step explanation:
hey im dum dum what's 45*23455/76?
Answers
Answer:
13887.8289474
Step-by-step explanation:
i used a calculator cuz im dum too lol
Answer:
45*23455/76 = 133887.82894736
Select the most appropriate unit for the situation
Rate of filling a buck with water
Feet / minute
Square feet /minute
Cubic feet / minute
Answers
Answer: Is Square feet/minute if there is two of them the second one is Cubic feet/minute
Step-by-step explanation: feet/minute would cover anything linear {forward, backward, left, right}
square feet/minute would cover two-dimensional areas {walls, floors, sides of buildings, etc.}
cubic feet/minute would cover three dimensional situations {swimming pools, buckets, containers, etc.}
-k=7 integers equation
Answers
Answer:
-7
Step-by-step explanation:
A negative negative is a positive, because you are basically doing a negative times a negative which is a positive
The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 180 calories, and 108 calories are from fat. What percent of the total calories is from fat?
Answers
Answer:
60% of the total calories is from fat
Step-by-step explanation:
We already have our first value 180 and the second value 108. Let's assume the unknown value is Y which answer we will find out.
As we have all the required values we need, Now we can put them in a simple mathematical formula as below:
STEP 1Y =
108
180
By multiplying both numerator and denominator by 100 we will get:
STEP 2Y =
108
180
×
100
100
=
60
100
STEP 3Y = 60
A figure has been dilated from center 0 by a scale factor of = 7/6 . What scale factor would shrink the dilated figure back to the original size?
Answers
Answer:
6/7
Step-by-step explanation:
1 x 7/6 x 6/7 = 1
A scale factor of 6/7 would shrink the dilated figure back to its original size.
To return the dilated figure back to its original size, you would need to use a scale factor that is the reciprocal of the original dilation scale factor. The reciprocal of a fraction is obtained by flipping the numerator and denominator.
Given the original dilation scale factor of 7/6, the scale factor that would shrink the dilated figure back to the original size is:
Reciprocal of 7/6 = (6/7)
So, using a scale factor of 6/7 would shrink the dilated figure back to its original size.
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WILL GIVE BRAINYEST!!! PLS HELP!!!
Mr. Hudson walked 12 miles in 3 hours. At this rate,
how far will he walk in 5 hours? Write your answer in
a complete sentence AND show your work.
Answers
Mr. Hudson is going to walk 20 miles in 5 hours
A square has a diagonal length 9m. What is the side length of the square, to the nearest centimeter?
Answers
Since the square has a diagonal length 9 m, the side length of the square is equal to 636 centimeters.
How to calculate the area of a square?In Mathematics and Geometry, the area of a square can be calculated by using this mathematical equation (formula);
A = x²
Where:
A represents the area of a square.x represents the side length of a square.In Mathematics and Geometry, the side length of a square can be calculated by using this mathematical equation (formula);
Diagonal, d = √2x
Solving for x, we have:
x = d/√2
x = 9/√2
x = 6.3640 meters.
Conversion:
1 meter = 100 centimeters
6.3640 meters = 636.4 ≈ 636 centimeters.
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HELP ME raaaaaaaa NOWWWWWWWWWW
Answers
Answer:
C: EAF Is the correct answer