The measure of distance x, that is, the distance between a point P and the point of horizon, is equal to 284.372 miles.
How to find the distance to the earth horizon from a given point
In this problem we must determine the distance between a point P located about earth's circumference and the point of horizon, located on earth's circumference. Since the line between these two points is tangent to earth, then, distance x can be found by Pythagorean theorem:
x = √[(3959 mi + 10.2 mi)² - (3959 mi)²]
x = 284.372 mi
The distance x is equal to 284.372 miles.
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Find the circumference and the area of a circle with radius 4 m.
Use the value 3.14 for , and do not round your answers. Be sure to include the correct units in your answers.
4m
Circumference:
Area:
Please Factorise 8x - 6
Answer:
2(4x-3)
Step-by-step explanation:
Find common numbers between 8 and 6, which is 2. 2x4= 8 2x3=6
x is only on 8 so you can't put x on the outside of the bracket. so you put it with the 4 so it comes out correct
solve the rational equation 2/x-2+3/x-4=1/x^2=6x+8
the solution to the original rational equation is: [tex]x = 4.678[/tex] (rounded to three decimal places)
What is the rational equation?A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. In other words, it is a number that can be written in the form of a/b, where a and b are integers and b is not equal to zero
According to InformationThere are two equal signs in the equation, which is incorrect. Assuming you meant to write:
[tex]2/(x-2) + 3/(x-4) = 1/(x^2 + 6x + 8)[/tex]
We can start by finding a common denominator for the left-hand side of the equation:
[tex]2/(x-2) + 3/(x-4) = 1/[(x+2)(x+4)][/tex]
Multiplying both sides of the equation by (x-2)(x-4)(x+2)(x+4), we get:
[tex]2(x-4)(x+2)(x+4) + 3(x-2)(x+2)(x+4) = (x-2)(x-4)[/tex]
Expanding and simplifying, we get:
[tex]5x^3 - 19x^2 - 39x + 56 = 0[/tex]
This polynomial equation does not factor nicely, so we can use the rational root theorem or numerical methods to find approximate solutions. Using a calculator or computer, we find that there is one real solution to the equation:
[tex]x \approx 4.678[/tex]
Therefore, the solution to the original rational equation is:
[tex]x = 4.678[/tex] (rounded to three decimal places)
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A dot plot titled seventh grade test score. There are 0 dots above 5, 6, 7, 8 and 9, 1 dot above 10, 1 dot above 11, 2 dots above 12, 1 dot above 13, 1 dot above 14, 2 dots above 15, 3 dots above 16, 3 dots above 17, 2 dots above 18, 2 dots above 19, 3 dots above 20. A dot plot titled 5th grade test score. There are 0 dots above 5, 6, and 7, 1 dot above 8, 2 dots above 9, 10, 11, 12, and 13, 1 dot above 14, 3 dots above 15, 2 dots above 16, 1 dot above 17, 2 dots above 18, 1 dot above 19, and 1 dot above 20.
Students in 7th grade took a standardized math test that they also had taken in 5th grade. The results are shown on the dot plot, with the most recent data shown first.
Find and compare the means to the nearest tenth.
7th-grade mean:
5th-grade mean:
What is the relationship between the means?
Note that 7th grade mean = 277.86
the 5th grade mean = 254.77
So th relationship between the mean is that the 7 th grade mean is higher than the 5 th grade mean .
How is this so ?To compute the means here is what we did
7 th grade mean = (1 × 10) + (1 × 11) + (2 × 12) + (1 × 13) + (1 × 14) + (2 × 15) + (3 × 16) + (3 × 17) + (2 × 18) + (2 × 19) + (3 × 20) / 21
= 277.857142857
≈ 277.86
For the 5th grade mean
5th grade mean = (1 × 8) + (2 × 9) + (2 × 10) + (2 × 11) + (2 × 12) + (1 × 13) + (3 × 15) + (2 ×16) + (1 × 17) + (2 × 18) + (1 × 19) + (1 × 20) / 26 = 12.5
= 254.769230769
≈ 254.77
This means that trully, the relationship between the mean is that the 7 th grade mean is higher than the 5 th grade mean.
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Pls, HELP!!
Law of Cosines
Solve for c. Round your final answer to the nearest tenth
The value of side c to the nearest tenth is 4.2.
What is the value of side c?The law of cosines signifies the relation between the lengths of sides of a triangle with respect to the cosine of its angle.
It is expressed as:
c² = a² + b² - ( 2ab × cosC )
From the diagram:
a = 7
b = 8
Angle C = 32 degrees
Plug these values into the above formula and solve for c.
c² = a² + b² - ( 2ab × cosC )
c = √( a² + b² - ( 2ab × cosC ) )
c = √( 7² + 8² - ( 2 × 7 × 8 × cos32 ) )
c = √( 49 + 64 - ( 112 × cos32 ) )
c = √( 113 - 94.98 )
c = √18.02
c = 4.2
Therefore, the value of c is 4.2.
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fill in "blanks"
blank g = blank kg = 3/10 kg
The amount of grams that is equivalent to 3/10 of a kg is given as follows:
300 grams.
How to obtain the amount of grams?The amount of grams that is equivalent to 3/10 of a kg is obtained applying the proportions in the context of the problem.
The amount of kg is 3/10 of a kilogram is given as follows:
3/10 = 0.3kg.
(conversion of a fraction to decimal, divide the numerator by the denominator).
Each kg is composed by 1000 grams, hence the amount of grams in 0.3 kg is given as follows:
0.3 x 1000 = 300 grams.
(proportion applied to obtain the conversion).
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PLS I NEED HELP WITH THIS I WILL MARK YOU AS THE BRAINLIEST!!
Answer:
linearlinearquadraticexponentialStep-by-step explanation:
You want to classify the functions shown in the tables as linear, quadratic, or exponential.
DifferencesWe notice all of the tables have x-values that are evenly spaced. this means we can look at the differences between y-values to determine the kind of function the table represents.
The differences have the following interpretation:
differences are constant — lineardifferences have a constant difference — quadraticdifferences (and terms) have a constant ratio — exponential5, 3, 1, ...The differences of y-terms are constant at 3 -5 = -2.
The function is linear.
2, 5, 8, ...The differences of y-terms are constant at 5 -2 = 3.
The function is linear.
5, 1, 5, ...We observe that the y-values have a minimum. We don't need to take differences to know this is not linear or exponential. Of the offered choices, the only one that makes sense is "quadratic."
The differences of y-terms are ...
1 -5 = -4, 5 -1 = 4, 17 -5 = 12, 37 -17 = 20
The differences of differences are ...
4 -(-4) = 8, 12 -4 = 8, 20 -12 = 8
The second differences are constant.
The function is quadratic.
1, 3, 9, ...The first differences are ...
3 -1 = 2, 9 -3 = 6, 27 -9 = 18, 81 -27 = 54
The second differences are
6 -2 = 4, 18 -6 = 12, 54 -18 = 36
We note that the first and second differences are not constant, but the ratio of terms at every level is 3/1 = 6/2 = 12/4 = 3.
The function is exponential.
Write a form of 1 that you can use to rationalize the denominator of the expression.
A form of 1 that you can use to rationalize the denominator of the expression 8/(∛4), the rationalizing factor is 9.
Describe Rationalization?In mathematics, rationalization refers to the process of eliminating radical or irrational expressions from the denominator of a fraction. This is done by multiplying both the numerator and the denominator of the fraction by a suitable expression that will result in a rational denominator.
The resulting fraction has a rational denominator, which makes it easier to work with and manipulate algebraically. Rationalization is a useful technique in algebra, trigonometry, and calculus, and is often used to simplify expressions and solve equations.
To rationalize the denominator of the expression 8/(∛4), we need to multiply the numerator and the denominator by a rationalizing factor that will eliminate the radical in the denominator.
Since the root 4 is equal to 2, we can rewrite the expression as:
8/3²
The square of 3 is 9, so we can use 9 as the rationalizing factor.
Multiplying the numerator and denominator by 9, we get:
(8/3²) x (9/9) = 72/9
Simplifying, we get:
72/9 = 8
Therefore, the rationalizing factor is 9.
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diegos family spend 130$ total on a night ouy. they purchases 5 tickets to the fair and a family dinner for 55$ how much did each ticket to the fair cost
If Diego's family spent a total of $130, on a night out, then the each ticket for the fair cost's $15.
In order to find the "total-cost" of the tickets, we subtract the cost of the family dinner from the total amount spent;
⇒ Total cost of tickets = Total amount spent - Cost of family dinner,
⇒ Total cost of tickets = $130 - $55,
⇒ Total cost of tickets = $75.
Next, we divide the total cost of the tickets by the number of tickets purchased to find the cost of each ticket:
So, Cost per ticket = (Total cost of tickets)/(Number of tickets),
⇒ Cost per ticket = $75/5,
⇒ Cost per ticket = $15,
Therefore, each ticket to the fair cost $15.
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Which of the following explains why this inequality is true?
7 3/8 × 4/5 < 7 3/8
Answer:
Step-by-step explanation:
To compare these two values, we first need to convert the mixed number 7 3/8 to an improper fraction. To do so, we multiply the whole number (7) by the denominator of the fraction (8), then add the numerator (3), and put the result over the denominator:
7 3/8 = (7 x 8 + 3) / 8 = 59/8
Now we can rewrite the inequality as:
(59/8) × (4/5) < 59/8
To simplify the left-hand side of the inequality, we multiply the numerators and denominators:
(59/8) × (4/5) = (59 × 4) / (8 × 5) = 236/40 = 59/10
So the inequality becomes:
59/10 < 59/8
To compare these fractions, we need to find a common denominator. The least common multiple of 8 and 10 is 40, so we can convert both fractions to have a denominator of 40:
59/10 = (59 x 4) / (10 x 4) = 236/40
59/8 = (59 x 5) / (8 x 5) = 295/40
Now we can see that 236/40 < 295/40, which means that:
59/10 < 59/8
Therefore, the inequality 7 3/8 × 4/5 < 7 3/8 is true.
What is the end behavior of this radical function?
The end behavior of this radical function is "as x approaches positive infinity, f(x) approaches positive infinity".
As we know that the function f(x) = 4√(x − 6) is a radical function with an even index (4), which means that the function is defined for all non-negative values of x.
As x approaches positive infinity, the value of x − 6 also approaches positive infinity, and the square root function grows without bound.
Since the function is multiplied by a positive constant (4), the entire function f(x) also grows without bound as x approaches positive infinity.
Therefore, the end behavior of the function is that as x approaches positive infinity, f(x) approaches positive infinity.
Hence, option A correctly describes the end behavior of the function.
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Which ordered pair is a solution of y = x + 12?
A.( 24, 12)
B. (–12, –24)
C.( 9, 21)
D. (0, –12)
(9,21) is a solution of y=x+12
Step-by-step explanation:When is an ordered pair a solution?
To find if an ordered pair (x,y) is a solution to an equation, substitute the x-value and y-value from the ordered pair into the equation, evaluate both sides of the equation individually, and see if the equation is true.
If the two sides are equal, the ordered pair is a solution.If the two sides are not equal, the ordered pair is not a solution.Warning: A common mistake is to use the first coordinate (the x-coordinate, on the left of the ordered pair) as the value on the left side of the equation, and the second coordinate (the y-coordinate, on the right of the ordered pair), as the value for the right side of the equation. Make sure to substitute the x-value for the "x" in the equation, and the y-value for the "y" in the equation.
Going through the choices:
Point A (24,12)
y = x+12
(12) ?? (24) + 12
12 ≠ 36
not equal -- not a solution
Point B (-12,-24)
y = x+12
(-24) ?? (-12) + 12
-24 ≠ 0
not equal -- not a solution
Point C (9,21)
y = x+12
(21) ?? (9) + 12
21 = 21
equal -- (9,21) is a solution
Point D (0,-12)
y = x+12
(-12) ?? (0) + 12
-12 ≠ 12
not equal -- not a solution
Can sum help me with this
Answer:
36°
Step-by-step explanation:
x+27+27+90=180
x=36°
Need the answer ASAP
A function whose graph is the graph of y = √x, but is shifted to the left 9 units is [tex]y=\sqrt{x+9}[/tex].
What is a translation?In Mathematics and Geometry, the translation of a geometric figure or graph to the left means subtracting a digit from the value on the x-coordinate of the pre-image;
g(x) = f(x + N)
Conversely, the translation a geometric figure upward means adding a digit to the value on the positive y-coordinate (y-axis) of the pre-image; g(x) = f(x) + N.
Based on the information provided, the transformed function should be written as follows:
y = √x
g(x) = (√x + 9)
[tex]y=\sqrt{x+9}[/tex]
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Find f(g(1)) and g(f(1))
F(x)=x^2+2;g(x)=2x-5
Answer:
Step-by-step explanation:
Given the functions f(x) = x^2 + 2 and g(x) = 2x - 5, we can find f(g(1)) and g(f(1)) by evaluating the inner function first and then using its result as the input for the outer function.
First, let’s find f(g(1)). We start by evaluating the inner function g(1):
g(1) = 2 * 1 - 5 = -3
Now we can use this result as the input for the outer function f(-3):
f(g(1)) = f(-3) = (-3)^2 + 2 = 9 + 2 = 11
Next, let’s find g(f(1)). We start by evaluating the inner function f(1):
f(1) = 1^2 + 2 = 3
Now we can use this result as the input for the outer function g(3):
g(f(1)) = g(3) = 2 * 3 - 5 = 6 - 5 = 1
So, f(g(1)) = 11 and g(f(1)) = 1.
Please can someone assist me on this question I have no idea
Answer:
x2+10x+25
Step-by-step explanation:
It goes like this:
X2+2*1x*5+5*5
Which shows one way to determine the factors of x³ + 5x² - 6x - 30 by grouping?
Ox(x²-5) + 6(x² - 5)
Ox(x²+5)-6(x²+ 5)
O x²(x - 5) + 6(x - 5)
O x²(x+5)-6(x+ 5)
Answer:
x^2(x+5)-6(x+5)!!!!!!!!
Look at this pictograph:
Library books checked out
December
January
February
March
April
Each = 5 books
How many more books were checked out in March than in April?
books
There were no more books checked out in March than in April.
What is the pictograph about?The pictograph provided shows the number of books checked out from the library during the months of December, January, February, March, and April. Each picture represents 5 books.
The pictograph tells us that for each of these months, 5 books were checked out. So, in March, 5 books were checked out, and in April, 5 books were also checked out.
To find the difference between the number of books checked out in March and April, we subtract the number of books checked out in April from the number of books checked out in March:
5 books (March) - 5 books (April) = 0 books
Therefore, The result shows that there were no more books checked out in March than in April. Both months had the same number of books checked out, which is 5.
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which value of x is in the solution set of -4/3x+5<17
A. -8
B. -9
C. -12
D. -16
Please help!
Answer:
-9
Step-by-step explanation: Definitely correct
Angle 3 is 120°.
What is the
measure of 25?
m45 = [?]°
Answer in degrees.
[?]°
1/2
4/3= 120°
5/6
8 7
Enter
Answer:
angle 5 is 120 since there is Z shape with angle 3
write a situation that matches this inequality 8x+14<100
Suppose you are a small business owner who sells handmade crafts. You have a budget of $100 to purchase materials for your next batch of products. You know that each craft requires some amount of materials, which costs $8 per unit. Additionally, you will need to pay a fixed cost of $14 for other expenses related to production and shipping.
How the situation matches inequality 8x+14<100 ?To make a profit, you must ensure that the cost of materials and fixed expenses does not exceed the $100 budget. Therefore, you can write an inequality to represent this situation:
8x + 14 < 100
Here, x represents the number of units of materials needed for each craft. The inequality states that the total cost of materials (8x) plus fixed expenses ($14) must be less than $100.
To solve this inequality, you can subtract 14 from both sides:
8x < 86
Finally, you can divide both sides by 8:
x < 10.75
This means that for each craft, you can use no more than 10.75 units of materials in order to stay within budget and make a profit.
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Michael purchased stereo equipment for $2500. His wife claims that was not a smart investment because stereo equipment decreases in value at a rate of 9% per year. How much will his stereo equipment be be worth after 8 years?
Based on an exponential decay factor, Michael's stereo equipment will be worth $2,116 after 8 years, given the decreasing rate of 9% per year.
What is an exponential decay factor?The decay factor is represented by (1 - r), where r is the constant periodic decreasing rate.
The decay factor is used in exponential decay functions to determine the depreciated value of an asset.
Current price of stereo equipment = $2,500
Annual decreasing rate = 9%
Decrease factor = 0.91 (100% - 9%)
The number of years = 8 years
Value of the equipment after 8 years = ($2,500 x 0.91^8)
= $2,116.125 ($2,500 x 0.47025)
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Julian is using a biking app that compares his position to a simulated biker traveling Julian's target speed. When Julian is behind the simulated biker, he has a negative position.
Julian sets the simulated biker to a speed of
20
km
h
20
h
km
20, start fraction, start text, k, m, end text, divided by, start text, h, end text, end fraction. After he rides his bike for
15
1515 minutes, Julian's app reports a position of
−
2
1
4
km
−2
4
1
km minus, 2, start fraction, 1, divided by, 4, end fraction, start text, k, m, end text.
What has Julian's average speed been so far?
To solve the problem, we need to find Julian's average speed, given that he started biking from a position behind the simulated biker at a speed of 20 km/h, and after 15 minutes, his position was reported as -214 km.
We can use the formula for average speed:
Average speed = total distance / total time
To find the total distance, we need to calculate the displacement of Julian from the initial position of -d (where d is the distance between Julian and the simulated biker when he started biking) to the position of -214 km after 15 minutes.
Displacement = final position - initial position
Displacement = (-214 km) - (-d) = d - 214 km
The total distance covered by Julian is equal to the absolute value of the displacement, since the direction of the motion does not matter when computing distance.
Total distance = |d - 214 km|
To find the total time, we need to convert 15 minutes to hours:
Total time = 15 minutes / 60 minutes/hour = 0.25 hours
Now we can substitute the values into the formula for average speed:
Average speed = total distance / total time
Average speed = |d - 214 km| / 0.25 hours
Since Julian was traveling at a constant speed of 20 km/h, we can also express the distance in terms of time:
Average speed = (20 km/h) x t / 0.25 hours
where t is the time Julian biked in hours.
Setting the two expressions for average speed equal to each other, we can solve for t:
|d - 214 km| / 0.25 hours = (20 km/h) x t / 0.25 hours
|d - 214 km| = 20 km/h x t
Solving for t:
t = |d - 214 km| / 20 km/h
Now we can substitute this expression for t into either expression for average speed:
Average speed = (20 km/h) x t / 0.25 hours
Average speed = |d - 214 km| / 0.25 hours
Substituting the expression for t:
Average speed = |d - 214 km| x 4 / |d - 214 km|
Simplifying:
Average speed = 80 km/h
Therefore, Julian's average speed so far has been 80 km/h.
The table below shows primary school enrollment for a certain country. Here, x represents the number of years after 1820, and y represents the enrollment percentage. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places.
x y
0 0.1
5 0.1
10 0.1
15 0.2
20 0.2
25 0.3
30 0.4
35 0.5
40 0.6
45 1.1
50 1.5
55 3.0
60 4.5
65 5.5
70 6.1
75 6.8
80 7.0
85 8.0
90 9.3
95 10.7
100 12.4
105 14.1
110 16.6
115 17.5
120 19.7
125 19.4
130 32.7
135 40.9
140 47.6
145 57.8
150 57.0
155 61.7
160 63.2
165 75.0
170 76.5
175 96.0
180 92.0
185 100.0
190 100.0
The best-fit linear regression equation gives us the equation y = 0.0804x + 1.1794, where the slope is 0.0804 and the y-intercept is 1.1794.
The trendline equation will give us the equation for the linear regression line, which can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.
Once we have the trendline equation, we can use it to make predictions about future enrollment percentages based on the number of years after 1820.
The slope of the line tells us the rate at which the enrollment percentage is increasing or decreasing over time, and the y-intercept tells us the enrollment percentage when x is equal to zero (i.e., in 1820).
Here we have find that the best-fit linear regression equation gives us the equation
=> y = 0.0804x + 1.1794,
where the slope is 0.0804 and the y-intercept is 1.1794.
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Find the perimeter of each figure
The hexagon with sides of length 5 inches, 4 inches, 4 inches, 5 inches, 3 inches, and 3 inches has a perimeter of 24 inches.
What is a hexagon?A hexagon is a regular polygon, meaning all sides and angles are equal in size. It is a symmetrical shape, which means it can be divided into two equal halves.
To calculate the perimeter of this hexagon, we must first identify the length of each side.
All sides of the hexagon have a length of either 5 inches, 4 inches, or 3 inches, as there are two sides of each length.
The perimeter of the hexagon is the sum of the length of all its sides. Adding the length of all the sides, we get
5 + 4 + 4 + 5 + 3 + 3 = 24.
Thus, the perimeter of the hexagon is 24 inches.
Hence, the sum of the length of the sides of a hexagon is always greater than the length of any one of its sides.
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please help for this question
The dilation of the object is given by the coordinates:
(-6,-8)
(-2, 0)
(-2, -8)
A dilation is a function f from a metric space M into itself that fulfills the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real integer.
For the first dilation
Original points are
(2,1)
(4,5)
(4,1)
Multiply by scale factor
(2,1) x 2 = (4,2)
(4,5) x 2 = (8, 10)
(4,1) x 2 = (8, 2)
This given us the coordinates of triangle B).
For the second dilation
(2,1)
(4,5)
(4,1)
Adjust for the center of dilation which is (5,5)
(2,1) less (5,5) = (-3, -4)
(4,5) less (5,5) = (-1, 0)
(4,1) less (5,5) =(-1, -4)
Multiply the New original point by scale factor
(-3, -4) x 2 = (-6,-8)
(-1, 0) x 2 = (-2, 0)
(-1, -4) x 2 = (-2, -8)
Thus, the new coordinates of the dilated triangle C are:
(-6,-8)
(-2, 0)
(-2, -8).
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A glass jug can hold (p+6) quarts less water than a plastic container. 2 glass jugs and 2 plastic containers contain 6p quarts of water in all.
How much water can the plastic container hold? Give your answer im terms of p.
The amount of water that the plastic container can hold is -p + 3.
How to determine the amount of water that can be heldTo determine the amount of water that can be held, we will first assume that the container can hold x quantity of water.
So, the glass jug can hold:
p + 6 - x
2 glass jugs and 2 plastic containers can hold 6p quarts of water.
= 2(p + 6 - x) - 2x = 6p
2p + 12 - 2x -2x = 6p
2p + 12 -4x = 6p
12 - 4x = 6p - 2p
-4x = 6p -2p - 12
-4x = 4p -12
x = 4p - 12/-4
x = -p - 3
or -p + 3
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PLS HELP ASAP 90 POINTS Kim and her friends watched the server making smoothies. The table shows the number of mangos that were used for each of the different sizes of smoothies that the friends ordered.
Mangos Used Smoothie Size
Bri 1 7 oz
Kim 3 21 oz
Angela 4 28 oz
Which statement is correct based on the data?
The ratio of smoothie size to mangos used for Kim is 1:7, and the ratio of smoothie size to mangos used for Bri is 3:28.
The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.
The ratio of smoothie size to mangos used for Bri is 7:1, and the ratio of smoothie size to mangos used for Angela is 4:28.
The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela.
Answer:
The correct statement is "The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela".
The correct answer option is option A
How to solve ratio?
Mangos Used Smoothie Size
Angela 1 9 oz
Kim 3 27 oz
Bri 4 36 oz
Check the given options to determine which statement is correct;
The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela.
Kim = 27 : 3 = 9 : 1
Angela = 9 : 1
True
The ratio of smoothie size to mangos used for Kim is 1:9, and the ratio of smoothie size to mangos used for Bri is 4:27.
Kim = 27 : 3 = 9 : 1
Bri = 36 : 4 = 9 : 1
False
The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.
Angela = 9 : 1
Kim = 27 : 3 = 9 : 1
False
The ratio of smoothie size to mangos used for Bri is 9:1, and the ratio of smoothie size to mangos used for Angela is 4:36.
Bri = 36 : 4 = 9 : 1
Angela = 9 : 1
False
Therefore, Kim and Angela has equal ratio of smoothie size to mangoes used.
Graph the equation y = − x² + 8 x − 12 on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Using the graph, determine the roots of the equation − x² + 8 x − 12 = 0
A graph that represent the quadratic equation y = -x² + 8x - 12 is shown in the image attached below.
The roots of the equation are (2, 0) and (6, 0).
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).
Since the leading coefficient (value of a) in the given quadratic function y = -x² + 8x - 12 is negative 1, we can logically deduce that the parabola would open downward and the x-intercept (roots) is given by the ordered pair (2, 0) and (6, 0).
In conclusion, the turning point and vertex is given by the ordered pair (4, 4).
Read more on quadratic functions here: brainly.com/question/29499209
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Explain how you know what a fraction was multiplied by when the product is greater than a factor.
When the product of a fraction and a factor is greater than the factor, it means that the fraction is greater than 1.
Why is this true of fractions ?Due to the principles of multiplication, when multiplying a value greater than 1 with a given amount, the product will be larger than the original number. To provide an example, if we multiply 5 by 2, the result will be 10, which is greater than 5.
By extension, if we multiply a fraction with a factor that's greater than 1, the resulting product will be greater in size as compared to the initial quantity. For instance, when we calculate 1/2 multiplied by 3, the outcome is 3/2, which surpasses the worth of 1/2. Hence, it can be deduced that any result which exceeds its own source was obtained through multiplication by value greater than 1.
Find out more on fractions at https://brainly.com/question/30340082
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