The equation of the parabola in intercept form is y = -6(x+ 16 )(x + 2).
What is Parabola?A parabola is a type of curve that is formed when a point called the focus moves along a straight line called the directrix.
In other words a parabola is defined as the set of all points in a plane that are equidistant to the focus and the directrix.
The shape of a parabola is similar to a U or a V shape, and it can either be open upwards or downwards, depending on the orientation of the curve.
The Intercept form of a parabola is given by
y = a(x - p)(x - q)
Where p and q are the x - coordinates at which the parabola crosses the x-axis (i.e, the x-intercepts).
Here we have
The parabola in intercept form that passes through (-18,72) with x-intercepts of -16 and -2
Let y = a(x-p)(x-q) is the equation of parabola
From the data, x-intercepts p = - 16 and p = -2
=> y = a(x+ 16 )(x + 2) ---- (1)
Given that the parabola passes through (-18, 72)
=> 72 = a(- 18 + 16 )(-8 + 2)
=> 72 = a(-2)(-6)
=> 72 = - 12a
=> a = - 6
Substitute a = -6 in equation (1)
=> y = -6(x+ 16 )(x + 2)
Therefore,
The equation of the parabola in intercept form is y = -6(x+ 16 )(x + 2).
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Write an equation of the line passing through the point $\left(1,\ 9\right)$ that is parallel to the line $y=3x-2$ .
Equation of straight line parallel to y = 3x - 2 and passing through (1, 9) is
y = 3x + 6
What is straight line?A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity. A straight line is a figure formed when two points A (x1, y1) and B (x2, y2) are connected with the shortest distance between them, and the line ends are extended to infinity.
Given,
Line y = 3x - 2
Comparing with y = mx + c
slope = 3
Line parallel to y = 3x - 2 and passing through (1, 9)
Slope of the parallel line = slope of line y = 3x - 2
slope m = 3
Equation of the line,
y - y' = m(x - x')
y - 9 = 3(x - 1)
y - 9 = 3x - 3
y = 3x + 6
Hence y = 3x + 6 is equation of line parallel to y = 3x - 2 and passing through (1, 9)
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what’s the range of this function graph
a. [-2, infinite]
b. (-2, infinite)
c. [2, infinite)
d (- infinite, 2)
answer = c
its not a or b because the range starts at y = 2
The graph shows the relationship between the time Katrina spends jogging and her total distance traveled. Which function represents the relationship?
The function which represent the distance and time is y=6x-17.5.
What is function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Here according to the given data, let us take to points to find linear function then,
[tex](x_1,y_1)=(0.5,3)[/tex] and [tex](x_2,y_2)=(1,6)[/tex].
Now using slope formula, m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> Slope m = [tex]\frac{6-3}{1-0.5} = \frac{3}{0.5}[/tex] = 6
Now using equation formula , [tex]y-y_1=m(x-x_1)[/tex] then,
=> y-0.5=6(x-3)
=> y-0.5=6x-18
=> y=6x-18+0.5
=> y=6x-17.5
Hence the function which represent the distance and time is y=6x-17.5.
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If g(v)=11v^(4)+29v^(3)+19v^(2)+22v+39, use synthetic division to find g(-2). Submit
The answer is g(-2) = 15.
To find g(-2) using synthetic division, we need to follow these steps:
Write down the coefficients of the polynomial in descending order. The coefficients are 11, 29, 19, 22, and 39.
Write down the value of the divisor in the leftmost column. In this case, the divisor is -2.
Bring down the first coefficient (11) to the bottom row.
Multiply the bottom row value (11) by the divisor (-2) and write the result (-22) in the next column.
Add the coefficient in that column (29) to the result (-22) and write the sum (7) in the bottom row.
Repeat steps 4 and 5 until you reach the last column. The final result in the bottom row is the remainder.
The synthetic division should look like this:
-2 | 11 29 19 22 39
| -22 -14 -10 -24
-------------------
11 7 9 12 15
Therefore, g(-2) = 15.
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Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 3x^(2)+3x^(-3)-2
Yes, the algebraic expression [tex]3x^(2)+3x^(-3)-2[/tex] is a polynomial.
A polynomial is an algebraic expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication, as well as non-negative integer exponents. The given algebraic expression satisfies these conditions, so it is a polynomial.
To write the polynomial in standard form, we need to rearrange the terms in descending order of exponents. In this case, the term with the highest exponent is [tex]3x^(2)[/tex], followed by the term with the lowest exponent, [tex]3x^(-3)[/tex], and finally the constant term, -2.
Therefore, the polynomial in standard form is:[tex]3x^(2)+3x^(-3)-2 = 3x^(2)-2+3x^(-3)[/tex] So, the polynomial in standard form is [tex]3x^(2)-2+3x^(-3)[/tex].
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Can anyone help with the fractions ?
The tabs can be completed in the following way:
1. Fraction for 25% = 25/100 = 5/20 = 1/4
2. 90 percent: Decimal 0.90: Fraction: 90/100 =9/10
3. 60 percent: Decimal 0.60: Fraction: 60/100 = 6/10 = 3/5
4. 35 percent: Decimal 0.35: Fraction: 35/100 = 7/20
5. 33 percent: Decimal 0.33: Fraction: 33/100
6. 65 percent: Decimal 0.65: Fraction: 65/100 = 13/20
What is a percentage?A percentage is a value that is obtained as a fraction of the number 100. In the above question, we are given a list of values in percentages and told to convert them to decimal and fraction forms.
To do this, we need to divide the number 90 by 100 for the second expression and express this as a decimal. The resultant figure is 0.9. When converted to a fraction, the value now has a denominator and numerator.
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Given that,
x + 1: 3y = 1:7 and 2x : y + 3 = 2:5
Find x and y
The value of 'x' and 'y' in x + 1 : 3y = 1 : 7 and 2x : y + 3 = 2 : 5.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
We know, We can write a : b as, a/b.
Therefore, The given equations can be formed as,
(x + 1)/3y = 1/7 and 2x/(y + 3) = 2/5.
7x + 7 = 3y.
7x - 3y = - 7...(i)
And,
10x = 2y + 6.
10x - 2y = 6...(ii)
Now, Multiplying eqn(i) by 10 and (ii) by 7 we have,
70x - 30y = - 70...(iii) and 70x - 14y = 42...(iv)
Now, By Subtracting (iii) and (iv) we have,
- 16y = - 112
y = 7 and hence x = 2
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The functions f(x) and g(x) are inverses.
f(x) involves the following operations in the following order:
Divide by 2
Add 5
Which operations must be part of g(x)?
The functions involved in g(x) are multiply by 2 and subtract the value of 5.
What is inverse function?A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. The graph of the inverse of a function shows the function and the inverse of the function, which are both plotted on the line y = x. This graph's line traverses the origin and has a slope value of 1.
Given that, f(x) involves the following functions:
Divide by 2
Add 5
Also, g(x) is the inverse of the function of f(x) hence, the function involved are inverse of the original function.
Hence, the functions involved in g(x) are multiply by 2 and subtract the value of 5.
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List the decimal numbers 4.76, 4.9, 4.08, and 4.7 in order from least to greatest.
4.9, 4.7, 4.08, 4.76
4.7, 4.76, 4.9, 4.08
4.08, 4.7, 4.76, 4.9
4.08, 4.76, 4.9, 4.7
The order of the decimal number from least to greatest is
4.08< 4.7<4.76<4.9.
What is decimal number?Decimals are a form of number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal number is, for instance, 34.5.
Here the given decimal numbers are,
=> 4.76, 4.9, 4.08,4.7
Now ordering the number from smallest to largest
=>4.08< 4.7<4.76<4.9.
Hence the order of the decimal number from least to greatest is 4.08< 4.7<4.76<4.9.
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Find the missing variable and indicated
angle measure.
X =
G
50°
K
H
28°
(15x-3)°
m2KHL =
J
O
The value of x is 7
What is angle on a straight line?The total sum of angles on a straight line is 180°. This means by adding all angles on a line ,it must give 180°.For example , if four angles, A, B , C ,D are align on a straight line, the sum of these angles, A+B+C +D = 180°
Therefore ;
50+28+15x-3 = 180
78-3 +15x = 180
75 +15x = 180
collect like terms
15x = 180-75
15x = 105
divide both sides by 15
x = 105/15
x = 7
therefore the value of the missing variable (x) is 7
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If angle HIJ is congruent to angle JTS, then is
In the given triangle, using congruency, ∠JHI is congruent to ∠SJT.
What is Triangle ?
Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
In the given figure, we can see that there are two pairs of vertically opposite angles, which are opposite to each other at the intersection of two straight lines. These angles are:
What is the equation for triangle congruence?According to the ASA Rule, triangles are congruent to one another if any two angles and the side between them are comparable to the corresponding angles and side. According to the AAS Rule, the triangle's angles and excluded side are equal in the same way.
In the given triangle, using congruency, ∠JHI is congruent to ∠SJT
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Are these two matrices equal? Justify your answer. [[3,-1,7],[2,6,-9],[-5,4,-2]]*[[-2,-9,7],[4,6,-1],[-5,2,3]]
No, these two matrices are not equal.
The first matrix is a 3x3 matrix with the elements [[3,-1,7],[2,6,-9],[-5,4,-2]] and the second matrix is also a 3x3 matrix with the elements [[-2,-9,7],[4,6,-1],[-5,2,3]]. In order for two matrices to be equal, they must have the same dimensions and the corresponding elements must be equal. In this case, the dimensions are the same, but the corresponding elements are not equal. For example, the first element in the first matrix is 3, but the first element in the second matrix is -2. Therefore, these two matrices are not equal.
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Morganville and Newton are 36 miles apart. On a map, the two cities are 6 inches apart. What is the map scale?
The scale of the map is 1 inch for 6 miles
How to determine the scale of the mapFrom the question, we have the following parameters that can be used in our computation:
Distance apart = 36 miles
Distance on the map = 6 inches
Using the above as a guide, we have the following:
Scale = Distance on the map/Distance apart
Substitute the known values in the above equation, so, we have the following representation
Scale = 6 inches/36 miles
Evaluate
Scale = 1 inch/6 miles
Hence, the scale is 1 inch per 6 miles
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Select each equation that has no real solution
The equation that has no real solution is 12x + 12 = 3(4x + 5), the correct option is (d).
To determine whether an equation has real solutions, we need to solve it and check whether the solutions are real numbers or not.
-5x - 25 - 5x + 25 = 0 simplifies to -10x = 0, which has the solution x = 0. This is a real number solution.
7x + 21 = 21 simplifies to 7x = 0, which has the solution x = 0. This is a real number solution.
12x + 15 = 12x - 15 simplifies to 15 = -15, which is false. This equation has no solution, but it doesn't have any variables left to solve for, so it's not an option for our answer.
12x + 12 = 3(4x + 5) simplifies to 12x + 12 = 12x + 15, which simplifies further to 12 = 15. This is false, which means the equation has no solutions. Therefore, this is the equation that has no real solution, the correct option is (d).
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The complete question is:
Select each equation that has no real solution
a. -5x- 25 - 5x + 25
b. 7x + 21 = 21
c. 12x + 15 = 12x - 15
d. 12x + 12 = 3(4x + 5)
A young group and their leaders visited mammoth cave. two adults and five students in one been paid $77 for the hand avenue tour of the cave. Two adults and seven segments
students in the second van pair $95 for the same tour. Find the adults price and the student pieces
price of the tour.
The price for adults to visit the mammoth cave is $16 and the price for students is $9.
What is the adult and students price?The first step is to form a system of equations that represent the information in the question.
2a + 5s = 77 equation 1
2a + 7s = 95 equation 2
Where:
a = price of one adult
s = price of one student
The elimination method would be used to solve the equations.
Subtract equation 1 from equation 2:
2s = 18
Divide both sides of the equation by 2
s = 18/2
s = $9
Substitute for s in equation 1:
2a + 5(9) = 77
2a + 45 = 77
2a = 77 - 45
2a = 32
a = 32 / 2
a = 16
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(x+4)^2=15
solving by talking the square root
Answer:
x = -4 + √15 and x = -4 - √15.
Step-by-step explanation:
To solve for x in the equation (x + 4)^2 = 15 using square roots, we can take the square root of both sides of the equation, remembering to include both the positive and negative square root:
(x + 4)^2 = 15
Taking the square root of both sides:
±(x + 4) = √15
Now we can isolate x by subtracting 4 from both sides of the equation:
x + 4 = ±√15
x = -4 ±√15
Therefore, the solutions to the equation (x + 4)^2 = 15 are x = -4 + √15 and x = -4 - √15.
If the prices of new cars increase an average of 4 times in one year, find the probability of:
(a) No price hikes in a randomly selected in one year and half. (3 marks)
(b) Four price hikes in 2 years. (2 marks)
(c) At most of one price hikes in one year.
The probability of at most one price hike in one year is 0 + 0 = 0.
No price hikes in a randomly selected one and a half year:
The probability of no price hikes in one year is 0, since the average is 4. Therefore, the probability of no price hikes in one and a half years is also 0.
Four price hikes in 2 years:
The average number of price hikes in one year is 4, so the average number of price hikes in 2 years is 8. The probability of exactly 4 price hikes in 2 years is therefore 0, since it is less than the average.
At most one price hike in one year:
The probability of at most one price hike in one year is the sum of the probabilities of 0 and 1 price hikes. The probability of 0 price hikes is 0, as mentioned before. The probability of 1 price hike is also 0, since it is less than the average of 4. Therefore, the probability of at most one price hike in one year is 0 + 0 = 0.
Overall, the probability of no price hikes in a randomly selected one and a half year, four price hikes in 2 years, and at most one price hike in one year are all 0, since they are all less than the average number of price hikes.
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Rewrite the product using a sum or difference of two functions.
2 sin (2???? /3 )sin (5????/ 6)
Two functions as cos (5x/6 - 4x/9) - cos (5x/6 + 4x/9)
We can rewrite the product using a sum or difference of two functions as follows:2 sin (2x/3) sin (5x/6)In order to rewrite the product using a sum or difference of two functions, we can use the following formula:2 sin A sin B = cos (A - B) - cos (A + B)Where A and B are two angles or expressions that contain an angle.So, 2 sin (2x/3) sin (5x/6) can be written as follows:2 sin (2x/3) sin (5x/6) = cos [(5x/6) - (2x/3)] - cos [(5x/6) + (2x/3)]On simplifying the above expression, we get2 sin (2x/3) sin (5x/6) = cos [(5x/6 - 4x/9)] - cos [(5x/6 + 4x/9)]= cos (5x/6 - 4x/9) - cos (5x/6 + 4x/9)Therefore, 2 sin (2x/3) sin (5x/6) can be rewritten using a sum or difference of two functions as cos (5x/6 - 4x/9) - cos (5x/6 + 4x/9).
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Which values in the data set are outliers? Show all work.
72, 81, 82, 83, 83, 85, 100, 54, 75, 81, 83
List the following (and show work if needed): Q1, Median, Q3, Lower Fence, Upper Fence, and Outliers
The median, Q₁, Q₃, lower fence and upper fence of the given data set are 82, 75, 83, 63 and 95.
What is Inter quartile range?
In a range of values, from lowest to highest, the IQR denotes the median 50% of values. Find the median (middle value) of the lower and higher half of the data first, then use that number to calculate the interquartile range (IQR). The first quartile (Q1) and third quartile (Q3) of these values (Q3). What separates Q3 from Q1 is known as the IQR.
Given data set : 72, 81, 82, 83, 83, 85, 100, 54, 75, 81, 83
Firstly, we will arrange the data into ascending order.
we get, 54, 72, 75, 81, 81, 82, 83, 83, 83, 85, 100.
Here, no. of terms is 11
So, Median = (n+1)/2 th = (11+1)/2 = 6th term
So, Median = 82.
Q₁ = (n+1)/4 th term = (11+1)4 th = 3rd term
= 75
Q₃ = 3(n+1)/4 th term = 9th term = 83
Inter-quartile range = Q₃ - Q₁
= 83 - 75 = 8.
Now, Lower fence = Q₁ - 1.5*IQR
= 75 - 1.5× 8
= 75 - 12 = 63
Upper fence = Q₃ + 1.5*IQR
= 83 + 1.5×8
= 83 + 12
= 95.
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Work out the area of trapezium L.
If your answer is a decimal, give it to 1 d.p.
Step-by-step explanation:
Refer to pic............
Please can someone help me
Answer:
Matt is a lawyer who used to charge his clients $330 per hour. Matt recently reconsidered his rates and ultimately decided to charge $231 per hour. What was the percent of decrease in the billing rate?
Step-by-step explanation:
c is the ansswer
Please explain this more in depth. How does the chain rule allow
the first equation to reduce to the second equation? Some simple
explanation of the chain rule would also be helpful.
The chain rule allows us to reduce the first equation to the second equation by finding the derivative of the composite function and substituting it for the original function. This provides a simpler and more concise explanation of the relationship between the two equations.
The chain rule is a formula for calculating the derivative of a composite function. It states that the derivative of a composite function f(g(x)) is equal to the derivative of f with respect to g times the derivative of g with respect to x. In mathematical notation, this is expressed as (f(g(x)))' = f'(g(x)) * g'(x).
In the case of the first equation, we can use the chain rule to reduce it to the second equation by applying the formula mentioned above. First, we need to identify the composite function and its components. In this case, the composite function is f(g(x)) and the components are f and g.
Next, we need to find the derivative of f with respect to g and the derivative of g with respect to x. Once we have these derivatives, we can multiply them together to get the derivative of the composite function.
Finally, we can reduce the first equation to the second equation by substituting the derivative of the composite function for the original composite function. This will give us the second equation, which is a simplified version of the first equation.
In conclusion, the chain rule allows us to reduce the first equation to the second equation by finding the derivative of the composite function and substituting it for the original function. This provides a simpler and more concise explanation of the relationship between the two equations.
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Please help ⚠️⚠️ will give thanks, 5 stars and brainliest if possible.
Answer: ∠ABC = 29.745°
Step-by-step explanation:
I believe this is the answer , you should be golden.
Answer:
no se y ademas me aparece en ingles :(
Step-by-step explanation:
Han bought a chest of drawers for $210 and sold it 4 years later for $139. Calculate his loss as a percentage of the original price correct to 2 decimal places.
Therefore, Han's loss amounts to 33.81% of the original cost because he spent $210 on a chest of drawers before selling it for $139 four years later.
what is percentage ?A figure can be expressed as a fraction of 100 using a percentage. It is frequently utilised to compare two values or to convey a portion of a whole. "%," which stands for "per hundred," is the symbol used to indicate percentages. 50%, for instance, is 50/100, or 50 out of 100. Calculating percentages involves dividing a portion by a whole and multiplying the result by 100. For instance, if a bag contains 75 blue spheres and 25 red balls, the proportion of red balls is as follows:
(Number of red balls / Total Number of Balls) times 100% equals the percentage of red balls.
Red ball percentage equals (25/100) times 100%
25% of the balls are crimson.
given
You can compute the cost as follows:
Loss is calculated as Initial Price - Selling Price ($210 - $139).
Loss = $71
We must divide the loss by the initial price and multiply by 100 to determine the percentage loss:
(Loss / Original price) times 100 equals the percentage of loss.
($71 / $210) times 100 equals the percentage loss.
Loss as a percentage: 33.81%
Therefore, Han's loss amounts to 33.81% of the original cost because he spent $210 on a chest of drawers before selling it for $139 four years later.
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Calculate the simple interest earned on an investment of $6740 at 5% per year for 3 years. Give the answer to the nearest cent.
intrest=$
Answer:
1011.00
Step-by-step explanation:
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A store is having a holiday sale and offers no down payment on each credit items. A sound system will cost $29.99 per week for a year. What is the total price?
Answer:$20.40
Step-by-step explanation:
20% off means that the new price of the skirt will be 80% of the original price:
$30(100% – 20%) = $30(80%)
Converting the percent to a decimal gives:
$30(0.8) = $24.00
There is an additional 15% off the sale price of $24.00, so the final price is 85% of the sale price:
$24(100% – 15%) = $24(85%)
Again converting the percent to a decimal gives:
$24(0.85) = $20.40
5. CREATE A GRAPH AND WRITE AN
EQUATION to represent the list of
ordered pairs listed below. y = mx
+ b
(2, -3) (1, -1) (-1, 3) (3, -5)
To create a graph and write an equation to represent the list of ordered pairs given, we need to plot each point on a coordinate system.
x | y
--|--
2 |-3
1 |-1
-1| 3
3 |-5
Plotting these points on a coordinate plane, we get:
![Graph of ordered pairs]
To write an equation to represent these ordered pairs in the form y = mx + b, we need to find the slope of the line and the y-intercept.
To find the slope:
m = (y2 - y1) / (x2 - x1)
Let's use the points (1, -1) and (3, -5) to find the slope:
m = (-5 - (-1)) / (3 - 1)
m = -4 / 2
m = -2
Now that we know the slope, we can use any point and the slope to find the y-intercept (b).
Using the point (1, -1):
y = mx + b
-1 = (-2)(1) + b
b = 1
So the equation that represents these ordered pairs in the form y = mx + b is:
y = -2x + 1
And the graph of this equation looks like:
![Graph of equation y = -2x + 1]
10
#6
Three vertices of parallelogram MNPQ are M(2,2). N(4,0), and P(1,-1). Plot points M, N, P, and Q in the coordinate plane below.
The points M, N, P, and Q have been plotted in the coordinate plane below.
How to determine the midpoint of a line segment?In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Substituting the given parameters into the midpoint of a line segment formula, the midpoint of the diagonal is given by;
Midpoint MP = [(2 + 1)/2, (-1 + 2)/2]
Midpoint MP = [3/2, 1/2]
Midpoint MP = (1.5, 0.5).
For the fourth vertex Q, we have:
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
(1.5, 0.5) = [(4 + x₂)/2, (0 + y₂)/2]
4 + x₂ = 2(1.5)
x₂ = -4 + 3
x₂ = -1.
0 + y₂ = 2(0.5)
y₂ = 1.
Therefore, vertex Q = (-1, 1).
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1 divided 2/6 and i want to know the answer ASAP
1 divided by 2/6 is equal to 3.
Division is a mathematical operation used to divide one number (the dividend) by another number (the divisor) to find out how many times the divisor is contained within the dividend
To divide 1 by 2/6, we need to find out how many times the denominator (2/6) fits into the numerator (1).
One way to approach this is to convert the fraction 2/6 to an equivalent fraction with a denominator of 1. To do this, we can multiply both the numerator and denominator of 2/6 by the same number, in this case 3:
2/6 = (23)/(63) = 6/18
Now, we can divide 1 by 6/18:
1 ÷ 6/18
= 1 x 18/6 (reciprocal of 6/18 is 18/6, which is equivalent to 3)
= 3
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Phil spent $21 of his $115 pocket money on eating out for one meal. What percent of Phil's pocket money did he spend on eating out for one meal? Round your answer to the nearest hundredth.
Phil spent 18.26% of his pocket money on eating out for one meal.
How do you calculate the percentage difference between two values?The following is the formula for calculating the percentage difference between two values:
100% of ((new value - old value) old value)
In order to describe the change as a percentage, this formula calculates the difference between the new and old values, divides that difference by the old value, and multiplies the result by 100.
Given that, Phil spent $21 of his $115 pocket money.
Thus,
$21 ÷ $115 × 100% = 18.26%
Hence, Phil spent 18.26% of his pocket money on eating out for one meal.
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