Answer:
31 - 61a
Step-by-step explanation:
We distribute, being especially careful with the negative signs:
1 + 2a - 3(4 + 5a) + 6(7 - 8a)
1 + 2a - 3 * 4 - 3 * 5a + 6 * 7 - 6 * 8a
1 + 2a - 12 - 15a + 42 - 48a
31 - 61a
The required simplified expression of the given expression is 31 - 61a.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
As mentioned in the quesiton, to simplify the expression 1 + 2a - 3(4+5a) + 6(7-8a),
⇒ 1 + 2a - 3(4+5a) + 6(7-8a),
⇒ 1 + 2a - 12 - 15a + 42 - 48a
Adding alike terms,
⇒ 31 - 61a
Thus, the required simplified expression of the given expression is 31 - 61a.
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An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. they report the angles of elevation as 14° and how high is the airplane? round to the nearest hundredth of a mile.
The total cost (c) in dollars of renting a sailboat for n days is given by the inequality c≥120+60n. what is the maximum number of days for which a sailboat could be rented if the total cost was $360?
Answer:
4 days
Step-by-step explanation:
The equation of a parabola is 1/32 (y−2)2=x−1 .
What are the coordinates of the focus?
(1, 10)
(1, −6)
(−7, 2)
(9, 2)
The given equation of parabola is
[tex] \frac{1}{32} (y-2)^2 = x-1 [/tex]
Which can also be written as
[tex] x = \frac{1}{32} (y-2)^2 +1 [/tex]
Here vertex (h,k) is (1,2)
And value of a is
[tex] a = \frac{1}{32} [/tex]
Formula of focus is
[tex] (h+ \frac{1}{4a} , k) [/tex]
Substituting the values of h,k and a, we will get
[tex] (1+ \frac{1}{4*(1/32) } , 2} = (1+ 8,2) = (9,2) [/tex]
Therefore the correct option is the last option .
Answer: The correct option is (D) (9, 2).
Step-by-step explanation: We are given to find the co-ordinates of the focus for the following parabola:
[tex]\dfrac{1}{32}(y-2)^2=x-1~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that the standard form equation of a parabola is
[tex](y-k)^2=4p(x-h),[/tex]
where the co-ordinates of the focus are (h+p, k).
From equation (i), we have
[tex]\dfrac{1}{32}(y-2)^2=x-1\\\\\\\Rightarrow (y-2)^2=32(x-1)\\\\\Rightarrow (y-2)^2=4\times 8(x-1).[/tex]
Comparing the above equation with the standard form equation of the parabola, we get
h = 1, k = 2, and p = 8.
Therefore, the co-ordinates of the focus are
[tex](h+p,k)=(1+8,2)=(9,2).[/tex]
Thus, option (D) is CORRECT.
What is the value of the rational expression 2x+1/x2 when x = 5?
The solution is A = 11/25
The value of the equation A = ( 2x + 1 ) / x² is 11/25
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = ( 2x + 1 ) / x²
when x = 5 , substitute the value of x as 5 in the equation , we get
A = ( 2 ( 5 ) + 1 ) / 5²
The value of A = ( 10 + 1 ) / 25
The value of A = 11/25
Therefore , the value of A = 11/25
Hence , The value of the equation A = ( 2x + 1 ) / x² is 11/25
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Graphic lesions to solve the system Y equals 1/3 X +6 and why equals 1/3 X +4
Which of the following sequences of numbers are arithmetic sequences? Check all that apply.
A.99, 100, 101, 102, 103, ...
B.-3, -5, -7, -9, -11, ...
C.2, -2, 2, -2, 2, ...
D.1, 6, 11, 16, 21, ...
E.-4, 7, -10, 13, -16, ...
Please help me idk this
In sakura’s garden, for every 5 red flowers, there are 10 yellow flowers. There are a total of 75 yellow and red flowers in her garden. How many ref flowers are in Sakura’s garden?
Which line of symmetry for the parabola (x-1)^2= 4(y-1)^?
The line of symmetry for the parabola is x = 1.
The line of symmetry for the parabola is x = 1. In the given equation (x-1)^2 = 4(y-1)^2, the x-coordinate of the vertex is 1, which means the line of symmetry is a vertical line passing through x = 1.
Difference between ellipse circle parabola and hyperbola equations
The solution is: these have a subtraction operation, the exact opposite ellipse.
What is parabola?The parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. It fits several superficial different mathematical descriptions.
here, we have,
The equation of a circle is:
(x - h)² + (y - k)² = r²
The equation of a parabola is:
(x - h)² = 4p(y - k)
The equation of an ellipse is:
(x - h)²/ a² + (y - k)²/ b² = 1
where variables a and b and the two different measurements of the vertices
The equation of a hyperbola is:
(x - h)²/ a² - (y - k)²/ b² = 1 if it is with a horizontal transverse axis
(y - k)²/ b² - (x - h)²/ a² = 1 if it is with a vertical transverse axis
Notice these have a subtraction operation, the exact opposite ellipse.
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Nikolai has a jar filled with 120 marbles. he has 72 red marbles, 17 blue marbles, 13 green marbles, and 18 purple marbles. what is the probability that he will randomly select a blue marble, without replacement, and then a purple marble from the jar
The probability of selecting a blue marble followed by a purple marble from a jar containing 120 marbles with different colors is approximately 2.2%.
The probability of grabbing a blue marble and then a purple marble is determined by multiplying the probability of grabbing a blue marble first and the probability of grabbing a purple marble second. Here's the calculation:
Probability of selecting a blue marble first: 17/120
Probability of selecting a purple marble second (after one blue marble is already taken out): 18/119
Multiplying the probabilities: (17/120) * (18/119) ≈ 0.022, or 2.2%
The quarters, buckled, and dimes totaled 20 and their value was $2.05. How many kind were there if there were 3 times as many dimes as quarters
An isoceles triangle has congruent side of 20 cm. The base is 10 cm. Find the height of the triangle
Farmer toby's chickens and pigs have a total of 30 heads and 84 legs. a chicken has 2 legs, a pig has 4 legs, and each animal has 1 head. how many of each type of animal does toby have
Another geometry question! Please help!
The area of a parallelogram is 3.36 square feet. the base is 2.8 feet. if the measures of the base and height are each doubled, find the area of the resulting parallelogram
the mean mark for the class was 70%. There are 30 students in the class, 20 of whom are boys. The mean mark for the boys is 62%. What is the mean mark for the girls?
The slope of a line in a blueprint must be . A line is drawn that contains the points 5/6 < | m | <7/4. Determine if the line meets the required specifications.
A.No, the rooftop does not meet the specifications, because the absolute value of the roof’s slope is greater than the parameters.
B.No, the rooftop does not meet the specifications, because the absolute value of the roof’s slope is less than the parameters.
C.Yes, the rooftop does meet the specifications, because the absolute value of the roof’s slope is within the parameters.
D.Yes, the rooftop does meet the specifications, because the absolute value of the roof’s slope is less than the parameters.
The function h=−16t2+26t models the height h (in feet) of the dolphin after t seconds. after how many seconds is the dolphin at a height of 5 feet? round your answers to the nearest tenth.
Answer:
The dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.
Step-by-step explanation:
Given : The function [tex]h=-16t^2+26t[/tex]models the height h (in feet) of the dolphin after t seconds.
To Find: After how many seconds is the dolphin at a height of 5 feet?
Solution:
Function: [tex]h=-16t^2+26t[/tex]
h is the height
t is the time
Now we are supposed to find After how many seconds is the dolphin at a height of 5 feet
Substitute h = 5
So, [tex]5=-16t^2+26t[/tex]
[tex]16t^2-26t+5=0[/tex]
[tex]16t^2-26t+5=0[/tex] ---1
Using quadratic formula : [tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
General quadratic equation: [tex]ax^2+bx+c=0[/tex] ---A
On Comparing equation 1 with A
a = 16
b = -26
c=5
Substitute the values in the quadratic formula.
[tex]x = \frac{-(-26)\pm\sqrt{(-26)^2-4(16)(5)}}{2(16)}[/tex]
[tex]x = \frac{26\pm 18.86796}{32}[/tex]
[tex]x = \frac{26+18.86796}{32},\frac{26-18.86796}{32}[/tex]
[tex]x = 1.4021,0.2228[/tex]
Thus the dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.
The dolphin is at a height of 5 feet at 0.2 second and 1.4 seconds.
Polynomial
Polynomial is an expression that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Let h represent the height of dolphin at t seconds.
Given the function:
h = −16t² + 26tFor a height of 5 ft.:
5 = −16t² + 26t
16t² - 26t + 5 = 0
t = 0.2 or t = 1.4
The dolphin is at a height of 5 feet at 0.2 second and 1.4 seconds.
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.48 divided by 9.23 rounded by nearest tenth
Evaluate at the given value
4x^2+6x-5 when x=-3
Someone please help me?
Amy owns a graphic design store. She purchases a new printer to use in her store.
The printer depreciates by a fixed rate of 14% per year. The function
V = 2,400(1 – 0.14)t can be used to model the value of the printer in dollars after
t years.
Question:
Part A: Explain what the parameter 2,400 represents in the equation of the function.
Part B: What is the factor by which the printer depreciates each year?
Part C: Amy also considered purchasing a printer that costs $4,000 and depreciates by 25% each year. Which printer will have more value in 5 years? Justify your answer by showing/explaining your work.
i really need help :( im working hard to get all my school work done and this one thing is making my head hurt :(
The parameter 2,400 in the depreciation function represents the initial value of Amy's printer. The printer depreciates by a factor of 0.86 each year. After calculations, the first printer has more value ($1,004.40) after 5 years compared to the second printer ($949.24).
Part A: The parameter 2,400 represents the initial purchase price or the original value of the printer that Amy owns in her graphic design store.
Part B: The factor by which the printer depreciates each year is 0.86 (which is calculated as 1 - 0.14, meaning the value retains 86% of its worth each subsequent year).
Part C: To compare which printer will have more value in 5 years, we need to calculate the future value of both printers using their respective depreciation rates:
First printer: V = 2,400(1 - 0.14)^5Second printer: V = 4,000(1 - 0.25)^5After calculating:
Value of the first printer after 5 years: V \\approx 2,400(0.86)^5 \\approx 2,400(0.4185) \\approx $1,004.40Value of the second printer after 5 years: V \\approx 4,000(0.75)^5 \\approx 4,000(0.2373) \\approx $949.24Therefore, the first printer will have more value after 5 years.
A tractor was purchased for $30,000 six years ago. what is the value of the tractor today if the depreciation rate was 2.5%?
plz help me!!!!
A cross country coach records the number of miles his athletes on the Junior Varsity and Varsity teams ran today and displays the data in the provided dot plots. Given the shape of each distribution, determine which measures of center and spread are appropriate for him to use to summarize the data from each team.
Answer:
Step-by-step explanation:
solve the equation 2 cos x + 1 = 0 , 0 <= x <= 2pi PLEASE HELP! WILL AWARD!
The solution of the given trigonometric expression is x = 2π/3.
Use the concept of trigonometric ratio defined as:
Trigonometric ratios depend on the value of the ratio of sides of a triangle which is right-angled and contains the values of all trigonometric functions.
The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as it's trigonometric ratios.
The given expression is:
2 cos x + 1 = 0
Where,
0 ≤ x ≤ 2π
To solve it,
Subtract both sides,
2 cos x = - 1
Divide by 2 on both sides,
cos x = -1/2
Take cos inverse on both sides,
[tex]x = cos^{-1} (\frac{1}{2})[/tex]
Since cos(2π/3) = -1
x = 2π/3
Now since 2π/3 lies between 0 ≤ x ≤ 2π
Hence,
The solution of the given expression is x = 2π/3
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Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 - 6x + 5 y = x2 + 7x - 11 y = -x2 - 8x - 16
pppppppllllllleeeeaaaassssseeeee ANSWER FASRT
According to the discriminant:
[tex]y = -3x^2 + x + 12[/tex] has two real solutions.[tex]y = 2x^2 - 6x + 5[/tex] has zero real solutions.[tex]y = x^2 + 7x - 11[/tex] has two real solutions.[tex]y = -x^2 - 8x - 16[/tex] has one real solution.The number of real solutions of quadratic equation [tex]y = ax^2 + bx + c[/tex] depends on the discriminant [tex]\Delta = b^2 - 4ac[/tex].
If [tex]\Delta > 0[/tex], the equation has two real solutions.If [tex]\Delta = 0[/tex], the equation has one real solution.If [tex]\Delta < 0[/tex], the equation has zero real solutions.Equation [tex]y = -3x^2 + x + 12[/tex]
The coefficients are: [tex]a = -3, b = 1, c = 12[/tex]The discriminant is: [tex]\Delta = 1^2 - 4(-3)(12) = 145[/tex].Positive, thus two real solutions.Equation [tex]y = 2x^2 - 6x + 5[/tex]
The coefficients are: [tex]a = -2, b = -6, c = 5[/tex]The discriminant is: [tex]\Delta = (-6)^2 - 4(2)(5) = -4[/tex].Positive, thus zero real solutions.Equation [tex]y = x^2 + 7x - 11[/tex]
The coefficients are: [tex]a = 1, b = 7, c = -11[/tex]The discriminant is: [tex]\Delta = (7)^2 - 4(1)(-11) = 93[/tex].Positive, thus two real solutions.Equation [tex]y = -x^2 - 8x - 16[/tex]
The coefficients are: [tex]a = -1, b = -8, c = -16[/tex]The discriminant is: [tex]\Delta = (-8)^2 - 4(-1)(-16) = 0[/tex].Positive, thus one real solutions.A similar problem is given at https://brainly.com/question/19776811
Solve for c in the equation 3x^2-18x+5=47
I think its B
A researcher finds a negative correlation between the total number of people driving for pleasure and the sales of electric cars.
Which variable is most likely the lurking variable that explains the correlation?
population
gas prices
amount of rainfall
water prices
The correct answer is:
gas prices
Explanation:
As the number of people driving for pleasure goes down, the sales of electric cars go up. This is likely due to gas prices. As gas prices go up, fewer people drive for pleasure and more people purchase electric cars. Both are ways to reduce the amount of money spent on gasoline.
The option 'gas prices' variable is most likely the lurking variable that explains the correlation.
Given that a researcher finds a negative correlation between the total number of people driving for pleasure and the sales of electric cars.
It is required to find which variable is most likely the lurking variable that explains the correlation.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
We have a negative correlation between:
The total number of people driving for pleasure and the sales of electric cars.
We know that the negative correlation means one variable decreases and as the other increases and vice versa.
If the sales of electric cars increase the total number of people driving for pleasure goes down.
This can happen if the gas prices go up fewer people drive for pleasure and more people buy an electric car.
Thus, the option 'gas prices' is correct.
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The dollar amount (d) that erin earns varies directly as the number of hours (t) that she works. if she earns $206.25 in 25 hours, how many hours did she work if she earned $264?