Answer:
[tex]x=\frac{3\left(1+\sqrt{3}\right)}{2},\:x=\frac{3\left(1-\sqrt{3}\right)}{2}[/tex]
Step-by-step explanation:
[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:2\left(-9\right)}}{2\cdot \:2} < - InsertQuadraticFormula[/tex]
[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \:6\sqrt{3}}{2\cdot \:2}[/tex]
[tex]x_1=\frac{-\left(-6\right)+6\sqrt{3}}{2\cdot \:2},\:x_2=\frac{-\left(-6\right)-6\sqrt{3}}{2\cdot \:2} < - Separate THE Solutions[/tex]
[tex]x=\frac{3\left(1+\sqrt{3}\right)}{2},\:x=\frac{3\left(1-\sqrt{3}\right)}{2}[/tex]
A television sells for $550. Instead of paying the total amount at the time of the purchase, the same television can be
bought by paying $200 down and $50 a month for 14 months. How much is saved by paying the total amount at the
time of the purchase?
Convert the angle to Degrees, Minutes, and Seconds. 56.38°
Answer:
56 degrees
22 minutes
48 seconds
I need help with 4B please. Thank you!
The equation to the tangent line to [tex]y = e^{(x^2)}[/tex] at point (1,0) is given by:
y = 2e(x - 1).
What is the equation to the tangent line of a function of a point?Supposing that we have a function f(x) at a point [tex](x_0, y_0)[/tex], the equation of the tangent line to this function is given by:
[tex]y - y_0 = f^{\prime}(x_0, y_0)(x - x_0)[/tex]
In which f' is the derivative.
In this problem, the function is:
[tex]f(x) = e^{(x^2)}[/tex]
Applying the chain rule, the derivative is:
[tex]f^{\prime}(x) = 2xe^{(x^2)}[/tex]
At x = 1, the derivative is:
[tex]f^{\prime}(1) = 2(1)e^{((1)^2)} = 2e[/tex]
Hence the tangent line at point (1,0) is given by:
y = 2e(x - 1).
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the sum of two consecutive integers is 187. find the integers
Answer:
92.5 and 94.5
___________________
Solve[tex]187 \div 2 = 93.5\\\mathrm{Split\:93.5\:into\:two\:integers\:by\pm1}\\93.5 - 1 = 92.5\\93.5 + 1 = 94.5[/tex]
→ Thus, we have our two integers.
_________________________
Susie saved up her money and bought a model train. Rack of the 8 cars on the train were the same length. When Susie put all the trains together the train was 3 feet long. How long was each car?
In linear equation , length of each car =.375 feet.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Rack of the cars on the train were the same length = 8
train was 3 feet long.
length of each car = 3/8 = .375 feet
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A recent study of 50 U.S. chess players details such things as the number of years the players have been active and the chess ratings of the 50 players. (A chess rating is a number, with a higher number indicating greater expertise.) The chess rating data for the sample of 50 players are summarized in the following histogram.
Using the given histogram, we have that 90% of the players in the sample have scores that are less than 2300.
What is the missing information?This problem is incomplete, but researching it on a search engine, we have that the histogram states as follows:
6 of these players have scores between 300 and 700.6 of these players have scores between 700 and 1100.13 of these players have scores between 1100 and 1500.14 of these players have scores between 1500 and 1900.6 of these players have scores between 1900 and 1300.5 of these players have scores between 2300 and 2700.It asks the proportion of players in the sample with scores that are less than 2300.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
Above, we already gave the amounts presented by histogram, and we have that 45 out of 50 players have scores that are less than 2300, hence the proportion is given by:
p = 45/50 = 0.9.
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Find the solutions of the quadratic equation –9x2 + 49 = 0.
Question 8 options:
A)
x = 9∕7, – 9∕7
B)
x = 3∕7, –7∕3
C)
x = 7∕3, –7∕3
D)
x = 7∕9, –7∕9
The solutions to the quadratic equation, -9x² + 49 = 0, are: C. x = 7∕3, –7∕3.
How to Find the Solutions to a Quadratic Equation?Given the quadratic equation, -9x² + 49 = 0, we can factorize to find the roots (the values of x) as shown below:
-9x² + 49 = 0
-(9x² - 49) = 0
Divide both sides by -1
-(9x² - 49)/-1 = 0/-1
9x² - 49 = 0
9x² - 49 + 49 = 0 + 49
9x² = 49
Divide both sides by 9
9x²/9 = 49/9
x² = 49/9
Take the square root of both sides
√x² = √(49/9)
x = ±7/3
Therefore, the solutions to the quadratic equation, -9x² + 49 = 0, are: C. x = 7∕3, –7∕3.
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Which measurement is closet to the lateral surface area in square centimeters of the cylinder?
H = 7.6
B = 5.8
Answers
A. 164.9 cm (2)
B. 277.0 cm (2)
C. 138.5 cm (2)
D. 191.3 cm (2)
The value closest to the lateral area of the cylinder is 138. 5cm^2. Option C
How to determine the valueThe formula for determining the lateral area of a cylinder is expressed as;
Lateral area = 2 πrh
Where;
r is the radiush is the height of the cylinderNote that radius is half the diameter;
radius, r = 5. 8/ 2 = 2. 9 cm
Substitute into the formula
Lateral area = 2 ( 3. 142 × 2. 9 × 7. 6)
Lateral area = 2 ( 69. 249)
Lateral area = 138. 49 cm^2
Thus, the value closest to the lateral area of the cylinder is 138. 5cm^2. Option C
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You have a Chick-fil-A gift card worth $50. After you buy lunch on Monday, its value is $46.50. After you
buy lunch on Tuesday, its value is $43. Write an explicit formula to represent the amount of money left on
the card as an arithmetic sequence.
What is the value of the gift card after you buy 12 lunches?
A movie company spent $12,000,000 making a feature film. If tickets to see the movie cost $8.00 each, determine the number of tickets that must be sold in order for the company to break even
Answer:
1500000
Step-by-step explanation:
what number is 5 the square root of
Answer: 25
Step-by-step explanation:
We know this because 5 × 5 = 25
or 5² = 25
and also √25 = 5
7. AB=x+9, BC = 3x-4. Find AC.
B
с
хто + 3x
-3x
3х
2
A
2х
-2x=
The value of AC = 4x + 5.
How to do addition of the variables?A variable is defined as any property, number, or amount that can be counted or measured.
Even despite their different operations, adding and subtracting variables follow the same rule: once adding or subtracting terms with the identical variables, you either add and otherwise subtract the coefficients and leave the result with the variable.
Addition. So because variables are the same in this equation, you can add every one of the coefficients (2, 5, and 4). (a).2a + 5a + 4a = 11a
Subtraction. Since the variables are equal in this equation, you could indeed subtract each of the coefficients (11, 5, and 4). (a).11a – 5a – 4a = 2a
Similarly with the question;
AB = x+9, BC = 3x-4
AC = AB + BC
AC = x + 9 + 3x - 4
Add the variable and constant part separately.
AC = 4x + 5
Thus, the value of AC is found as 4x + 5.
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A number, x, rounded to 1 decimal place is 12.3
Write down the error interval for x.
The error of interval for x will be [12.25, 12.35) for rounding off to 12.3 to 1 decimal place
In the given question, a number supposed to be 'x' is rounded off to the 1 decimal place, so that the number rounded off becomes 12.3. So, it is given that the number x is rounded off to 12.3 by 1 decimal place.
From this, we get that x should be greater than or equal to 12.25 and x should be smaller than 12.35. The equations will be :
=> x ≥ 12.25 and x < 12.35
So, the x lies between 12.25 and 12.35 which defines the error of interval for x.
Hence, the error of interval for x will be [12.25, 12.35)
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The three sides of a triangle are n, 3n+1, and 5n−8. If the perimeter of the triangle is 56cm, what is the length of each side?
Answer:
n = 7
Step-by-step explanation:
You will want to add all common factors with each other.
So that would be n + 3n + 5n which would be 9n.
Then -8 + 1 would be -7. So now it should be 9n - 7.
You are going to set 56 equal to 9n - 7, so that would be 9n - 7 = 56.
After that, you will have to leave 9n alone by itself, so you would have to add 7 to both sides. Your final equation should be 9n = 63.
After that, you should divide both sides by 9 since you want n alone.
So 63 ÷ 9 would be 7. So at the end, n = 7.
From this year to ten years, the number of people employed as physician assistants in the country is expected to increase by 39%. The number of people employed as physician assistants today is 56,000. Find the predicted number of physician assistants after ten years.
Answer:
the predicted number of physician assistants after ten years is 77840.
Step-by-step explanation:
The number of people employed as physician assistants today is 56,000.
increment in employment =39%
after 10 years
total physicians= 56000*(1+0.39)
[ total =initial + profit]
[profit =profit*initial]
=77840
the predicted number of physician assistants after ten years is 77840.
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What is the quotient of 20/8 divided by 5/12?
85/12
12
16
25/9
Answer:
6 (None of the above)
Step-by-step explanation:
Let's solve the problem,
→ 20/8 ÷ 5/12
→ 20/8 × 12/5
→ 240/40 = 6
Hence, the answer is 6.
A square window has an area of x2 + 12x + 36 square feet. Find the length of one side of the square. Question 25 options: (x – 6) feet (x + 6) feet (x + 4) feet (x – 9) feet
The length of one side of the square is x+6
Area of a squareThe formula for calculating the area of a square is expressed as:
A = L^2
where
L is the side length of the square
Given the following parameters
A = x^2 + 12x + 36 square feet
A = (x+6)^2
(x+6)^2 = L^2
L = x + 6
Hence the length of one side of the square is x+6
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A 40-inch board is to be cut into three pieces so that the second piece is twice as long as the first piece, and the
third piece is 5 times as long as the first piece. If x represents the length of the first piece, find the lengths of all
three pieces.
Answer:
X represents 32
Step-by-step explanation:
Bc x plus 30 = 62 - 30 equals 32 0-0
Answer:
1st=5, 2nd=10, 3rd=25
Step-by-step explanation:
We can make an equation to figure out the lengths of all 3 peices:
1st piece is represented as x
2nd piece is twice as long as the first, so 2x will represent that.
3rd piece is 5 times as long as the first, so 5x will represent that
together that is x+2x+5x=40
you can then simplify that to be 8x=40
40/8=5 so x=5
You then plug 5 in as x to figure out the lengths of the other pieces
1st=
5
2nd=2(5)
10
3rd=5(5)
25
:D
6) Four pieces measuring 29.cm, 19.62cm, 32.49cm and 24.74cm are cut from a board that is 200cm long. Allowing 1cm for waste in cutting, what is the length of the remaining piece?
The Remaining length of the cardboard piece is 94.15 cm.
According to the statement
We have to find that the length of the remaining piece.
So, For this purpose, we know that the
Length is defined as the measurement or extent of something from end to end.
From the given information:
Four pieces measuring 29.cm, 19.62cm, 32.49cm and 24.74cm are cut from a board that is 200cm long.
Then
Total length of the four pieces become:
Four pieces length = 29+19.62+ 32.49 + 24.74
Four pieces length = 105.85 cm
Then the
Remaining length of the cardboard piece = total length - length of the four pieces.
Remaining length of the cardboard piece = 200 - 105.85
Remaining length of the cardboard piece = 94.15cm.
So, The Remaining length of the cardboard piece is 94.15 cm.
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Solve x≤0 and x≥−4 and write the solution in interval notation. If there is no solution, type ∅.
The answer is (-∞.∞).
Draw out a number line. Plot 0 and -4 on the number line.
Shade to the left of x = 0, and have a filled in circle at the endpoint. This is the graph of x≤0
Then graph x ≥−4 by plotting a filled in circle at -4, and shading to the right.
Note how the two graphs overlap to cover the entire real number line
So if we have x≤0 or x≥−4 then we're basically saying x is any real number. To write this in interval notation, we write (−∞,∞)
This is the interval from negative infinity to positive infinity (or just infinity). We exclude each endpoint because we can't actually reach infinity itself. Infinity is not a number. Infinity is a concept
Side note: if you change the "or" to "and", then the solution to x≤0 and x≥−4 would be [-4, 0][−4,0] to indicate the interval from x = -4 to x = 0, including both endpoints. This is the region where the two graphs overlap.
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At a cruising speed of 120 miles per hour, an airplane burns 8 gallons of fuel per hour. If the airplane covered 180 miles at cruising speed, how many gallons of fuel did it use?
A. 5.3
B. 12
C. 20
D. 22.5
Answer:
D. 22.5
Step-by-step explanation:
120 divided by 8
plus 60 divided by 8
= 22.5
I need help on question 82 a,b,c,d,e
Answer:642
Step-by-step explanation:
Look at the book and solve it
11. STEM Connection The world's biggest submarine
can sail at a speed of about 25.5 miles per hour on
the surface. How can you describe the relationship
between 5 and 0.5?
5 is at the one-place value, and 0.5 is at the tenth-place value. 5 is ten times the value of 0.5.
What is described as the once and tenth place?There are one or more digit numbers in a number. 43 has the digits 4 and 3. The value of a numeral is determined by its position in the number.The number one in the number twelve is located in the tens place. The 2 in 12 is now in the one position. 95 has a 9 with in tens position and a 5 with in ones position.The number 0 is significant. The zero in twenty indicates there are no ones. That tells us that the 2 in 20 are in the tens. 20 is made up of two tens and zero ones.For the given question;
The speed of the world's biggest submarine is 25.5 miles per hour on the surface.
Thus, in the value of 25.5, the digit 5 lies on the once place.
The value 0.5 lies on the tenth place.
Now, it is clear that the 5 is the 10 times the value of 0.5, which is the required relation.
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A car company uses the table below to show customers the approximate amount of gas used when a car has been driven a certain number of miles.
Gas Use
Miles driven
Gallons of gasoline used
120
6
300
15
360
18
480
?
If the car always uses the same amount of gasoline each mile, how many gallons of gasoline would be needed to travel 480 miles?
A.20
B.24
C.33
D.39
Please help?
I don’t understand this
Answer:
Please see the graph below
Step-by-step explanation:
The table is just selecting numbers for x and then solving for what y would be. Once we have the ordered pairs (x,y) We can graph the points and see the line.
Suppose you transform a square corn field by increasing one side by 2 units and decreasing the other side by 3 units. If the area of the resulting corn field equals 24, what was the length of the original corn field?
Answer:
8 and 3 are the length and the width
Step-by-step explanation:
3
Decrease -18 by 18.
The difference is ___?
( the answer is not 0 or -324)
Answer:
-36
Step-by-step explanation:
-18 - 18 = -36
In ANOP, OP = 12, PN = 7, and NO = 10. Which statement about the angles of ANOP
must be true?
Om/N> m/P> m/0
m/0> m/P> m/N
O m/0> m/N > m/P
Om/P> m/0> m/N
Om/P> m/N > m/0
Om/N> m/0> m/P
Submit Answer
Step-by-step explanation:
.............................-
The average professional hockey player makes $2.78 million a year. They play an average of 82 games
much does the average hockey player make per game?
x=b/4 = c solve for x
To solve for x, the given equation will be transformed as x = c - b/4
What is the equation?
A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions in order to express their equivalence. The meanings of the (one or more) word equation and its cognates in various(different) languages can vary slightly. For instance, an equation in French is described as having one or more variables, whereas, in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign. Finding the values of the variables that result in equality is the first step in solving a variable equation. The variables for which the equation must be solved are known as unknowns, and the unknown values that fulfill the equality are known as the equation's outcomes. Individual equations and conditional equations are the two types of equations.Given that,
x-b/4 = c
To solve for x, the given equation will be transformed as-
x = c - b/4
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