[tex]2m^2-7m-13=-10\ \ \ |+10\\\\2m^2-7m-3=0[/tex]
[tex]a=2;\ b=-7;\ c=-3\\\\b^2-4ac=(-7)^2-4\cdot2\cdot(-3)=49+24=73\\\\m_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ m_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\m_1=\dfrac{-(-7)-\sqrt{73}}{2\cdot2}=\dfrac{7-\sqrt{73}}{4}\\\\m_2=\dfrac{-(-7)+\sqrt{73}}{2\cdot2}=\dfrac{7+\sqrt{73}}{4}[/tex]
Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm, is a right triangle?
Answer:
Let first side= 5 cm
second side= 12 cm
third side = 13 cm
To prove this triangle to be right angle triangle, we need to prove Pythagoras Theorem
[tex]5^{2}[/tex]=25
[tex]12^{2}[/tex]=144
[tex]13^{2}[/tex]=169
169= 25+144
169=169
According to Pythagoras theorem ,
[tex]p^{2}[/tex]+[tex]b^{2}[/tex]=[tex]h^{2}[/tex]
since, it follows Pythagoras theorem,
Hence, it is a Right angle Triangle
A 45° sector in a circle has an area of 13.75π cm².
What is the area of the circle?
Use 3.14 for pi.
Enter your answer as a decimal in the box.
Answer:
345.4
Step-by-step explanation:
I took the test
What is the greatest common factor of the polynomial's terms? 14a3b4−7ab7+21a2b
The Answer is 7(ab).
I did the quiz.
Answer: 7ab
Step-by-step explanation:
The given polynomial : [tex]14a^3b^4-7ab^7+21a^2b[/tex]
The terms of the above polynomial can be written as :
[tex]14a^3b^4=(7\times2)a^{2+1}b^{3+1}=(7\times2)a^2(a)b^3b\\\\-7ab^7=-7ab^{6+1}=-7ab^6(b)\\\\21a^2b=(7\times3)a^{1+1}b=(7\times3)a(a)b[/tex]
Now, we can see that the greatest common factor of the polynomial's terms= [tex]7ab[/tex]
The simplest form of square root of eighty can be written as a times square root of b, where a
Use the number line to find the ratio BG/AD Simplify the ratio.
Angle 2 and angle 3 are vertical angles. true or false
Answer: If you don't know the answer don't put one down but i do believe the answer is false.
Step-by-step explanation:
The statement 'Angle 2 and Angle 3 are vertical angles' can be true depending on their position, as vertical angles are those directly opposite from each other at the intersection of two lines.
Explanation:The question is asking about vertical angles. Vertical angles are pairs of non-adjacent angles formed when two lines intersect. This means they are the angles that are directly opposite from each other where the two lines intersect. So if Angle 2 and Angle 3 are directly opposite each other at the point where two lines cross, then they are indeed vertical angles. So, the statement 'Angle 2 and Angle 3 are vertical angles' can be true depending on their placed positions.
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While in europe, if you drive 107 km per day, how much money would you spend on gas in one week if gas costs 1.10 euros per liter and your car's gas mileage is 42.0 mi/gal ? assume that 1euro=1.26dollars?
Answer:
The money spend on gas in one week = 46.13 Euro
The money spend on gas in one week = $58.12
Step-by-step explanation:
1 week = 7 days
You drive 107 km per day.
Kilometer driven for 7 days = 7 *107 = 749 kilometers.
Now let's convert kilometers to miles.
1 mile = 1.60934 kilometers
We have to divide 749 km by 1.60934.
So, 749 km = 465.41 miles.
Car mileage is 42 miles / gallon.
We need to find the number of gallons of gas needed to travel 465.41 miles.
So, we have to divide 465.41 miles by 42.
The number of gallons of gasoline needed = [tex]\frac{465.41}{42} = 11.08 gallons[/tex]
cost of 1 .10 Euros per liter.
Now we have to convert 11.08 gallons to liters.
1 gallon = 3.78541 liters.
So we have to multiply 11.08 by 3.78541
11.08 gallons = 41.94 liters.
Now to find the cost, we need to multiply 41.94 liters by 1.10 Euro.
The money spend on gas in one week = 46.13 Euro
To convert the cost in dollars.
1 euro = 1.26
We need to multiply 46.13 by 1.26
The money spend on gas in one week = $58.12
HELP! This circle graph shows the results of a survey that asked people to identify their favorite type of music. What percent of people chose rock or country as their favorite type of music? 9% 35% 45% 55%
A circle graph with 5 sections. The first section is labeled Rock 27 percent. The second section is labeled Hip Hop 28 percent. The third section is labeled Jazz 19 percent. The fourth section is labeled Country 18 percent. The fifth section is labeled Other 14 percent.
The percentage that choose rock or country is 45%
From the circle graph, we have the following parameters:
Rock = 27%.
Hip Hop = 28%
Jazz = 19%.
Country = 18%
Other = 14%
The percentage that choose rock or country is then calculated as:
Rock or Country = 27% + 18%
Rock or Country = 45%
Hence, the percentage that choose rock or country is 45%
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Moving a figure around a fixed point in the plane is called making a ___.
Answer:
Rotation.
Step-by-step explanation:
There are three rigid motions (which do not change the shape and size of the figures): rotation, translation and reflection.
You make a rotation of a figure when you turn it about a fixed point (which can be inside, on an edge or outside the figure) and it is measured in degrees. The rotation can be clockwise or counterclockwise.
Answer:
The answer is Reflection
please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
(2)
For this problem I did 2.5/8 = 1.5/4.8, then I cross multiplied and got 12=12 so I would assume that the polygons are infact similar? It must be B or C based on this, but I am pretty confused about the whole ratio part.
Thomas is saving pennies in a jar. The first day he saves 3 pennies, the second day 12 pennies, the third day 48 pennies, and so on. How many pennies does Thomas have on the eighth day?
What is the probability that the card is either a face card or a spade?
The sum of 4 interior angles of a pentagon is 402. Find the measure of the fifth interior angle.
108
62
138
42
The home that you are interested in purchasing is listed at $135,000. In order to get financing, you have to place a 15% down payment. From the given information, determine the amount of the down payment. a. $2,025 c. $114,750 b. $135,000 d. $20,250
Answer:
its D
Step-by-step explanation:
What is the following quotient? sqrt 120 / sqrt 30
Answer:
[tex]2[/tex]
Step-by-step explanation:
we have
[tex]\frac{\sqrt{120}}{\sqrt{30}}[/tex]
we know that
[tex]\frac{\sqrt{120}}{\sqrt{30}}=\sqrt{\frac{120}{30}}=\sqrt{4} =2[/tex]
The number of cents per kilometer it costs to drive a car depends on how fast you drive it. At low speeds the cost is high because the engine operates inefficiently. At high speeds the cost is high because the engine must overcome high wind resistance. At moderate speeds the cost reaches a minimum. Assume that the number of cents per kilometer varies quadratically with the number of kilometers per hour.
A) Suppose that it costs 28,21, and 16 cents per kilometer to drive at 10,20,and 30 kph,respectively. Write the particular function to represent this situation.
B)How much would it cost to drive at 150 kph?
C) Between what two speeds must you drive to keep your cost at no more than 13 cents per kilometer?
C)Is it possible to spend only 10 cents per kilometer?
D) What is the optimum speed and how much per kilometer will it cost? What part of the function represents this function?
Using the form of a quadratic equation f(x) = ax^2 + bx + c, we can derive an equation for each of three given points (10,20,30 kph and their corresponding costs). Solving these simultaneously we would get the particular equation representing the situation. We could then apply this to calculate costs at various speeds including checking if it is possible to spend only 10 cents/km, determining an optimal speed range for a 13 cents/km cost, and finding the optimal speed and cost per km.
Explanation:To write a particular function that represents this scenario, we can set up three equations using the general form of a quadratic equation, which is f(x) = ax^2 + bx + c. In this case, our x-values are the speeds (10, 20, and 30 kph) and our f(x) values are the corresponding costs (28, 21, and 16 cents/km).
Substitute these values into the equation f(x) = ax^2 + bx + c, we get three equations:
100a + 10b + c = 28
400a + 20b + c = 21
900a + 30b + c = 16
By solving the system of equations, we could find the values of a, b and c. Then we would substitute the speed into the function to calculate the cost at 150 kph, and to find the speed range for a cost of 13 cents/km and check if it is possible to spend only 10 cents/km. Finally, the optimal speed and cost per km would be represented by the minimum point of the function, which in the case of a parabola occurs at x = -b/2a.
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The explicit rule for a sequence is
an=17−5n .
What is the recursive rule for the sequence?
can you explain also
The total area of the rectangular prism shown is 30 sq. ft. 50 sq. ft. 62 sq. ft.
The Surface area of rectangular prism is given by:
[tex] S.A = 2(wl + hl+ hw) [/tex]
where ,
w=width=2 ft
h=height=5 ft
l=length.=3 ft
Plugging these values in the formula,
[tex] S.A = 2(2*3 + 3*5+ 5*2) [/tex]
Answer : Surface Area =62 square feet.
HELP!!!!!!!!!!!!!
To solve the equation 3x−2=4x−1 , Veronica graphs the functions f(x)=3x−2 and g(x)=4x−1
on the same set of coordinate axes.
Which statement describes the solution of the equation 3x−2=4x−1?
(A) The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.
(B) The solution of the equation cannot be found graphically. Veronica should solve the equation algebraically.
(C) The solution of the equation is the y-coordinate of the ordered pair where the graphs of the two functions intersect.
(D) The solution of the equation is the y-intercept of the linear equations.
we have that
f(x)=3x-2
g(x)=4x-1
3x-2=4x-1-------------> 4x-3x=-2+1--- > x=-1
find the value of f(x) or g(x) for x=-1
f(x)=3x-2 -------> f(-1)=3*(-1)-2 ------> f(-1)=-5
the solution is the point (-1,-5)
using a graph tool
see the attached figure
the answer is
case (A) The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.PLS HELP ME ANSWER THIS ASAP , I WILL GIVE EXTRA POINTS AND BRAINIEST.
Find the distance between the points given.
(-3, -6) and (3, 2)
4
10
√52
A cruise ship travels 1900 miles per trip. There are a total of 4 stops the ship makes, and the distance to the first stop is 460 miles. If the variable d stands for the distance left to travel after the first stop, which of the following units could apply to this variable?
A. ships
B. days
C. stops
D. miles
Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let x represent the length of each of the equal pieces of yarn that Julie decides to cut. What is the equation that can be used to determine the total length of all of the yarn that she ends up cutting, y? Is the graph of the equation continuous or discrete?
Which description is correct for the polynomial 4x² +3x +5?
cubic binomial
cubic trinomial
quartic monomial
quadratic trinomial
The answer is: D)quadratic trinomial
The solution is Option D.
The quadratic trinomial is given by A = 4x² + 3x + 5
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 4x² + 3x + 5 be equation (1)
On simplifying the equation , we get
There are 3 terms on the equations , so it is a trinomial
And , since the variable is x² , it is a quadratic equation
Therefore , the equation A is quadratic trinomial
Hence , the equation is quadratic trinomial
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Given f(x)=5x^2−2x and g(x)=3x ^2+x−4 .
The addition of the two functions f(x) and g(x) is 8x² − x − 4. Then the correct option is C.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The functions are given below.
[tex]\rm f(x)=5x^2-2x \\\\g(x)=3x ^2+x-4[/tex]
The addition of the functions is given as
f(x) + g(x) = 5x² − 2x + 3x² + x − 4
f(x) + g(x) = 8x² − x − 4
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If l = 65 cm and j = 33 cm, what is the length of k?
Answer:
The answer is 56 inches on Study Island.
Step-by-step explanation:
Three couples go to the movies and sit in six consecutive seats. if the couples must sit together, in how many ways can they be seated
Type the domain and range values for the corresponding variables that make these relations inverses of each other. a = b = c = d = e =
Please Hurry, I really need help! A cylinder has a height of 6" and the circumference of its base is 16π".
Find the volume of the cylinder. (P.S There is no picture of the cylinder)
96π cubic inches
192π cubic inches
384π cubic inches