Answer:-250
Step-by-step explanation:
what is the exact solutions of x^2-5x-1=0
For this case we must find the solutions of the following quadratic equation:
[tex]x ^ 2-5x-1 = 0[/tex]
We solve by means of
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
Where:
[tex]a = 1\\b = -5\\c = -1[/tex]
Substituting:
[tex]x = \frac {- (- 5) \pm \sqrt {(- 5) ^ 2-4 (1) (- 1)}} {2 (1)}\\x = \frac {5 \pm \sqrt {25 + 4}} {2}\\x = \frac {5\pm \sqrt {29}} {2}[/tex]
Finally, the roots are:
[tex]x_ {1} = \frac {5+ \sqrt {29}} {2}\\x_ {2} = \frac {5- \sqrt {29}} {2}[/tex]
Answer:
[tex]x_ {1} = \frac {5+ \sqrt {29}} {2}\\x_ {2} = \frac {5- \sqrt {29}} {2}[/tex]
10 points for correct answer
Answer:
[tex]y=\frac{1}{52}x^2[/tex]
Step-by-step explanation:
The focus of the parabola is (0,13)
and the directrix is y=-13.
The equation of this parabola is given by:
[tex]x^2=4py[/tex]
The vertex of this parabola is at the origin.
The value of p is the distance from the vertex to the focus.
p=13-0=13
The equation of the parabola is
[tex]x^2=4(13)y[/tex]
[tex]x^2=52y[/tex]
Or
[tex]y=\frac{1}{52}x^2[/tex]
Given the side lengths below, determine which triangle is not possible.
(A) 4, 5, 6
(B) 4, 3, 6
(C) 3, 4, 5
(D) 3, 3, 6
Answer:
(D) 3, 3, 6
Step-by-step explanation:
The triangle inequality says the sum of the shortest two legs must be longer than the longest. In the case of {3, 3, 6}, the sum is exactly equal to the longest, so the "triangle" will look like a line segment and have zero height and zero area,
Some authors describing the triangle inequality find that to be an acceptable condition. Apparently the author of this question does not.
F(x)=6x^2-x
Find f(-3)
Answer:
327
Step-by-step explanation:
You will plug in the -3 for x. 6 times -3 equals -18. -18 squared equals 324. 324 minus -3 equals 327.
Answer: [tex]f(-3)=57[/tex]
Step-by-step explanation:
Given the following function:
[tex]f(x)=6x^2-x[/tex]
To find [tex]f(-3)[/tex] you need to substitute the x value [tex]x=-3[/tex] into the function [tex]f(x)[/tex] given.
Therefore, when the input value (value of the variable "x") is -3, then the ouput value is:
[tex]x=-3\\\\f(-3)=6(-3)^2-(-3)[/tex]
Remember the multplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]
Then:
[tex]f(-3)=57[/tex]
Write the comparison below as a ratio in simplest form using a fraction a colon and the word to 11 ounces to 5 ounces
Answer:
Fraction Colon To
[tex]\frac{11}{5}[/tex] 11 : 5 11 to 5
Answer with explanation:
We have to write the comparison below as in fractions , in colon and in words to 11 ounces to 5 ounces.
In Fractions
[tex]\frac{11}{5}[/tex]
In Colon
11 :5
In Words
→1 Ounce=29 grams (Approx)
The ratio of Ash gourd bought by me and my mother was 11 ounce to 5 ounce.
What is the midpoint of OA
Answer should be A if I'm not wrong.
Answer:
Option A is the correct answer.
Step-by-step explanation:
Given
The coordinates of point A = (2m, 2n)
The diagram is plotted on the graph, where O represents origin.
As we know that O is the origin whose coordinates are (0,0)
The formula for mid-point is:
Mid-point=((x_1+x_2)/2,(y_1+y_2)/2)
So,
The x-coordinate of mid-point of OA=(2m+0)/2
=2m/2
=m
The y-cooridnate of mid-point of OA=(2n+0)/2
=2n/2
=n
So the mid-point of OA is (m,n) ..
Which is the graph of the equation
(X-1)^2/ 3^2 + y^/ 4^2 = 1 ?
Answer:
the answer is C
Step-by-step explanation:
The equation shows the third equation
What is Equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). 6.9
Parts of an Equation
There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation.
As, per the given equation
(X-1)^2/ 3^2 + y^/ 4^2 = 1
The graph which is well defined from this equation is graph (C).
As, shown below.
Learn more about graph here:
https://brainly.com/question/16608196
#SPJ2
Find the product. (-7p)^3
For this case we must resolve the following expression:
[tex](-7p) ^ 3[/tex]
So:
[tex](-7p) ^ 3 =\\(-7p) (- 7p) (- 7p) =[/tex]
By law of multiplication of signs we have:
[tex]- * - = +\\+ * - = -[/tex]
Also:
[tex]7 * 7 * 7 = 343\\p * p * p = p ^ 3[/tex]
Finally, we have that the expression is equivalent to:
[tex](-7p) ^ 3 = -343p ^ 3[/tex]
ANswer:
[tex]-343p ^ 3[/tex]
Match the equations representing parabolas with their directrixes. y + 8 = 3(x + 2)2 y − 14 = -(x − 3)2 y + 7.5 = 2(x + 2.5)2 y − 17 = -(x − 3)2 y + 7 = (x − 4)2 y − 6 = -(x − 1)2 Directrix Equation of Parabola y = -7.25 arrowRight y = 6.25 arrowRight y = 17.25 arrowRight y = 14.25 arrowRight
Answer:
Part 1) [tex]y+8=3(x+2)^{2}[/tex] -----> [tex]y=-8.08[/tex]
Part 2) [tex]y-14=-(x-3)^{2}[/tex] ----> [tex]y=14.25[/tex]
Part 3) [tex]y+7.5=2(x+2.5)^{2}[/tex] ----> [tex]y=-7.625[/tex]
Part 4) [tex]y-17=-(x-3)^{2}[/tex] -----> [tex]y=17.25[/tex]
Part 5) [tex]y+7=(x-4)^{2}[/tex] ----> [tex]y=-7.25[/tex]
Part 6) [tex]y-6=-(x-1)^{2}[/tex] ----> [tex]y=6.25[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola in vertex form is equal to
[tex]y-k=\frac{1}{4p}(x-h)^{2}[/tex]
where
(h,k) is the vertex
The directrix is
[tex]y=k-p[/tex]
case 1) we have
[tex]y+8=3(x+2)^{2}[/tex]
the vertex is the point (-2,-8)
[tex]\frac{1}{4p}=3[/tex]
[tex]p=\frac{1}{12}[/tex]
The directrix is equal to
[tex]y=-8-\frac{1}{12}=-8.08[/tex]
case 2) we have
[tex]y-14=-(x-3)^{2}[/tex]
the vertex is the point (3,14)
[tex]\frac{1}{4p}=-1[/tex]
[tex]p=-\frac{1}{4}[/tex]
The directrix is equal to
[tex]y=14+\frac{1}{4}=14.25[/tex]
case 3) we have
[tex]y+7.5=2(x+2.5)^{2}[/tex]
the vertex is the point (-2.5,-7.5)
[tex]\frac{1}{4p}=2[/tex]
[tex]p=\frac{1}{8}[/tex]
The directrix is equal to
[tex]y=-7.5-\frac{1}{8}=-7.625[/tex]
case 4) we have
[tex]y-17=-(x-3)^{2}[/tex]
the vertex is the point (3,17)
[tex]\frac{1}{4p}=-1[/tex]
[tex]p=-\frac{1}{4}[/tex]
The directrix is equal to
[tex]y=17+\frac{1}{4}=17.25[/tex]
case 5) we have
[tex]y+7=(x-4)^{2}[/tex]
the vertex is the point (4,-7)
[tex]\frac{1}{4p}=1[/tex]
[tex]p=\frac{1}{4}[/tex]
The directrix is equal to
[tex]y=-7-\frac{1}{4}=-7.25[/tex]
case 6) we have
[tex]y-6=-(x-1)^{2}[/tex]
the vertex is the point (1,6)
[tex]\frac{1}{4p}=-1[/tex]
[tex]p=-\frac{1}{4}[/tex]
The directrix is equal to
[tex]y=6+\frac{1}{4}=6.25[/tex]
The correct matches are: Directrix y = -7.25 → Equation of Parabola: y + 7 = (x - 4)², Directrix y = 6.25 → Equation of Parabola: y - 6 = -(x - 1)², Directrix y = 17.25 → Equation of Parabola: y - 17 = -(x - 3)², Directrix y = 14.25 → Equation of Parabola: y - 14 = -(x - 3)².
To match the equations representing parabolas with their directrixes, it's essential to understand the standard form of a parabola's equation related to its axis of symmetry.
For a vertical parabola, the standard form is y = a(x - h)² + k, where the vertex is at (h, k) and the directrix is y = k - 1/(4a) for a parabola that opens upwards, or y = k + 1/(4a) for a parabola that opens downwards.
For a horizontal parabola, the standard form is x = a(y - k)² + h. In our case, all given equations are in the vertical form where x is squared.
Let's take each equation and find its directrix:
y + 8 = 3(x + 2)² opens upwards; its directrix is y = -8 - 1/(4*3) = -8.25 or y = -8 - 1/12.y - 14 = -(x - 3)²opens downwards; its directrix is y = 14 + 1/4 = 14.25.y + 7.5 = 2(x + 2.5)²opens upwards; its directrix is y = -7.5 - 1/(4*2) = -7.75 or y = -7.5 - 1/8.y - 17 = -(x - 3)² opens downwards; its directrix is y = 17 + 1/4 = 17.25.y + 7 = (x - 4)² opens upwards; its directrix is y = -7 - 1/4 = -7.25.y - 6 = -(x - 1)² opens downwards; its directrix is y = 6 + 1/4 = 6.25.With the directrix found for each equation, the correct matches are:
Directrix y = -7.25 → Equation of Parabola: y + 7 = (x - 4)²Directrix y = 6.25 → Equation of Parabola: y - 6 = -(x - 1)²Directrix y = 17.25 → Equation of Parabola: y - 17 = -(x - 3)²Directrix y = 14.25 → Equation of Parabola: y - 14 = -(x - 3)²Suppose that you are driving and you come to an intersection where you can only turn in one of three directions....
Hello There!
The "Probability" of turning on the right road is 1/3 also known as a 33.3% chance. This would be unlikely
5. What is angel 8 use picture above
Answer:
Angle 8 = Angle 4
Step-by-step explanation:
Answer:
4. ∠3 and ∠5
5. 75°
Step-by-step explanation:
4. Same-side interior angles.
If you look at the figure, the INTERIOR angles are those between the two parallel lines (JL and MP), these are angles #3, #4, #5 and #6. The other angles are exterior angles.
The question asks for same-side... meaning both on the left of NK or on the right side of it. So, the two sets that match this are: 3 with 5 and 4 with 6.
The last option gives you ∠3 and ∠5, so that's your answer.
That makes sense since angles 1 and 2, present in all other choices, are exterior angles.
5. If ∠4 = 75 degrees, what's the value of ∠8?
Since JL and MP are parallel lines crossed by another line (NK), we know that ∠4 and ∠8 will have the same measurement. Those two angles are located on the same position compared to each other and one of the parallel line.
So, since ∠3 = 75°, ∠8 also has to be 75°, same for their opposing angles 2 and 5. While the other angles are complements... so they're 105 degrees angles.
The force pulling a truck downhill is 2,000N, the mass of the truck is 40,000 kg. What is the acceleration?
For this case we have that Newton's second law is given by:
[tex]F = m * a[/tex]
Where:
m: It's the mass
a: Acceleration
F: It's the force
According to the data we have:
[tex]2,000 = 40,000 * a[/tex]
Dividing between 40,000 on both sides of the equation:
[tex]a = \frac {2,000} {40,000}\\a = 0.05[/tex]
Thus, the acceleration is [tex]0.05 \frac {m} {s ^ 2}[/tex]
Answer:
[tex]0.05 \frac {m} {s ^ 2}[/tex]
Sandy wants to cover a wooden cylinder with a diameter of 1 ft and a height of 4 ft with carpet to build a scratching post for her cats. What are the steps she needs to take to complete this task?
Final answer:
To cover the wooden cylinder with carpet, Sandy needs to find the surface area of the cylinder and then cut out a piece of carpet that matches that area.
Explanation:
To cover the wooden cylinder with carpet, Sandy needs to find the surface area of the cylinder and then cut out a piece of carpet that matches that area. The surface area of a cylinder can be found using the formula: SA = 2πr(r+h), where r is the radius of the base and h is the height of the cylinder. In this case, the diameter of the cylinder is 1 ft, so the radius is 1/2 ft. The height of the cylinder is 4 ft. Plugging these values into the formula, we get: SA = 2π(1/2)(1/2 + 4) = 2π(1/2)(9/2) = 9π square ft.
What are the vertex and x-intercepts of the graph of the function below?
y=x^2-6x-7
A. Vertex: (3, -16); Intercepts: x= -1, 7
B. Vertex: (3, -2); Intercepts: x= 1, -7
C. Vertex: (3, -2); Intercepts: x= -1, 7
D. Vertex: (3, -16); Intercepts: x= 1, -7
Answer: 3,-16 x=-1,7
Step-by-step explanation:
the plot in A - D all show ________ correlation.
A. negative
B. No
C. positive
D. prime
I think it's Answer C. but I'm not sure. please help and thank you
Answer:
C. Positive
Step-by-step explanation:
When x and y are both increasing, the slope of the line of best fit is positive, and so is the correlation. Hope this helps!
Answer
positive
Explanation
The answer is positive correlation, since all four of the graphs indicate the increase of all the variables.
It could not be negative correlation, because the line on graph would have more of a downward appearance.
A trinket factory can produce 3,000 trinkets per day. The warehouse has a capacity of 50,000 trinkets. Currently, there are 8,000 trinkets in the warehouse. Assume that no trinkets are going to be shipped out of the warehouse for a while.
1) Write an equation for the number of trinkets T in the warehouse after D days.
2) How many days will it take to fill the warehouse?
An equation for the number of trinkets in the warehouse after x days:
8,000 + 3,000x = 50,000
How many days will it take to fill the warehouse?
8,000 + 3,000x = 50,000
3,000x = 42,000
x = 14
Answer:
Per day production = 3000
The capacity of the warehouse = 50000
Current count of trinkets = 8000
Part 1:
Assuming that no trinkets are going to be shipped out,
The equation for the number of trinkets T in the warehouse after D days:
[tex]T=8000+3000D[/tex]
Part B:
We will put T=50000 in above equation.
[tex]50000=8000+3000D[/tex]
=> [tex]3000D=50000-8000[/tex]
=> [tex]3000D=42000[/tex]
D = 14
Hence, it will take 14 days to fill the warehouse.
What can you say about the relationship between M and P? Which letter is the correct answer?
Answer:
Choice C is correct
Step-by-step explanation:
The first step is to re-write the equations in exponential form.
The first equation can be written as;
[tex]\frac{M}{N}=10^{4}[/tex] since the base is 10 and 4 the exponent.
The second equation can be written as;
[tex]\frac{P}{N}=10^{5}[/tex]
The second step is to make N the subject of the formula in both equations.
Solving for N from this equation [tex]\frac{M}{N}=10^{4}[/tex], yields;
[tex]N=\frac{M}{10^{4}}[/tex]
Solving for N from the second equation [tex]\frac{P}{N}=10^{5}[/tex], yields;
[tex]N=\frac{P}{10^{5}}[/tex]
Therefore;
[tex]\frac{M}{10^{4}}=\frac{P}{10^{5} }\\\\P=10M[/tex]
Which is the least common multiple of 8 and 10
i’m pretty sure the answer is 40
Answer:
The answer is 40.
Step-by-step explanation:
Because the multiples of 8: 8, 16, 24, 32, 40, 48...etc
and 10: 10, 20, 30, 40, 50....etc and both of them have 40 so that's your LCM.
Hope i helped you! :)
Simplify 1+3+5+7+...199/2+4+6+8+...+200
Answer: Multiply 100 to both the numerator and denominator.
The problem is simplifying a sequence of numeric addition. It involves finding the average of a range of sequential odd and even numbers and dividing the two averages. This simplifies to 100/101.
Explanation:The problem presented is to simplify the sequential addition of odd numbers from 1 to 199, divided by the sequential addition of even numbers from 2 to 200. This is also known as calculating the average or mean of a set of sequential numbers, a concept in statistics.
To solve this, we need to understand that the average of a set of sequential numbers can be found by taking the sum of the first number and the last number, dividing it by two. Therefore, the sum of odd numbers from 1 to 199 can be simplified as (1+199)/2, and the sum of even numbers from 2 to 200 can be simplified as (2+200)/2.
Simplifying these gives us 100 for odd numbers and 101 for even numbers. Therefore, the simplification of the presented sequence is 100/101.
Learn more about Numeric sequences here:https://brainly.com/question/33575531
#SPJ2
Plz help!!
The set of all points in a plane that are equidistant from a given point is called a ______. The given point is called ________.
Answer:
Circle and Center
Step-by-step explanation:
In geometry, the set of points equidistant from a given point in a plane is called a circle. The given point from which all points on the circle are equidistant is known as the center.
Explanation:The definition you're looking for pertains to the geometric concept of a circle. The set of all points in a plane that are equidistant from a particular point is called a circle. Meanwhile, the given point that is equidistant from all other points of the circle is called the center of the circle. So, in a two-dimensional plane, this center point and the constant distance (also known as the radius) from it to any point on the circle define a circle.
Learn more about Circle here:https://brainly.com/question/12930236
#SPJ3
standard form of the equation x^2 + 4y^2 = 4.
Answer:
This equation in standard for would be x^2/4 + y^2 = 1
Step-by-step explanation:
Find the surface area and volume of each figure. Round each answer to the nearest hundredth.
Answer: Surface area is equal to 200[tex]cm^{2}[/tex]
Volume is equal to 333.33[tex]cm^{3}[/tex]
Step-by-step explanation:
First, let's do surface area.
The surface area of a pyramid is equal to 1/2(perimeter of base)(lateral height) + area of the base
The perimeter of the base is 10(4) = 40; as the base is a square with a side length of 10.
The lateral height is given as 5 cm.
The area of the base is 10(10) = 100.
We can plug those numbers into the equation to get 1/2(40)(5) + 100, which comes out to be 200[tex]cm^{2}[/tex].
Now for volume.
The volume of a pyramid is equal to 1/3(area of the base)(height).
We already have the area of the base, which is 100.
The height is given as 10 cm.
Plugging those numbers into the equation, we get 1/3(100)(10), which is 1000/3 or about 333.33[tex]cm^{3}[/tex].
Hope this helps!
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Answer:
Angle B: 135 degrees
Angle A: 60 degrees
Angle C: 75 degrees
Step-by-step explanation:
Angle B is 135 degrees
We have the complement of angle B, which is the lowest left corner of the triangle and it says 45 degrees.
So, B = 180 - 45 = 135 degrees
Angle A.
The lines crossing form 2 pair of identical angles from their tip... The exterior angle is 60 degrees, so the interior angle A is also 60 degrees.
Angle C.
Just like for angle B, we get angle C by subtracting its complement:
C = 180 - 105 = 75 degrees.
We can also validate by calculating the sum of the interior angles of the triangle: 45 + 60 + 75 = 180, which is perfect.
ivan pays an $8 monthly service fee so he can rent movies for $1.50 each and games for 3.00 each. Last month, Ivan rented 6 movies and 5 games. Which expression and result show the total amount that Ivan spent last month on his movie and game rentals?
I think 24 dollars without the monthly fee
Answer:
Expression: 8 + m(1.5) + g(3)
Result: 32
Step-by-step explanation:
Let m represent the number of movies and g represent the number of games Ivan rent, then total amount he spent is
8 + m(1.5) + g(3)
Since he rented 6 movies and 5 games
→ 8 + 6(1.5) + 5(3)
→ 8 + 9 + 15
→ 32
Multiply the quantity 5 less than 3 times a number by the quantity 2 times the same number added to five. Please show your work.
Answer:
[tex](3x-5)(2x+5)[/tex]
Step-by-step explanation:
Let
x ----> the number
we know that
The algebraic expression of the phrase "Multiply the quantity 5 less than 3 times a number by the quantity 2 times the same number added to five" is equal to
[tex](3x-5)(2x+5)\\ \\6x^{2}+15x-10x-25\\ \\6x^{2}+5x-25[/tex]
If you exert a force of 10.0 n to lift a box a distance of 0.75 m how much work do you do
A. 0.075 J
B. 7.5 J
C. 10.75 J
D. 75 J
Answer:
The work done is 7.5 Joules.
Step-by-step explanation:
Work Done is the product of the distance covered and the force applied.
[tex]WorkDone=Force\times Distance[/tex],
The force applied is 10.0N.
The distance covered is 0.75m.
This implies that:
[tex]WorkDone=10\times0.75[/tex],
[tex]WorkDone=7.5J[/tex].
The work done is 7.5 Joules.
Between which X-values and y-values does the cluster in this scatter plot Lie 30 POINTS
The green circle shows the cluster. This is where most of the data tends to stay. The smallest x-value is 4 (shown by the vertical pink line) and the largest x-value is 6 (shown by the vertical blue line). As for the y-value: the smallest is shown by the horizontal pink line at 6 and the largest is 9 shown by the horizontal blue line. This means the answer is C.
Hope this helped :)
What is the value of -5^6?
Answer:
-15625 i think
For this case we must find the value of the following expression:[tex]-5 ^ 6 = -1 * 5 ^ 6[/tex]
This means that we must multiply the 5 six times, and then multiply by -1, that is:
[tex]5 ^ 6 = 5 * 5 * 5 * 5 * 5 * 5 = 15,625[/tex]
Then multiply by -1:
[tex]-15,625[/tex]
Answer:
[tex]-5 ^ 6 = -15,625[/tex]
Which of the following relations is a function?
A. (2,4), (-5, 6), (2, 3), (-6, 2)
B. (8, 1), (-5, 4), (2, 1), (8, 2)
C. (2,4), (-5, 2), (8, 1), (-6, 2)
D.
(2,0).(-5, 3), (8, 1), (-5,5)
Answer: OPTION C
Step-by-step explanation:
A relation is a function when each input value has one and only output value.
For option A:
(2,4), (-5, 6), (2, 3), (-6, 2)
You can observe that the input value "2" has two output values. Then it is not a function.
For option B:
(8, 1), (-5, 4), (2, 1), (8, 2)
You can observe that the input value "8" has two output values. Then it is not a function.
For option C:
(2,4), (-5, 2), (8, 1), (-6, 2)
You can observe that each input value has only one output values. Then it is a function.
For option D:
(2,0).(-5, 3), (8, 1), (-5,5)
You can observe that the input value -5 has two output values. Then it is not a function.
For a set of data to be a function each x value has to have different y values.
A. (2,4), (-5, 6), (2, 3), (-6, 2)
B. (8, 1), (-5, 4), (2, 1), (8, 2)
D. (2,0).(-5, 3), (8, 1), (-5,5)
The bolded coordinates are the ones of each data set that makes it not a function. As you can see the x values all have different y values.
This leaves C. as the answer!
Hope this helped!
Simply 7+3 • (8 ÷ 4)
7+3= 10
8/4=2
VEry easy okay
Answer: 13
Step-by-step explanation:
Given the expression [tex]7+3(8[/tex]÷[tex]4)[/tex], you can rewrite it as:
[tex]=7+3(\frac{8}{4})[/tex]
First, you need to solve the operation that is inside the parentheses. Then, you must divide 8 by 4:
[tex]=7+3(2)[/tex]
Now you need to eliminate the parentheses. To do this, you must multipy 3 by 2, then:
[tex]=7+6[/tex]
And finally, you must make the addition. Therefore, you get:
[tex]=13[/tex]