The solutions of the quadratic equation x² = -5x - 3 are [tex]\( x = \frac{-5 - \sqrt{13}}{2} \)[/tex] and [tex]\( x = \frac{-5 + \sqrt{13}}{2} \)[/tex].
To find the solutions of the quadratic equation x² = -5x - 3, first we rearrange it to the standard form:
x² + 5x + 3 = 0
We solve this using the quadratic formula, which is given by:
x = [tex]\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
For our equation, a = 1, b = 5, and c = 3. Substituting these values in, we get:
x = [tex]\frac{-5 \pm \sqrt{5^2 - 4*1*3}}{2*1}[/tex]
x =[tex]\frac{-5 \pm \sqrt{25 - 12}}{2}\\[/tex]
x =[tex]\frac{-5 \pm \sqrt{13}}{2}[/tex]
Hence, the solutions are:
x = [tex]\frac{-5 - \sqrt{13}}{2}[/tex] and x = [tex]\frac{-5 + \sqrt{13}}{2}[/tex]
Complete question: Which are the solutions of the quadratic equation? x² = -5x - 3
-5, 0[tex]\frac{-5 - \sqrt{13}}{2}[/tex], [tex]\frac{-5 + \sqrt{13}}{2}[/tex][tex]\frac{5 - \sqrt{13}}{2}[/tex], [tex]\frac{5 + \sqrt{13}}{2}[/tex]5,0Write the following linear equation in standard for: 2y = -8x - 18 ??
A.y = -4x - 9
B.8x + 2y = -18
C.2y + 18 = -8x
D.18 + 8x = -2y
Calculate population variance from population standard deviation
cuharra studied Monday and Tuesday for her math test she spent a total of 120 minutes studying. she spend an extra 15 minutes on Tuesday. how long did she study for on Monday and on tuesday
Cuharra studied for 52.5 minutes on Monday and 67.5 minutes on Tuesday.
Explanation:To find out how long Cuharra studied on Monday and Tuesday, we can set up an equation. Let's say C represents the amount of time she studied on Monday. According to the information given, on Tuesday she spent an extra 15 minutes studying, which means she studied for C + 15 minutes. The total time she studied was 120 minutes. So, we can write the equation as C + (C + 15) = 120.
Now, we can solve this equation to find the values of C and C + 15. Combining like terms, we get 2C + 15 = 120. Subtracting 15 from both sides, we get 2C = 105. Divide both sides by 2, and we get C = 52.5.
Therefore, she studied for 52.5 minutes on Monday and 52.5 + 15 = 67.5 minutes on Tuesday.
Final answer:
Cuharra studied for 52.5 minutes on Monday and 67.5 minutes on Tuesday to make a total of 120 minutes of study time over the two days.
Explanation:
The question involves solving for the number of minutes cuharra studied on Monday and Tuesday. Since the total study time for both days is 120 minutes and she studied 15 minutes extra on Tuesday, we can set up two variables to represent the study times on each day. Let x be the number of minutes studied on Monday, then x + 15 will be the number of minutes studied on Tuesday.
To solve for x, we set up the equation x + (x + 15) = 120. Simplifying, we get 2x + 15 = 120. Subtracting 15 from both sides gives us 2x = 105. Dividing both sides by 2, we find that x = 52.5. Therefore, cuharra studied for 52.5 minutes on Monday and 52.5 + 15 = 67.5 minutes on Tuesday.
The rule (x, y)→(x+2, y−4) represents a translation 2 units ______
left
right
up
down
and 4 units _______
left
right
up
down
The rule (x, y)→(x+2, y−4) represents a translation of 2 units right and 4 units down.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
The rule (x, y)→(x+2, y−4)
As we know, when we go right side of the x-axis we add to the x-coordinate, and when we go left side of the x-axis we subtract to the x-coordinate.
The rule (x, y)→(x+2, y−4) represents a translation of 2 units right.
When we go upside of the y-axis we add to the y-coordinate, and when we go down the side of the y-axis we subtract to the y-coordinate.
The rule (x, y)→(x+2, y−4) represents a translation 4 units down.
Thus, the rule (x, y)→(x+2, y−4) represents a translation of 2 units right and 4 units down.
Learn more about the geometric transformation here:
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Suppose you have 52 feet of fencing to enclose a rectangular dog pen. The function A = 26x = x2 where x = width, gives you the area of the dog pen in square feet. what width gives you the maximum area? what is the maximum area? round to the nearest tenth if necessary.
maximum area is a square
the side of the square would be 52/4 = 13 feet
area = 13*13 = 169 square feet
Answer:
Width = 13 ft
Maximum Area = 169 ft²
Step-by-step explanation:
Given: A rectangular dog pen whose fencing is 52 feet.
Let length be y and width be x
Fencing = 2(l+b)
52 = 2 (x+y)
x + y = 26
y = 26 - x
Area of rectangular pen = Length x width
= y . x
[tex]A=x(26-x)[/tex]
[tex]A=26x-x^2[/tex]
It is parabolic equation. Maximum/Minimum at vertex.
[tex]x=-\dfrac{b}{2a}[/tex]
where, a=-1, b=26
[tex]x=\dfrac{26}{2}=13[/tex]
Now we put x=13 into A
[tex]A=13(26-13)[/tex]
[tex]A=169[/tex]
Hence, The width is 13 feet and Maximum area is 169 ft²
Tammy takes a job after school to earn money to buy a violin. she knows that the more hours she works, the more money she will make.
a. the number of hours tammy works is a function of the amount of money she makes.
b. the amount of money tammy makes is a function of the number of hours she works.
c. tammy's job is a function of her interest in music.
Which graph represents the solution set of the system of inequalities?
{3y≥x−9
3x+y>−3
the solid line passes through (0,-3) and (0,9)
dotted line passes through (0,-3) and (0,-1)
see attached sketch
Answer:
The image shows the solution for the given inequalities.
Step-by-step explanation:
We are given the following information in the question:
[tex]3y \geq x-9\\3x+y>-3[/tex]
We have to plot the solution for the given inequality.
The image attached shows the solution to the given inequalities.
The red shaded portion is the solution to the first inequality and the blue shaded region is the solution for the second inequality.
The common shaded portion is the solution common to both the inequalities.
The dotted blue line is not a part of the solution for both the inequality.
how do you do number 10?
Solve 3c − 5f = 55 for f. Show your work.
[tex]\(f = \frac{3c - 55}{5}\)[/tex] is the solution for the given expression.
To solve the equation 3c - 5f = 55 for f, you need to isolate the variable f by performing a series of mathematical operations. Let's go step by step:
Start with the equation:
3c - 5f = 55
Add 5f to both sides to move the term involving f to one side of the equation:
3c = 5f + 55
Subtract 55 from both sides to isolate the term with f:
3c - 55 = 5f
Now, divide both sides by 5 to solve for f:
(3c - 55) / 5 = f
f = (3c - 55) / 5
So, [tex]\(f = \frac{3c - 55}{5}\)[/tex] is the solution for (f).
What shape has 6 sides?
Question 10 options:
pentagon
hexagon
decagon
octagon
Save
A B) hexagon is the shape with 6 sides.
A hexagon is a polygon with six straight sides and six angles. In geometry, hexagons are commonly used in various designs and structures due to their symmetry and stability.
Regular polygon refers to a polygon with equal sides and equal angles, such as a hexagon. Hexagons have the property of being equilateral and equiangular, making them regular polygons.
Six Electron Groups form an octahedron, which is a polyhedron made up of identical equilateral triangles and has six identical vertices, showcasing the connection between the number six and geometric shapes.
Therefore, option B is correct.
the base is 12 the height is 17. and the apothem is 10 inches they are all inches. Triangular pyramid volume
You review a lease for a new apartment. The lease requires you pay the first month's rent, last month's rent and a security deposit of one month's rent, at the time of signing. The monthly rent is $500. How much will you need at the time of signing?
Rachelle can walk 2.5 miles in 40 minutes. At this rate, how far can she walk in 1 hour?
The distance travel Rachelle in 1 hour (60 minutes) will be 3.75 miles.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Rachelle can walk 2.5 miles in 40 minutes.
Then the speed will be
Speed = 2.5 / 40
Speed = 0.0625 miles per minute
At this rate, distance travel Rachelle in 1 hour (60 minutes) will be
0.0625 = d / 60
d = 3.75 miles
The distance travel Rachelle in 1 hour (60 minutes) will be 3.75 miles.
More about the speed link is given below.
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How do I use the graph of the function to find the domain and range of f.
If the hypotenuse is 41 inches and one of the legs is 40 inches, what is the lengh of the other eleg in inches
Liam is setting up folding chairs for a meeting. If he arranges the chairs in 4 rows of the same length, he has 5 chairs left over. If he arranges the chairs in 2 rows of that same length, he has 17 left over. How many chairs does Liam have?
Which regular polygon can be used to form a tessellation?
octagon
decagon
triangle
nonagon
The regular polygon that could be used for tessellation is:
Triangle.
Step-by-step explanation:Tessellation is a geometry that is formed by a repeating pattern of same shape without any gaps.
We can use only three regular polygon for the formation of Tessellation:
1) Equilateral Triangle
2) Square
3) Regular Hexagon.
Hence, from the given option the regular polygon that can be used to form a tessellation is:
Triangle.
A probability distribution for all possible values of a sample statistic is known as a _____.
Answer:
Sampling Distribution
Step-by-step explanation:
A sample is a portion of the population chosen randomly or with certain techniques.
A statistic is a property of sample that describes the sample
Sampling distribution of statistic is a collection of all possible values of statistics for samples taken from the population. To be more precise it is probability distribution of all the outcomes of statistics of samples from the population.
Sample distribution of mean:
It can be defined as the probability distribution of all the feasible or possible means of samples of same size size taken from the population.
While traveling along a highway a driver slows from 24 m/s to 15 m/s in 12 seconds. What is the automobile’s acceleration? (Remember that a negative value indicates slowing down or deceleration)
We are given that:
vi, initial velocity = 24 m/s
v, final velocity = 15 m/s
t, time = 12 s
The formula for acceleration is:
a = (v – vi) / t
a = (15 – 24) / 12
a = - 0.75 m/s^2 (deceleration)
find gh if g(5,-1) and h(1,-3). write your answer in simplest radical form.
A cyclist rides his bike at a rate of
11
feet per second. What is this rate in miles per hour? How many miles will the cyclist travel in
3
hours? In your computations, use the fact that
1
mile is equal to
5280
feet. Do not round your answers.
What is gk can someone solve for gk
Answer:
7
Step-by-step explanation:
12 on the bottom right is 1 up the 11 on the bottom left, so 7 must be the right answer.
cosx - 4 = sinx -4
(0,2pi)
Find solutions
Determine if the lines are parallel, perpendicular, or neither x-3y= 15 and y = -3+4
Answer:
Step-by-step explanation:
A swimming pool can be filled by either or both of two pipes of different diameters. it takes the smaller pipe twice the time that the larger pipe takes to fill the pool. if water flows through both pipes it take 213 hours to fill the pool. how long will it take the larger pipe to fill the pool? [hint: let x be the amount of the pool filled by the small pipe in one hour]
Step-by-step explanation:
Let r₁ be the rate of filling of small pipe, r₂ be the rate of filling of large pipe and V be the volume of swimming pool.
[tex]\texttt{Rate of small pipe},r_1=\frac{V}{t_1}\\\\\texttt{Rate of large pipe},r_2=\frac{V}{t_2}=\frac{V}{0.5t_1}=2r_1[/tex]
If both pipes are combined it takes 213 hours, that is
[tex]t=\frac{V}{r_1+r_2}\\\\213=\frac{V}{r_1+2r_1}\\\\V=639r_1[/tex]
Now we need to find how much time it takes to fill the pool by large pipe,
That is
[tex]t_2=\frac{V}{r_2}=\frac{639r_1}{2r_1}=319.5hours[/tex]
By large pipe only it will take 319.5 hours to fill the pool.
Please i really need help on this one please!!!! :( I need an answer ASAP
Multiply r^2 + 7r + 10 / 3 by 3r - 30 / r^2 - 5r - 50
A. r + 2
B. 7r^2 - 20r - 300 / -5r - 5
C. (r + 5)( r + 2) / (r + 10)
D. 3r + 6 / 2
By factoring and simplifying the given polynomials, we found that the expressions simplify to r + 2. Therefore, the correct answer is option A. This process involves cancelling out common factors from the numerator and the denominator.
Polynomial Multiplication and Simplification
To solve the problem, we need to multiply the given rational expressions and simplify the result. The expressions are:
(r^2 + 7r + 10) / 3 and (3r - 30) / (r^2 - 5r - 50)
First, let's factor the polynomials where possible:
Factor the numerator of the first expression:[tex]r^2 + 7r + 10 = (r + 2)(r + 5)[/tex]Factor the denominator of the second expression: [tex]r^2 - 5r - 50 = (r - 10)(r + 5)[/tex]Now, the problem can be written as:
([tex](r + 2)(r + 5) / 3 ) * ( 3(r - 10) / (r - 10)(r + 5) )[/tex]
Next, we simplify by canceling out the common factors:
[tex]=( (r + 2)(r + 5) / 3 ) * ( 3(r - 10) / (r - 10)(r + 5) )[/tex]
The (r + 5) terms and the (r - 10) terms can be canceled:
[tex]= (r + 2) / 1[/tex]
So, the simplified answer is r + 2,
The correct option is A. r+2
Please help with 3 questions thank you.
1. an angle congruent to a given angle
2. x = 68, y = 75
3. corresponding angles
Please Help! Will give BRAINLIEST! I don't know how to do this.
Determine the x- and y-intercepts of the graph of y=−1/3x+3 .
Then plot the intercepts to graph the equation.
Answer:
you would graph (0,3) and (9,0)
Step-by-step explanation:
Consider the provided equation.
The x intercepts are the points where y value is zero. Similarly the y intercepts are the points where x values is zero.
In order to find the x intercept substitute y = 0 in the provided equation.
0=-1/3x + 3
-3=-1/3(x)
-9=-x
9=x
Thus, the x intercept is (9,0)
In order to find the y intercept substitute x = 0 in the provided equation.
y=-1/3(0) + 3
y=3
Thus, the y intercept is (0,3)
Now use the x and y intercepts to draw the graph of the equation.
The required graph is shown in figure 1.
Therefore, the x- and y- intercepts is (9,0) and (0,3)
What is the justification for each step in the solution of the equation 3(2x + 7) - 4 = 53 - 3x?
Step 1: 3(2x + 7) - 4 = 53 - 3x
Step 2: 6x + 21 - 4 = 53 - 3x
Step 3: 6x + 17 = 53 - 3x
Step 4: 9x + 17 = 53
Step 5: 9x = 36
Step 6: x = 4
Final answer:
The equation 3(2x + 7) - 4 = 53 - 3x is solved through algebraic processes: distributing, combining like terms, transposing terms, isolating the variable, and dividing to solve for x, resulting in the solution x=4.
Explanation:
The justification for each step in solving the equation 3(2x + 7) - 4 = 53 - 3x involves algebraic manipulation:
Distribute the 3 into the parenthesis: 3(2x) + 3(7) - 4 = 53 - 3x becomes 6x + 21 - 4 = 53 - 3x.Combine like terms on the left side: 6x + 17 = 53 - 3x.Add 3x to both sides to get all x terms on one side: 9x + 17 = 53.Subtract 17 from both sides to isolate the term with x: 9x = 36.Divide both sides by 9 to solve for x: x = 4.Each step is justified by the rules of algebra which allow us to simplify and rearrange equations to isolate the variable. The final step gives us the solution x = 4.
What is the smallest integer that is the sum of three different primes, each of which is greater than 10?