-5x^2+9=0 solve quadratic equation
Answers
We are asked to solve the following quadratic equation:
\(-5x^2+9=0\)To do that, we will solve for "x", first by subtracting 9 on both sides, like this:
\(\begin{gathered} -5x^2+9-9=-9 \\ -5x^2=-9 \end{gathered}\)Now we will divide both sides by -5, like this:
\(-\frac{5x^2}{-5}=-\frac{9}{-5}\)Solving the operations, we get:
\(x^2=\frac{9}{5}\)Now we take the square root on both sides of the equation, like this:
\(\sqrt[]{x^2}=\sqrt[]{\frac{9}{5}}\)Solving the operations:
\(\begin{gathered} x=\sqrt[]{\frac{9}{5}} \\ x=\pm\frac{3}{\sqrt[]{5}} \end{gathered}\)Since the square root has positive and negative solutions, the equation has two possible solutions, these are:
\(\begin{gathered} x=\frac{3}{\sqrt[]{5}}\text{ and} \\ x=-\frac{3}{\sqrt[]{5}} \end{gathered}\)Related Questions
Solve for x.
x+6= √2x+29 +9
Answers
The solution to the equation is x = 10 or x = -2.
What is an equation?An equation refers to a mathematical expression showing that two expressions are equal.
It must have variables (e.g. a, c, x, y), constants (like 1, 13, 50, etc), and mathematical operations (like +, -, *, /).
To solve for x, we shall start with the given equation:
x + 6 = √(2x + 29) + 9
Subtract 9 from both sides:
x - 3 = √(2x + 29)
Square both sides:
\((x - 3)^2\) = 2x + 29
Expand the left side:
\(x^2\) - 6x + 9 = 2x + 29
We then subtract 2x and 9 from both sides:
\(x^2\) - 8x - 20 = 0
Next, actor the quadratic equation:
(x - 10)(x + 2) = 0
Therefore, the equation x = 10 or x = -2
Learn more about equation at brainly.com/question/29174899
#SPJ1
SOMEONE PLEASE HELPP MEE
Answers
The end-points of the line segment will be negative 1.25 and 0.25.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
The length of the line segment is 1.50 units and the midpoint of the line segment is negative 0.50. Then the end-points of the line segment are given as,
⇒ - 0.50 ± (1.50) / 2
Simplify the expression, then we have
⇒ - 0.50 ± (1.50) / 2
⇒ - 0.50 - (1.50) / 2, - 0.50 + (1.50) / 2
⇒ - 0.50 - 0.75, - 0.50 + 0.75
⇒ - 1.25, 0.25
The end-points of the line fragment will be negative 1.25 and 0.25.
More about the number line link is given below.
https://brainly.com/question/13189025
#SPJ1
Mason is ordering a one-topping pizza. He can get either thin crust or hand tossed and can choose from 15 toppings. How many different pizzas can Mason order?
A. 15
B. 17
C. 7
D. 30
Answers
Find the value of x please help
Answers
Answer:
4
Step-by-step explanation:
8÷2=4
4x+1=20
that's all
A fish is 12 meters below the surface of the ocean. What is its elevation?
Answers
Answer:
-12 meters because it is BELOW the surface of the ocean
differenciate the Function 1/ X3
Answers
Step-by-step explanation:
To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:
Write the function: f(x) = 1/x^3.
Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).
Differentiate the function: In our case, n = -3, so the derivative is:
f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.
Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.
If someone can help me I’ll give you GOlD and a 5 star rating I need 9-12!!!!! Please help Prob and Stats
Answers
Answer:
9: 60
10: 28
11: 16
12: 44
Step-by-step explanation:
if 12 is right, I'm assuming the question is asking what the difference in percentage between the shows are.
Please look at the photo. Thank you.
Answers
The output value of (f∘g)(x) is: \((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)
The domain of (f∘g)(x) is (-∞, -3) U (-3, ∞).
How to determine the corresponding output value for this function?In this scenario, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations (multiplication) in simplified form as follows;
\(f(x) = \frac{x-6}{x +3}\)
g(x) = 4x - 15
Next, we would write the numerators and denominators in factored form as follows;
(x - 6)(4x - 15)
4x² - 15x - 24x + 60
4x² - 29x + 60
Now, we can derive the corresponding composite function of f(x) and g(x);
\((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)
For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;
x + 3 ≠ 0
x ≠ -3
Domain = (-∞, -3) U (-3, ∞).
Read more on domain here: brainly.com/question/17440903
#SPJ1
what is the measure of x
Answers
Answer:
x = 9 inches
Step-by-step explanation:
You want the value of x in the similar triangles shown.
ProportionCorresponding sides are proportional. This means the ratio of the horizontal side of the triangle to the vertical side is the same for both.
6/4 = (6+x)/10
15 = 6 +x . . . . . . . . multiply by 10
9 = x . . . . . . . . . subtract 6
The measure of x is 9 inches.
__
Additional comment
You could also write the proportion ...
6/4 = x/(10 -4)
x = 36/4 = 9 . . . . . . . multiply by 6
You can see this if you draw a horizontal line through the figure at the top of the side marked 4 in.
<95141404393>
Please help!!! I suck at algebra and this is middle school stuff:((
Answers
Answer:
77
Step-by-step explanation:
1. solve the first part by plugging in 7 for y.
14(7)+37/5
98+37/5
135/5
27
2. then solve the second part by plugging in 7 for y.
8(2(7)-1)
8(14-1)
104
3. then subtract 27 from 104
104-27=77
Howard's pawn shop bought an antique clock at the wholesale price of $725. Howard marked up the price of the clock
30%. What was the list price of the clock?
holour
Answers
Answer:
942.50
Step-by-step explanation:
725×30% or 0.3 = 217.5
217.5+725=942.5
wants to tile the surface of a rectangular storage case that is inches long, inches wide, and inches tall. If he uses all green tiles, how many tiles will he need?
Answers
The surface area of the rectangular prism is 396 square inches
He will need 504 tlles
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
7 in by 12 in by 6 in
The surface area of the rectangular prism is calculated as
Area = 2 * (7 * 12 + 7 * 6 + 12 * 6)
Evaluate
Area = 396
Hence, the area is 396 square inches
The number of tiles is 7 * 12 * 6 = 504
Read more about surface area at
brainly.com/question/26403859
#SPJ1
Question
wants to tile the surface of a rectangular storage case that is 7 inches long, 12 inches wide, and 6 inches tall. If he uses all green tiles, how many tiles will he need?
A rectangular parking lot has a perimeter of 254 inches. The length of the parking lot is 77 inches more than the width. Find the length and the width.
Answers
Answer:
L = 102 inches, w = 25 inches
Step-by-step explanation:
We are looking for the length and width of a rectangle. Since the length is defined in terms of the width, we let W= width. The length is 77 inches more than the width, so we let W+77=L. The following formula for the perimeter relates all of the given information:
P=2L+2W
So we substitute in the given information and solve for W to find
254254254254−154100100425=2(W+77)+2W=2W+154+2W=4W+154=4W+154−154=4W=4W4=W
The width is 25 inches. The length is then
L=W+77=25+77=102
or 102 inches.
The length of the parking lot is 102 inches and the width of the parking lot is 25 inches.
What is a perimeter?The perimeter of the rectangle is defined as the sum of all the sides of the rectangle. The formula to calculate the perimeter is written as,
P = 2 ( L + W )
The length is 77 inches more than the width, so we let W+77=L. The following formula for the perimeter relates to all of the given information:
P=2L+2W
Substitute in the given information and solve for W to find
P = 2L + 2(W+77)
The width is 25 inches. The length is then,
L = W+77
L = 25+77
L = 102 Inches
W = L - 77
W = 102 - 77
W = 25 inches
To know more about perimeter follow
https://brainly.com/question/19819849
#SPJ2
Which of the following best defines the sequence shown?
8, 24, 72, 216, ...
Answers
Answer:
Option (2)
Step-by-step explanation:
Given sequence is,
8, 24, 72, 216........
1st term of the sequence 'a' = 8
Ratio of 2nd and 1st term = \(\frac{24}{8}=3\)
Ratio of 3rd and 2nd term = \(\frac{72}{24}=3\)
There is a common ratio of 'r' = 3 in each successive and previous term.
Therefore, it's a geometric sequence.
Since, nth term of a geometric sequence is given by,
\(T_n=a(r)^{n-1}\)
Therefore, function representing the geometric sequence is,
f(n) = \(f(n)=8(3)^{n-1}\)
Option (2) is the answer.
50 POINTS A point in the figure is selected at random. Find the probability that the point will be in the shaded region.
about 70%
about 80%
about 95%
about 67%
Answers
The first step that we need to take before attempting to solve the problem is to understand what the problem is asking us to do and what they are giving us to help solve the problem. Looking at the problem statement they are asking for us to determine the probability that a point will randomly be plotted in the shaded region. We are not given much of anything else which means that we will need to use our own numbers.
The picture that was provided has a square with four equal circles inside right next to each other. Therefore, we can say that each side of the square is going to be 2 units which causes the diameter of the circle to be half that or 1 unit. We can go even further and determine that the radius is going to be 0.5 units for each circle. Let's determine the area of all the shapes.
Area of the square
\(A_{square} = s^2\)\(A_{square} = (2\ units)^2\)\(A_{square} = (2)^2 * (units)^2\)\(A_{square} = 4\ units^2\)Area of a circle
\(A_{circle} = \pi * r^2\)\(A_{circle} = \pi * (0.5\ units)^2\)\(A_{circle} = \pi * (0.5)^2 * (units)^2\)\(A_{circle} = \pi * (0.25\ units)^2\)\(A_{circle} = 0.7854\ units^2\)The area that we got from the circle only gives us the area for one of the circles so we need to multiply the number by four to give us the total area of the circles.
Total area of the circles
\(A_{circles} = 0.7854\ units^2 * 4\)\(A_{circles} = 3.1416\ units^2\)Now that we determined the area of both the square and the circles we can move onto the part of finding the probability of a point randomly landing on a circle.
Determine the probability
\(\textsf{probability = circles / square}\)\(\textsf{probability = } \frac{3.1416\ units^2}{4\ units^2}\)\(\textsf{probability = } \frac{3.1416}{4}\)\(\textsf{probability = } 0.785\)However, now that we have determined what the probability, looking at the answer options we can see that all of the are in percentages. So let's convert our probability into a percentage.
Convert to percentage
\(\textsf{probability = } 0.785 * 100\)\(\textsf{probability = } 78.5\%\)Therefore, looking at the options given, the option that would best fit this choice would be option B, about 80%.
What is the value of s?
units
KY
$
00
8
15
D
Answers
Answer:
Too Short Zoom In And Repost And I Can Help
Step-by-step explanation:
Zoom In
Answer:
17 units
Step-by-step explanation:
The sides of the right triangle are 8 and 15. Thehypotenuse is s:
8^2 + 15^2 = x^2
289 = x^2
x = 17 units
.
Which function is equivalent to g(x)=x2 - 15%-542
O
g(x)= ( x-18)( x + 3)
g(x)= ( x-9)( x + 6)
g(x) = (x+18)(x-3)
g(x)= (x+9)(x-6)
Answers
Answer:
fortnite
Step-by-step explanation:
need points
Find the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0)
Answers
The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.
To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.
The slope of a line can be found using the formula:
slope = (change in y) / (change in x)
For the line containing (1,2) and (5,3), the slope is:
slope1 = (3 - 2) / (5 - 1) = 1 / 4
To find the slope of the line containing (x,4) and (3,0), we use the same formula:
slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)
Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.
So, we can set up the equation:
-1 / (1/4) = -4 / (3 - x)
Simplifying this equation:
-4 = -4 / (3 - x)
To remove the fraction, we can multiply both sides by (3 - x):
-4(3 - x) = -4
Expanding and simplifying:
-12 + 4x = -4
Adding 12 to both sides:
4x = 8
Dividing both sides by 4:
x = 2
For more such questions on line.
https://brainly.com/question/280216
#SPJ8
pls answer all this questionsd the process pls I nee
answers
I Rs 624000
ii rs 1164
iii rs 10476
Answers
The salary structure is explained in the answer below.
Given that the monthly salary of Swarnima is Rs 48,000, she is eligible fir 1% income tax,
She also pays in CIT and receives 10% back in income tax,
Her annual income = 48,000 × 12 = Rs 5,76,000
So, income tax to be paid by her = 5,76,000 × 10% = 5,76,000 × 0.1
= Rs 57,600
Now, since pays in CIT and receives 10% back =
57,600 × 10% = Rs 5760
Therefore, she receives Rs 5760 after paying income tax.
Learn more about income tax click;
https://brainly.com/question/17075354
#SPJ1
quadratic formula decimal answer solve the equation to the nearest tenth
Answers
First, recall that given the equation
\(ax^2+b+c=0\)The solutions are given by
\(x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)where the sign in the middle means that we get one root by taking a plus sign and we get the other root by taking a minus sign.
In our case, we have a=1, b=-6 and c=-41. So the solutions of this equation are given by
\(x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(-41)}}{2}=\frac{6\pm\sqrt[]{36+164}}{2}=\frac{6\pm\sqrt[]{200}}{2}\)Note that
\(\sqrt[]{200}=\sqrt[]{100\cdot2}=\sqrt[]{100}\cdot\sqrt[]{2}=10\sqrt[]{2}\)Then
\(x=\frac{6\pm10\sqrt[]{2}}{2}=3\pm5\sqrt[]{2}\)taking sqrt(2) as 1.4142, we get
\(x=3+5\cdot\sqrt[]{2}=10.071\approx10\)and
\(x=3-5\sqrt[]{2}=-4.071\approx-4\)Which is the equation of a parabola with a directrix at y = −3 and a focus at (5, 3)?
Answers
The equation of a parabola with a directrix at y = −3 and a focus at (5, 3) is y=1/12(x - 5)² .
What is Parabola?A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
Given that the directrix of parabola is at y=-3.
Focus at (5, 3)
parabola with equation (x - h)² = 4p(y - k)
p = 3 because the distance from the focus to the directrix is 6 and p = 6/2.
The vertex (5, 0)
Substitute h as 5 and k as 0.
(x - 5)² = 4(3)(y - 0)
(x - 5)² = 12y
Divide both sides by 12
y=1/12(x - 5)²
Hence, the equation of a parabola with a directrix at y = −3 and a focus at (5, 3) is y=1/12(x - 5)² .
To learn more on Parabola click:
https://brainly.com/question/21685473
#SPJ1
What is the equivalent to the product below when x>_0?
√5x² •√15x²
Answers
√(5x²) • √(15x²) = √(5x² * 15x²)
Using the property of square roots that √(a * b) = √a * √b, we can simplify further:
√(5x² * 15x²) = √(5 * 15 * x² * x²)
Next, we simplify the numerical part:
√(5 * 15 * x² * x²) = √(75 * x² * x²)
Since x ≥ 0, x² is always non-negative, so we can remove the square root:
√(75 * x² * x²) = x * x * √75
Finally, we simplify the square root of 75:
x * x * √75 = x² * √75
Therefore, the equivalent expression is x² * √75 when x ≥ 0.
Which of the following is the probability that something in the sample space will occur?
a. 0
b. 1
c. 0.50
d. impossible to determine from the given information
Answers
The probability that something in the sample space will occur is option (b) 1
Sample space is the set of all possible outcomes in an experiment
The probability is the possibility of occurrence of a random event. The probability is the ratio of the number of favorable outcomes to the total number of outcomes. The probability may varies from zero to one.
The probability = Number of favorable outcomes/ Total number of outcomes.
So here the probability that something in the sample space will occur is 1. Because it contains all the possible outcomes.
Hence, the probability that something in the sample space will occur is option (b) 1
Learn more about probability here
brainly.com/question/11234923
#SPJ1
Please help find the answer. Thank You!
Answers
Answer:
Step-by-step explanation:
208
what is a possible scale factor for the dilation of the quadrilateral ABCD?
a) 2
b) 3/2
c) 1/2
d) 3
explain your answer choice.
Answers
Answer:
\(\dfrac {1}{2}\)
Step-by-step explanation:
According to the diagram
if
The center is o
Then Distance from O to B'C'=1
Distance from O to BC=1+1=2
\(\therefore\sf Ratio\:is\:1:2.\)
More to know:-Formulas related to surface area and volume:-\(\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}\)
Marcie's gross pay is $360.00 After deductions of 10% what is her net pay?
Answers
Answer: 324.00 i think
Step-by-step explanation:
what is the answer and explain how you got it
Answers
Answer:
290
Step-by-step explanation:
multiply the volume value by 10
Dylan is conducting an experiment and wants to choose the ball with the lowest density.
Ball A = diameter 7cm, mass 1.742kg
Ball B = diameter 6cm, mass 1.040kg
4
Volume of sphere =
3 773
Density
= mass = volume
TT = 3.142
Which ball should he choose?
Answers
Dylan should choose Ball B which having lowest density.
What is volume of spere?
The volume of a sphere is calculated using the formula volume = 4/3πr³ where r is the sphere's radius.
Given that:
Ball A = diameter 7cm, mass 1.742kg
Ball B = diameter 6cm, mass 1.040kg
As we know that,
volume of a sphere =4/3πr³
1) For Ball A,
volume of a Ball A = 4/3π(3.5)³
volume of a Ball A = 179.6 cm³
given mass for Ball A is 1.742 kg = 1742 g.
So, Density = \(\frac{mass}{volume}\)
Density of Ball A will be 9.7 g/cm³.
2) For Ball B,
volume of a Ball B = 4/3π(3)³
volume of a Ball B = 113.11 cm³
given mass for Ball B is 1.040 kg = 1O40 g.
So, Density = \(\frac{mass}{volume}\)
Density of Ball B will be 9.19 g/cm³.
By comparing density of both balls,
Density of Ball A > Density of Ball B
Hence, Dylan should choose Ball B which having lowest density.
To know more about Volume of sphere visit,
https://brainly.com/question/22807400
#SPJ1
What meaning of the statement this?
Answers
The statement is discussing Proposition 3.5, which provides a strategy or method for finding the subgroups of any finite group.
What is the strategy?The strategy involves listing all the cyclic subgroups first. Then, subgroups with two generators can be found by taking the union of two cyclic subgroups and considering inverses. Subgroups with three generators can be found by taking the union of a subgroup with two generators and a cyclic subgroup, and so on.
The statement also mentions that if the group is not too large, this strategy can quickly yield all subgroups. Additionally, it suggests making use of Lagrange's theorem (Corollary 3.14) to further aid in finding the subgroups.
This process can be repeated to find all subgroups of the given finite group. The statement also suggests that using Lagrange's theorem (specifically, Corollary 3.14) can help in efficiently finding all the subgroups, especially if the group is not too large.
Read more about subgroups here:
https://brainly.com/question/30865357
#SPJ1
What meaning of the statement this?
Proposition 3.5 provides a strategy for finding the subgroups of any given finite group. First list all cyclic subgroups. Subgroups with two generators are also generated by the union of two cyclic subgroups (which is closed under inverses). Subgroups with three generators are also generated by the union of a subgroup with two generators and a cyclic subgroup; and so forth. If the group is not too large this quickly yields all subgroups, particularly if one makes use of Lagrange's theorem (Corollary 3.14 below).
Given the definitions of f(x) and g(x) below, find the value of (fog)(-3).
f(x) = 3x² - 7x-3
g(x) = -4x - 10
Answers
The value of the composite function (f o g)(3) is 1603
How to evaluate the composite function?The functions are given as
f(x) = 3x² - 7x - 3
g(x) = -4x - 10
Next, calculate (f o g)(x) using
(f o g)(x) = f(g(x))
So, we have
(f o g)(x) = 3(-4x - 10)² - 7(-4x - 10) - 3
Substitute 3 for x.
So, we have
(f o g)(3) = 3(-4 x 3 - 10)² - 7(-4 x 3 - 10) - 3
Evaluate
(f o g)(3) = 1603
Hence, the value of the composite function (f o g)(3) is 1603
Read more about composite function at
https://brainly.com/question/10687170
#SPJ1