x^2-15=0 Find the number of real number solutions for the equation.
1.1 Factoring: x2-15
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 15 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
2.1 Solve : x2-15 = 0
Add 15 to both sides of the equation :
x2 = 15
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 15
The equation has two real solutions
These solutions are x = ± √15 = ± 3.8730
Final answer:
Explaining the number of real number solutions for the given quadratic equation x²-15=0.
Explanation:
x²-15=0
To find the number of real number solutions for the equation, we start by setting the expression to zero:
x² - 15 = 0
x² = 15
x = ±√15
Therefore, the equation has two real number solutions, which are ±√15.
PLEASE HELP
8.02
1. Find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by sixty four = 1.
A) Center: (0, 0); Vertices: (-10, 0), (10, 0); Foci: (-8, 0), (8, 0)
B) Center: (0, 0); Vertices: (0, -10), (0, 10); Foci: (0, -8), (0, 8)
C) Center: (0, 0); Vertices: (-10, 0), (10, 0); Foci: (-6, 0), (6, 0)
D) Center: (0, 0); Vertices: (0, -10), (0, 10); Foci: (0, -6), (0, 6)
2. Find the center, vertices, and foci of the ellipse with equation 2x2 + 6y2 = 12.
A) Center: (0, 0); Vertices: point negative square root of six comma zero and point square root of six comma zero ; Foci: (-2, 0), (2, 0)
B) Center: (0, 0); Vertices: (0, -6), (0, 6); Foci: Ordered pair zero comma negative four square root two and ordered pair zero comma four square root two ;
C) Center: (0, 0); Vertices: point zero comma negative square root of six and point zero comma square root of six ; Foci: (0, -2), (0, 2)
D) Center: (0, 0); Vertices: (-6, 0), (6, 0); Foci: Ordered pair negative four square root two comma zero and ordered pair four square root two comma zero
3. Graph the ellipse with equation x squared divided by twenty five plus y squared divided by four = 1.
A) A vertical ellipse is shown on the coordinate plane centered at, five, two, with vertices at, five, seven, and five, negative three and minor axis endpoints at three, two, and seven, two.
B) A horizontal ellipse is shown on the coordinate plane centered at five, two, with vertices at zero, two, and ten, two and minor axis endpoints at five, four and five, zero.
C) A vertical ellipse is shown on the coordinate plane centered at the origin with vertices at zero, five and zero, negative five and minor axis endpoints at, negative two, zero and two, zero.
D) A horizontal ellipse is shown on the coordinate plane centered at the origin with vertices at, negative five, zero and, five, zero and minor axis endpoints at, zero, two and zero, negative two.
4. Find an equation in standard form for the ellipse with the vertical major axis of length 6 and minor axis of length 4.
A) x squared divided by two plus y squared divided by three = 1
B) x squared divided by nine plus y squared divided by four = 1
C) x squared divided by three plus y squared divided by two = 1
D) x squared divided by four plus y squared divided by nine = 1
5. An elliptical riding path is to be built on a rectangular piece of property, as shown below.
A vertical ellipse is shown centered on the coordinate plane, surrounded by a rectangle of equal length and width.
The rectangular piece of property measures 8 mi by 6 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides.
What do all members of the family of linear functions f(x)=1m(x+3) have in common?
All linear function has a constant slope and degree as 1.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
Linear functions are lines in the coordinate and describe itself that the slope will be the same irrespective of the point.
A linear function is given by ;
y = mx + x where m is slope.
As we can see the degree of x and y both are 1 so the linear function has a degree of 1.
Hence "All linear function has a constant slope and degree as 1".
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simplify:
...............
a cone is not a polyhedron. true or false?
Answer:
The answer is true
Step-by-step explanation:
we know that
A polyhedron is is a solid with flat faces and a cone is a solid with a curved side
therefore
A cone is not a polyhedron ( Is true)
Solve for x. 35x+5=45 Enter your answer in the box. x =
A real estate broker sold your house for $72,000. The broker's commission was 6% of the selling price. How much would you get for the house after the commission is paid? A. $70,800 B. $76,320 C. $67,680 D. $73,200
Kite QRST has sides RS, ST, TQ and QR. What are the diagonals of this figure? Select all that apply.
Mila graphs the point A
(
5
,
0
)
5,0 on a coordinate plane.
Which of the following statements are true?
Select all that apply.
A.
Point A is 5 units to the right of the origin and up 1 unit.
B.
The x-coordinate of point A is 5.
C.
The y-coordinate of point A is 5.
D.
Point A is on the y-axis.
E.
Point A is on the x-axis.
what are the answers
Answer:
B,E
Step-by-step explanation:
B,E
Emma, Steve, Maria, and George are comparing the solution of a math assignment problem below.
Select the student who correctly subtracted the rational expressions.
Answer:
A. Steve
Step-by-step explanation:
We are given the expression, [tex]\frac{1}{x-1}-\frac{3}{x^{2}+2x-3}[/tex].
So, upon simplifying the expression, we get,
[tex]\frac{1}{x-1}-\frac{3}{x^{2}+2x-3}[/tex]
implies [tex]\frac{1}{x-1}-\frac{3}{(x-1)(x+3)}[/tex]
i.e. [tex]\frac{1(x+3)-3}{(x-1)(x+3)}[/tex]
i.e. [tex]\frac{x+3-3}{(x-1)(x+3)}[/tex]
i.e. [tex]\frac{x}{(x-1)(x+3)}[/tex]
So, from the options, we see that,
Steve has correctly subtracted the rational expressions.
Thus, option A is correct.
If a right triangle has sides of length a, b and c and if c is the largest, then it is called the "hypotenuse" and its length is the square root of the sum of the squares of the lengths of the shorter sides (a and b). assume that variables a and b have been declared as doubles and that a and b contain the lengths of the shorter sides of a right triangle: write an expression for the length of the hypotenuse. submit
The expression for the length of the hypotenuse is c = [tex]\sqrt{a^2 + b^2}[/tex].
The length of the hypotenuse of a right triangle can be calculated using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse c is equal to the sum of the squares of the lengths of the other two sides a and b.
So, the expression for the length of the hypotenuse c is:
c = [tex]\sqrt{a^2 + b^2}[/tex]
This expression calculates the length of the hypotenuse given the lengths of the shorter sides a and b.
NEED HELP ASAP PLEASE HELP
What are the measures of the two angles in the figure below?
Select one:
a. 95° and 85°
b. 100° and 80°
c. 105° and 75°
d. 110° and 70°
Math help? One question?
The equation y = 8.1x models the relationship between the number of hours Alexander works, x, and the dollar amount he earns, y. Which is the graph of the equation y = 8.1x? Image for option 1 Image for option 2 Image for option 3
Answer with explanation:
⇒ y=8.1 x
This is a Linear equation depicting linear relationship between y and x which is between the number of hours Alexander works, x, and the dollar amount he earns, y.
To determine a line you need two points.
→Put, x=0,in y=8.1 x, gives y=0 gives a Point (0,0).
→Put,x=1 gives , y=8.1 × 1→y=8.1 gives another point (1,8.1).
→So, Drawn a line passing through (0,0) and (1, 8.1),which is the required image of the equation given.
Cesar is building a shelf at an angle so that it appears to be leaning against the wall. The shelf touches the wall 7 ft. above the floor and the distance between the floor from the wall to the front of the shelf is 1.5 ft. What is the angle the shelf makes with the floor?
A. 77.9 degrees.
B. 77.6 degrees.
C. 12.1 degrees.
D. 12.4 degrees.
A 15-ft. building casts a shadow of 12 ft. What is the approximate angle of inclination of the sun?
A. 51.3 degrees.
B. 53.1 degrees.
C. 36.9 degrees.
D. 19.2 degrees.
1) The angle the shelf makes with the floor is approximately 77.905°. (Choice A)
2) The approximate angle of inclination of the sun is approximately 51.340°. (Choice A)
How to apply trigonometric relations to determine angles
1) In this case we know that shelf has a vertical height ([tex]h[/tex]) of 7 feet and a horizontal distance between the floor from the wall to the front of the shelf ([tex]l[/tex]) is 1.5 feet. The angle ([tex]\theta[/tex]), in degrees, is determined by tangent function:
[tex]\theta = \tan^{-1} \frac{7\,ft}{1.5\,ft}[/tex]
[tex]\theta \approx 77.905^{\circ}[/tex]
The angle the shelf makes with the floor is approximately 77.905°. (Choice A) [tex]\blacksquare[/tex]
2) The length of the shadow ([tex]l[/tex]) is 12 feet and the height of the building ([tex]h[/tex]) is 15 feet. The angle of inclination of the sun is determined by tangent function:
[tex]\theta = \tan^{-1} \frac{15\,ft}{12\,ft}[/tex]
[tex]\theta \approx 51.340^{\circ}[/tex]
The approximate angle of inclination of the sun is approximately 51.340°. (Choice A) [tex]\blacksquare[/tex]
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Lindesy wants a new bike that costs $230. Her father says that if she saves up 30% of the cost he will pay the rest. How much money does Lindesy need to save?
Meg constructed triangle POQ and then used a compass and straightedge to accurately construct line segment OS, as shown in the figure below:
Which could be the measures of angle POS and angle POQ?
Measure of angle POS is 25 degrees, measure of angle POQ is 40 degrees
Measure of angle POS is 25 degrees, measure of angle POQ is 30 degrees
Measure of angle POS is 20 degrees, measure of angle POQ is 40 degrees
Measure of angle POS is 20 degrees, measure of angle POQ is 30 degrees
The correct answer is:
Measure of angle POS is 20 degrees, measure of angle POQ is 40 degrees
Explanation:
OS is an angle bisector of ∠POQ. This means it splits ∠POQ into two congruent pieces.
This tells us that ∠POS+∠SOQ = ∠POS+∠POS = ∠POQ.
If m∠POS = 20, this means that m∠POQ = 20+20 = 40°.
What is the density of a cube with sides of 4 cm and a mass of 512g?
The density of the cube whose volume is 64 cm³ and mass is 512 g is given by the equation D = 8 g/cm³
What is the Volume of a Cube?
The formula of volume of the cube is given by:
Volume of Cube = a x a x a
Volume of Cube = a³
where a is the length of its sides or edges
Given data ,
Let the density of the cube be represented as D
Let the volume of the cube be represented as V
Now , the equation will be
The mass of the cube = 512 g
The side length of the cube a = 4 cm
So , Volume of Cube = a³
Substituting the values in the equation , we get
Volume of Cube V = 4 x 4 x 4
Volume of Cube V = 64 cm³
Now ,
The density of the cube D = mass of the cube / Volume of Cube
Substituting the values in the equation , we get
The density of the cube D = 512 / 64
The density of the cube D = 8 g/cm³
Therefore , the value of D is 8 g/cm³
Hence , the density of the cube is 8 g/cm³
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Which are solutions of the equation 4x2 – 7x = 3x + 24? Check all that apply. x = –4 x = –3 x = -3/2 x = 2/3 x = 2 x = 4
Answer: b. -3 or 2
Step-by-step explanation:
the longest side of an acute isosceles triangle is 8 centimeters. rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?
A:4.0
B:4.1
C:5.6
D:5.7
Joseph wants to cover a rectangular box with wrapping paper. The length of the box is 2 feet, its width is 1 foot, and its height is 1 foot. The cost of wrapping paper is $0.80 per square foot. How much will it cost Joseph to cover the box with wrapping paper?
If the minute hand of a clock is 20 degrees behind the hour hand at this moment, then in 18 minutes, the minute hand will be how many degrees ahead of the hour hand?
Answer:
I got 79 degrees in my pocket, gonna solve this math problem, its just like a pick on a locket, no wonder your grades are gonna skyrocket.
Step-by-step explanation:
The number of degrees ahead of the hour hand will be 128 degrees.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
If the minute hand of a clock is 20 degrees behind the hour hand at this moment.
We know that the rotation of the minute hand in each minute is 6°.
The angle when minutes shows 18 minutes is given as,
⇒ 18 x 6°
⇒ 108°
The number of degrees ahead of the hour hand will be given as,
⇒ 108° + 20°
⇒ 128°
The number of degrees ahead of the hour hand will be 128 degrees.
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A horse race has 14 entries and one person owns 5 of those horses. assuming that there are no ties, what is the probability that those five horses finish first comma second comma third comma fourth comma and fifth (regardless of order)
Final answer:
The probability that the five horses finish first through fifth in any order is 0.0004995 or 0.04995%.
Explanation:
The probability that the five horses owned by one person finish first through fifth, regardless of order, in a horse race with 14 entries can be calculated using combinatorics. First, we determine the number of ways to choose 5 horses out of 14 to finish in the top 5 positions, which is C(14,5). Then we calculate the number of favorable outcomes, which, since the order doesn't matter for the set of horses owned by the person, is just 1. To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes, resulting in 1/C(14,5). Using the formula for combinations C(n,r) = n! / (r! * (n-r)!), where n is the total number of entries and r is the number of horses owned by the person, we can calculate the exact probability.
The formula gives us C(14,5) = 14! / (5! * (14-5)!) = 14! / (5! * 9!) = 2002. Therefore, the probability is 1/2002, which simplifies to 0.0004995 or 0.04995%.
Which expression is a rational number? A) ( 25 + 25 )2 B) ( 25 + 50 )2 C) ( 50 + 75 )2 D) ( 25 + 72 )2
All expressions given, A, B, C, and D, are rational numbers. This is because they all result in a number that can be expressed as the quotient of two integers when the operations are performed according to the order of operations and squared.
A rational number is a number that can be expressed as the quotient or fraction rac{p}{q} of two integers, a numerator p and a non-zero denominator q. To determine which expression represents a rational number, we look for an outcome that is expressible as such a fraction after carrying out any operations involved in the expression.
Let's evaluate whether the expressions given result in rational numbers when the operations are performed:
A) ( 25 + 25 )2 = [tex](5+5)^2[/tex] = [tex]10^2[/tex] = 100 which is a rational number.B) ( 25 + 50 )2 = [tex](5+10)^2[/tex] = [tex]15^2[/tex] which is a rational number.C) ( 50 + 75 )2 = [tex](2+3)^2[/tex] = [tex]5^2[/tex] which is a rational number.D) ( 25 + 72 )2= [tex](5+14.4)^2[/tex] = [tex]19.4^2[/tex] which is not a perfect square but still a rational number since 19.4 is a rational number and squaring it results in another rational number.Therefore, all given expressions A, B, C, and D result in rational numbers when squared.
Option A, B, C, and D is a rational number.All given expressions result in rational numbers, as each step of their calculations simplifies to integers. Each integer can be expressed as the quotient of two integers, confirming they are rational.
To determine which expression results in a rational number, let's evaluate each option step by step. A rational number is any number that can be expressed as the quotient of two integers.
(25 + 25)2: First, we simplify inside the parentheses: 25 + 25 = 50. Then we square the result: 502 = 2500.(25 + 50)2: Simplify inside the parentheses: 25 + 50 = 75. Then we square the result: 752 = 5625.(50 + 75)2: Simplify inside the parentheses: 50 + 75 = 125. Then we square the result: 1252 = 15625.(25 + 72)2: Simplify inside the parentheses: 25 + 72 = 97. Then we square the result: 972 = 9409.All the results are integers, which are rational numbers because any integer n can be expressed as n/1. Therefore, all given expressions result in rational numbers.
The value of x is
.
we know that
The Exterior Angles of a Polygon add up to [tex]360[/tex] degrees
so
in this problem
[tex]130+134+x=360[/tex]
Solve for x
[tex]264+x=360[/tex]
Subtract [tex]264[/tex] from both sides
[tex]264+x-264=360-264[/tex]
[tex]x=96\ degrees[/tex]
therefore
the answer is
the value of x is [tex]96\ degrees[/tex]
The beginning balance in a savings account is $64.98. After a deposit of $73.87, two withdrawals of $51.00 and $23.50, and $1.15 of interest earned, what is the balance? $138.85 $65.50 $64.35 $87.85
Your teacher took a survey of student’s eye colors. She found that 15 students have brown eyes, 6 students have green eyes, and 4 students have blue eyes. Make a table showing the frequency
What is the approximate area of the shaded sector in the circle shown below
A.30.7 in^2
B.246 in^2
C.15.4 in^2
D.491 in^2
Answer: IT WAS B. -_-
Answer:
246 in^2
Step-by-step explanation:
just took the test
Convert 302 inches into yards
PLEASE HELP
Andre must pay a co-pay of $15 for an office visit. his insurance company will then pay 80% of the cost of the visit. how much will andre pay for an office visit that costs $310
$62
$65
$77
$80
Answer:
C. $77
Step-by-step explanation: