Answer:
g = 16Step-by-step explanation:
[tex]Domain:\\\\2g+8\neq0\ \wedge\ g^2-16\neq0\\\\g\neq-4\ \wedge\ g\neq4\\====================\\\\\dfrac{3}{2g+8}=\dfrac{g+2}{g^2-16}\qquad\text{cross multiply}\\\\3(g^2-16)=(2g+8)(g+2)\\\\\text{use the distributive property}:\ a(b+c)=ab+ac\\\text{and}\ FOIL:\ (a+b)(c+d)=ac+ad+bc+bd\\\\(3)(g^2)+(3)(-16)=(2g)(g)+(2g)(2)+(8)(g)+(8)(2)\\\\3g^2-48=2g^2+4g+8g+16\qquad\text{subtract}\ 2g^2\ \text{from both sides}\\\\g^2-48=12g+16\qquad\text{subtract}\ 12g\ \text{and}\ 16\ \text{from both sides}[/tex]
[tex]g^2-12g-64=0\\\\g^2+4g-16g-64=0\\\\g(g+4)-16(g+4)=0\\\\(g+4)(g-16)=0\iff g+4=0\ \vee\ g-16=0\\\\g+4=0\qquad\text{subtract 4 from both sides}\\g=-4\notin D\\\\g-16=0\qquad\text{add 16 to both sides}\\g=16\in D[/tex]
If y is 5 when x is 2.5 and y varies directly with x, find y when x is 10
Answer:
If x varies directly as y, then x=ky. y=5 and x=2.5 are substituted into x=ky to find k.
2.5=5k
k=2.5/5
k=5.
K =5 is substituted in x=ky to find y where x is 10.
x=5y
10=5y
y=10/2
y=2
Answer: The required value of y is 20.
Step-by-step explanation: Given that y is 5 when x is 2.5 and y varies directly with x.
We are to find the value of y when x is 10.
According to the given information, we can write
[tex]y\propto x\\\\\Rightarrow y=kx~~~~~~~~~~[\textup{where k is the constant of proportionality}][/tex]
When y = 5 and x = 2.5, then we have
[tex]5=k\times2.5\\\\\Rightarrow k=\dfrac{5}{2.5}\\\\\Rightarrow k=2.[/tex]
So, we get
[tex]y=2x.[/tex]
Therefore, when x = 10, then the value of y is
[tex]y=2\times10=20.[/tex]
Thus, the required value of y is 20.
If sin pheta < 0 and tan pheta < 0 then:
sin(θ) < 0 is another way to say sin(θ) is negative.
tan(θ) < 0 is another way to say tan(θ) is negative.
let's recall that, on the III Quadrant sine and cosine are both negative, and thus the tangent is positive, recall tan(θ)=sin(θ)/cos(θ).
on the IV Quadrant however, sine is negative and cosine is positive, thus tangent is negative.
(50 points! please help me!)a store was trying to sell a bed set for $475. after a while, the marked the price tag down 35% off . if tax is 5% (of the sale price), how much would the bed set cost?
Answer:
$324.19
Step-by-step explanation:
First, find the price when marked down. Multiply 475 with 0.35:
475 x 0.35 = 166.25
Subtract 166.25 from the total cost:
475 - 166.25 = 308.75
Now, solve for the tax. Tax is 5% (0.05). Multiply 0.05 with the new cost:
308.75 x 0.05 = ~$15.44
Add 15.44 to the sales price:
308.75 + 15.44 = $324.19
$324.19 is your answer.
~
Factor k2 - 81.
(k + 9)(K + 9)
(k - 9)(k - 9)
(k - 9)(k + 9)
Answer:
(
k
+
9
)
(
k
−
9
)
(k+9)(k-9)
Step-by-step explanation:
Answer:
It's C
Step-by-step explanation:
q2 + 3q - 18 = (q + 6)(q - ?)
The strength of a bar magnet's magnetic field decreases with distance according to what is known as an inverse cube law; multiplying the distance from the magnet by a factor of k divides the magnetic field strength by a factor of k^3. Suppose the magnetic field strength of the magnet is 64 Gauss at a distance of 10 cm away. What is the magnetic field strength of the magnet, 20 cm away?
Answer:
8 Gauss
Step-by-step explanation:
Since your moving the magnet from 10 to 20cm you're essentially multpliying the distance by 2.
K = 2
Therefore k ^ 3 = 2^3
64/2^3
=8
Answer:
8 Guass
Step-by-step explanation:
We multiply the distance by a factor of $2$, and thus divide the magnetic field strength by a factor of $2^3 = 2 \cdot 2 \cdot 2 = 8$. We get a magnetic field strength of 64/8 = 8
Which is the correct formula to calculate the volume of a cone?
Answer
πr^2 h/3
Step-by-step explanation:
pi radius squared multiplied by h/3
Find the perimeter of the image below
A 32.1 units
B 35.8 units
C 37.6 units
D 39.2 units
Answer:
We need to solve the each side as though it is the hypotenuse:
AB: 6^2 + 5^2 = 61 => 7.81
BC: 8^2 + 5^2 = 89 => 9.43
CD: 4^2 + 3^2 = 25 => 5
DE: 4^2 + 2^2 = 20 => 4.47
EA: 2^2 + 5^2 = 29 => 5.39
Total 32.10 Units
Step-by-step explanation:
Please mark brainliest and have a great day!
a golf ball is dropped onto concrete from 2 meters up. Each time it bounces, it rebounds to 2/3 of its previous height. On the sixth rebound, how much will it rise
Step-by-step explanation:
The ratio is the same each time (2/3), so this can be modeled as a geometric sequence.
an = a₁ (r)^(n-1)
where an is the nth term, a₁ is the first term, and r is the common ratio.
On the first rebound, the ball rises to 2/3 × 2 = 4/3, so a₁ = 4/3.
an = 4/3 (2/3)^(n-1)
On the sixth rebound, the ball rises to:
a₆ = 4/3 (2/3)^(6-1)
a₆ = 4/3 (32/243)
a₆ = 128/729
a₆ ≈ 0.176
Two lines that do not intersect are skew. Always Sometimes or Never
Answer:
Never.
Step-by-step explanation:
What is the y-intercept of the linear equation x-1/2y=-6?
a) –6
b) –3
c) 0
d) 12
Answer:
[tex]\large\boxed{d)\ 12}[/tex]
Step-by-step explanation:
[tex]x-\dfrac{1}{2}y=-6\\\\\text{y-intercept is for x = 0. Substitute:}\\\\0-\dfrac{1}{2}y=-6\\\\-\dfrac{1}{2}y=-6\qquad\text{multiply both sides by (-2)}\\\\\left(-2\!\!\!\!\diagup^1\right)\left(-\dfrac{1}{2\!\!\!\!\diagup_1}y\right)=(-2)(-6)\\\\y=12[/tex]
What is the slope of the linear equation 30x-60y=12
Answer:
60y = 30x - 12
y = 1/2x - 1/5
The slope is 1/2
Answer:
1/2
Step-by-step explanation:
30 over 60 is half
Find the missing value 4 = -8 - ?
Answer: -12
Step-by-step explanation:
Answer:
Hi there!
The answer to this question is negative 12.
What is the value of x?
ANSWER
58°
EXPLANATION
The relationship between the measure of the bigger arc and the smaller arc and the angle created by the secant and the tangent is
[tex]51 \degree = \frac{1}{2} (160 - x)[/tex]
Multiply through by 2
This implies that
[tex]2 \times 51 \degree =2 \times \frac{1}{2} (160 - x)[/tex]
We simplify to get:
[tex]102 \degree =160 - x[/tex]
Solve for x.
[tex]102 \degree - 160 \degree =- x[/tex]
[tex] - 58 \degree =- x[/tex]
[tex]58 \degree =x[/tex]
Solve 3x + 11 = k for x.
3x +11 = K
To solve for X, we need to isolate x on one side.
Subtract 11 from both sides:
3x = K -11
Divide both sides by 3:
x = (k-11)/3
Answer:
3x +11 = K
x = (k-11)/3
Step-by-step explanation:
An equilateral triangle has an altitude of 45. Find the length of a side of the triangle.
Answer:
See attachment.
If altitude = 45 then
side = 2 * height (or altitude) / square root of 3
side = 2 * 45 / 1.7320508076
side = 90 / 1.7320508076
side = 51.9615242271
Step-by-step explanation:
Follow below steps;
When dealing with an equilateral triangle, dividing it by an altitude creates two 30-60-90 right triangles. Since we know the length of the altitude (45), which corresponds to the shorter leg in the 30-60-90 triangle, we can find the length of the side of the equilateral triangle (which is the hypotenuse of the 30-60-90 triangle) using the properties of this special right triangle.
To begin, we recognize that the ratios of the sides of a 30-60-90 triangle are 1:\\(extbackslashsqrt{3}\\):2. Thus, if the shorter leg is 45, the hypotenuse will be twice that length, because the ratio of the shorter leg to the hypotenuse is 1:2. Therefore, the length of a side of the equilateral triangle is 45 * 2, which equals 90.
how many terms does the polynomial x^2+xy-y^2 have
Answer:
3 TERMS
Step-by-step explanation:
There are total 3 terms in the polynomial [tex]x^{2} + xy - y^{2}[/tex] .
What is the total number of terms of given polynomial ?The given polynomial expression is [tex]x^{2} + xy - y^{2}[/tex] .
The number of terms of any expression is the total number of independent variables present in the given polynomial expression.
We can see that there are total 3 independent variables present in the polynomial expression and therefore the number of terms present is also three.
Thus, there are total 3 terms in the polynomial [tex]x^{2} + xy - y^{2}[/tex] .
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There are eight planets in our solar system. Venus is the hottest planet, with an average temperature of 460°C. The average temperatures of some other planets are given in the table.
Planet
Average Temperature
Venus
460°C
Earth
14°C
Mars
-60°C
Neptune
-214°C
Answer:
what is the question i dont get it
Step-by-step explanation:
Find the solution set
2x^2 -2x -4 =0
please use a comma to separate your answer.
Answer:
2,-1
Step-by-step explanation:
2x^2 -2x -4 =0
Factor out a 2
2(x^2 -x-2) =0
What 2 number multiply to -2 and add to -1
-2*1 = -2
-2 +1 = -1
2(x-2) (x+1) =0
Using the zero product property
x-2 = 0 x+1 = 0
x-2+2=0+2 x+1-1=0-1
x=2 x=-1
Simplify the expression 3x3^ 648x 4 y8
Answer: B.) 18x^2y^2 3squareroot 3xy^2
Step-by-step explanation:
Answer:
B. [tex]18x^{2} y^{2} \sqrt[3]{3xy^{2} }[/tex]
Step-by-step explanation:
To simplify this expression, use the fact that the root of a number (in this case is the cube root) can be expressed like a fractional exponent (1/3). Using this, the expression changes to:
[tex]3x(648x^{4}y^{8})^{(1/3)}[/tex]
Next step is to put the exponent inside the parenthesis:
[tex]3x(648^{1/3}x^{4/3}y^{8/3})[/tex]
Find the prime factorization of 648:
648 =3⋅3⋅3⋅3⋅2⋅2⋅2
648=3⁴∗2³
[tex]3x(3^{(4/3)}2^{(3/3)}x^{4/3}y^{8/3})[/tex]
Change all improper fractions in exponent to mixed fractions
[tex]3x(3^{1(1/3)}2^{1}x^{1(1/3)}y^{2(2/3)})[/tex]
Separate integers exponents from fractional:
[tex]3x(3\cdot3^{(1/3)}\cdot 2 \cdot x\cdot x^{1/3}\cdot y^{2}\cdot y^{2/3})[/tex]
Re-arrange (all numbers with fractional exponents must be together):
[tex]3x(3 \cdot 2\cdot x\cdot y^{2}\cdot 3^{(1/3)}x^{1/3}y^{2/3})[/tex]
Multiply the 3x with the numbers that have an integer exponent:
[tex]18x^{2}y^{2}(3^{(1/3)}x^{1/3}y^{2/3})[/tex]
Take out the exponent 1/3 from the parenthesis:
[tex]18x^{2}y^{2}(3xy^{2})^{1/3}[/tex]
And change the representation of the root to use a radical symbol
[tex]18x^{2} y^{2} \sqrt[3]{3xy^{2} }[/tex]
The side lengths of different triangles are given. Which triangle is a right triangle? A. 6,7,13 B. 21−−√,99−−√,11 C. 10,60,61 D. 35−−√,14−−√,7
Answer:
D
Step-by-step explanation:
By definition for a right triangle with sides a, b, c, where c is the hypotenuse,
the following must be true:
a² + b² = c²
By using this formula on all the choices, we find that only D satisfies this formula
i.e.
for
a = √35 --------> a² = 35
b = √14 --------->b² = 14
c = 7 ------> c² = 49
a² + b² = 35 + 14 = 49 which is equal to the value of c² above
The correct answer is √35 , √14 , 7
What is Pythagoras theorem?Pythagoras' theorem that the square of a right triangle's hypotenuse is equal to the sum of the squares of the other two sides.
p^2 + b^2 = h^2 ( In a right angled triangle)
p = perpendicular of the triangle
b = base of the triangle
h = hypotenuse of the triangle
According to the Pythagoras theorem:
p^2 + b^2 = h^2 (In a right angled triangle)
In Option D
(√35)^2 + (√14)^2 = 7^2
49 = 49
Pythagoras theorem is followed in this triangle, hence it is a right angled triangle.
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simplify (4x-6)-(3x+6)
Answer:
[tex]x-12[/tex]
Step-by-step explanation:
First open the brackets
[tex]=(4x-6)-(3x+6)\\\\\\=4x-6-3x-6[/tex]
Then collect the like terms
[tex]4x-3x-6-6[/tex]
Solve the like terms
[tex]4x-3x=x\\\\\\-6-6=-12\\\\\\=x-12[/tex]
The simplified form is
[tex]x-12[/tex]
Combine the following expressions 2√5+ 5√5. A.)35 B.)7√5 C.)7√10
Answer:
B.)7√5
Step-by-step explanation:
2√5+ 5√5 = 7√5
we simply let √5 = x
therefore;
2√5+ 5√5 = 2x + 5x
2x + 5x = 7x
but x = √5
2√5+ 5√5 = 7√5
Solve the following equations 4x + 3y =17 3x + 2y = 13
Answer:
(5,-1)
Step-by-step explanation:
4x+3y=17
3x+2y=13
So elimination sounds fun but we will have to do manipulation:
Multiply top equation by 2 and bottom equation by 3. This will cause the second term in both by 6y which means we would be setup for elimination.
8x+6y=34
9x+6y=39
--------------------now subtract the equations
-x+0=-5
So x=5
Now plug it into either question (no matter which-pick and choose)
I will go with the second original 3x+2y=13
So if x=5 we have 15+2y=13
Subtract 15 on both sides: 2y=-2
Now divide both sides by 2: y=-1
Answer (5,-1)
Final answer:
To solve the simultaneous linear equations 4x + 3y = 17 and 3x + 2y = 13, the elimination method shows that the solution is x = 5 and y = -1.
Explanation:
To solve the simultaneous linear equations 4x + 3y = 17 and 3x + 2y = 13, one could use either the substitution method, the elimination method, or matrix methods. However, as per the guidance, we will follow the elimination method which is efficient and easily understandable.'
Let's multiply the first equation by 2 and the second equation by 3, which will give us:
8x + 6y = 34 (equation 1 multiplied by 2)
9x + 6y = 39 (equation 2 multiplied by 3)
Now, subtract the first new equation from the second new equation to eliminate y:
9x - 8x + 6y - 6y = 39 - 34
x = 5
Substitute x = 5 into one of the original equations to find y. For example, put x = 5 in 4x + 3y = 17:
4(5) + 3y = 17
20 + 3y = 17
3y = -3
y = -1
Therefore, the solution to the system of equations is x = 5 and y = -1.
Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
0 8, 12, 15
O 10, 24, 26
O 12, 20, 25
15, 18, 20
Mark this and retum
Save and Exit
Next
Answer:
The set {10 , 24 , 26} formed a right triangle
Step-by-step explanation:
* Lets explain how to check the sides lengths which formed a
right triangle
- In triangle ABC
# If AC is the longest side in length
# If (AC)² = (AB)² + (BC)²
∴ AB , BC , AC formed a right angle triangle
∴ m∠B = 90° (The angle opposite to the longest side)
∴ AC is the hypotenuse
* Now lets solve the problem
- In set 8 , 12 , 15
∵ The longest side is 15 cm
∴ (15)² = 225
∵ (8)² + (12)² = 64 + 144 = 208
∵ (15)² ≠ (8)² + (12)²
∴ The set not formed a right triangle
- In set 10 , 24 , 26
∵ The longest side is 26 cm
∴ (26)² = 676
∵ (10)² + (24)² = 100 + 576 = 676
∵ (26)² = (10)² + (24)²
∴ The set formed a right triangle
- In set 12 , 20 , 25
∵ The longest side is 25 cm
∴ (25)² = 625
∵ (12)² + (20)² = 144 + 400 = 544
∵ (25)² ≠ (12)² + (20)²
∴ The set not formed a right triangle
- In set 15 , 18 , 20
∵ The longest side is 20 cm
∴ (20)² = 400
∵ (15)² + (18)² = 225 + 324 = 549
∵ (20)² ≠ (15)² + (18)²
∴ The set not formed a right triangle
* The set {10 , 24 , 26} formed a right triangle
What are the solutions of the given equation 2x^2+9x+10=0
Answer:
see explanation
Step-by-step explanation:
Given
2x² + 9x + 10 = 0
To factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × 10 = 20 and sum = + 9
The factors are + 4 and + 5
Use these factors to split the x- term
2x² + 4x + 5x + 10 = 0 ( factor the first/second and third/fourth terms )
2x(x + 2) + 5(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(2x + 5) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - [tex]\frac{5}{2}[/tex]
Answer:
1. x = 2
2. x = - 5/2
Step-by-step explanation: First put parenthesis around the equation
( 2x^2 + 4x ) + ( 5x + 10) = 0
2x ( x+ 2) 5 (x + 2),
when you have the same answer inside the parenthesis you know your right.
2x + 5 = 0
x + 2 = 0
Next preform basic algebra
2x = -5
x = -2x = - 5/2find next number of 32,1312,11131112,31133112
Answer:
The next number is 1321232112
Step-by-step explanation:
32 is read off as "one 3, one 2" = 1312
1312 is read off as "one 1, one 3, one 1, one 2" = 11131112
11131112 is read off as "three 1s, one 3, three 1s, one 2" = 31133112
31133112 is read off as "one 3, two 1s, two 3s, two 1s, one 2" = 1321232112
For the equations below which statement is true ? -2x=14 6x=-42
At the beginning of a class period, half of the students in a class go to the library. Later in the period, half of the remaining students go to the computer lab. If there are eight students remaining in class, how many students were originally in the class?
Answer:
32 students
Step-by-step explanation:
We are given that at the beginning of a class period, half of the students in a class go to the library and half of the remaining to the computer lab.
Given that there are 8 students remaining, we are to find the total number of students in the class initially.
At beginning = [tex]x[/tex] students
After half of them leave = [tex]\frac{x}{2}[/tex] students
After half of the remaining leave = [tex]\frac{x}{4}[/tex] students
So, [tex]\frac{x}{4} = 8[/tex]
[tex]x=8\times 4[/tex]
x = 32
Therefore, there were 32 students in the class originally.
there were 32 students in the class originally.
because in the computer lab before there were 16. 16 times 2 equals 32.
What is the y-intercept for the graph of the equation y=4(3^x)
A. (0,8)
B. (0,3)
C. (0,4)
D. (0,12)
ANSWER
C. (0,4)
EXPLANATION
The given graph has equation:
[tex]y = 4( {3}^{x} )[/tex]
The y-intercept is where the graph touches the y-axis.
At this point the value of x is zero.
We substitute x=0 into the equation to obtain:
[tex]y = 4( {3}^{0} )[/tex]
Recall that any non-zero number exponent zero is 1.
This implies that,
[tex]y = 4( 1 ) = 4[/tex]
Hence the y-intercept is (0,4)
The correct answer is C.