the solutions are (x = 2) and (y = 4).
To find the values of x and y in the given equations, let's solve them step by step:
1. (3^{2x-y} = 1)
For any nonzero number raised to the power of 0, the result is always 1. Therefore, we can rewrite the equation as:
[2x - y = 0]
Now, we have one equation in terms of (x) and (y).
2.[tex]\( \frac{16^x}{4} = 8^{3x-y} \)[/tex]
We'll simplify the left side first:
[tex]\[ \frac{16^x}{4} = \frac{(4^2)^x}{4} = \frac{4^{2x}}{4} = 4^{2x-1} \][/tex]
Now, the equation becomes:
[4^{2x-1} = 8^{3x-y}]
We know that (8 = 2^3), so we can rewrite the right side of the equation in terms of 2:
[4^{2x-1} = (2^3)^{3x-y} = 2^{9x-3y}]
Now, we have:
[4^{2x-1} = 2^{9x-3y}]
Since (4 = 2^2), we can rewrite the left side as:
[ (2^2)^{2x-1} = 2^{4x-2} ]
So, the equation becomes:
[2^{4x-2} = 2^{9x-3y}]
Since the bases are the same, the exponents must be equal:
[4x - 2 = 9x - 3y]
Now, we have two equations:
[2x - y = 0]
[4x - 2 = 9x - 3y]
From the first equation, we can solve for (y):
[y = 2x]
Substituting (y = 2x) into the second equation:
[4x - 2 = 9x - 3(2x)]
[4x - 2 = 9x - 6x]
[4x - 2 = 3x]
[x = 2]
Now, substituting (x = 2) into the first equation to find (y):
[2(2) - y = 0]
[4 - y = 0]
[y = 4]
So, the solutions are (x = 2) and (y = 4).
How many dinner specials are possible?
HELP PLEASEEEEEE!!!!!!!!!!!!!!!!!!!!
[tex]3\cdot3\cdot4\cdot4=144[/tex]
plz help which expression is equivalent to 4-2/2^-3
8
16
-8
-16
Answer:
The answer is 16.
Step-by-step explanation:
In this expression 4-2/2^-3, first of all we will solve the numerator.
Subtract 4 and 2
4-2= 2
So, the expression will become 2/2^-3
Now notice that the numerator has the base 2 and exponent 1 where as the denominator has the base 2 and exponent -3. Both the numerator and denominator have the same base
So we will use the property a^m/a^n=a^m-n.
=2/2^-3
=2^1-(-3)
=2^1+3
=2^4
2^4 means that 2 will be multiplied 4 times.
=2*2*2*2
=16
Thus the answer is 16....
A company's forecasted
sales are $300,000 and
its sales at break-even
are $180,000. Its margin
of safety % is:
Answer:
$120,000
Step-by-step explanation:
It's easy ,
all you got to do is just minus $300,000 from $180,000 so it'll be :
$300,000 − $180,000 = $120,000
$120,000 Will be your answer !
Answer:
$120,000
It's easy ,
all you got to do is just minus $300,000 from $180,000 so it'll be :
$300,000 − $180,000 = $120,000
$120,000 Will be your answer !
Step-by-step explanation:
What is the degree of polynomial 3x⁴-4x³y+6x²y²-8x²y³-7y⁴+2
Answer:
5
Step-by-step explanation:
Find the degree of each monomial term of the polynomial. The highest degree is the answer.
deg(3x^4)=4
deg(-4x^3y)=3+1=4
deg(6x^2y^2)=2+2=4
deg(-8x^2y^3)=2+3=5
deg(-7y^4)=4
deg(2)=0
The highest degree there is 5 so that is the degree of the polynomial.
The degree of a polynomial is the highest power of any variable in that polynomial. For the polynomial 3x⁴-4x³y+6x²y²-8x²y³-7y⁴+2, because the highest power is 4, the degree of the polynomial is 4.
Explanation:The highest exponent of the variable in a polynomial determines its degree. In the provided polynomial, 3x⁴-4x³y+6x²y²-8x²y³-7y⁴+2, the degree of this polynomial is 4 because the highest power of the variable is 4. which can be seen in the terms 3x⁴ and -7y⁴.
It's important to note that while determining the degree of a polynomial, we consider the power (or degree) of individual terms and not their combined power. For example, in the term -4x³y, x has a degree of 3 and y has a degree of 1. The degree of -4x³y will still just be 3 (and not 4) as we only consider the highest degree within that term.
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Which is the graph of x ≤ 2? Graph of a dashed vertical line 2 units to the right of the origin with everything shaded to the right. Graph of a solid vertical line 2 units to the right of the origin with everything shaded to the right. Graph of a dashed vertical line 2 units to the right of the origin with everything shaded to the left. Graph of a solid vertical line 2 units to the right of the origin with everything shaded to the left.
Answer:
Graph of a solid vertical line 2 units to the right of the origin with everything shaded to the left.
Step-by-step explanation:
The solid line shows it is greater than or equal to. Shade to left of vertical line if less than and right of it if greater than.
Answer:
A graph of a solid vertical line 2 units to the right of the origin with everything shaded to the right.
Step-by-step explanation:
The inequality x≤ 2 means that for any coordinate picked to the left of the line x=2 including 2 satisfies the argument for x. The less than or equal to sign means the value of x is 2 or less.
If for example you pick (2,5) or even (-1,150), the x coordinate satisfies the inequality.
what is the complete factor of 12Xsquared + 28X
Answer:
12x^2 + 28x = 0
3x^2 + 7x = 0
x(3x+7)=0
x=0 or
3x+7=0
3x= - 7
x= - 7/3
Answer:
4x(3x + 7)
Step-by-step explanation:
Given
12x² + 28x ← factor out 4x from each term
= 4x(3x + 7) ← in factored form
12. A bridge is 1,595 feet long. Each cable holding up the
bridge is 1,983 feet longer than the bridge itself. How
long is each cable?
Answer:
3,578
Step-by-step explanation:
Add the two values together. If the bridge is 1,595 feet long, and if each cable holding that is 1,983 feet longer than the length of the bridge then adding them together is the way to go.
1,595+1,983=3,578
To get the length of each cable, you add the length of the bridge (1,595 feet) to the extra length of each cable (1,983 feet), which results in 3,578 feet.
Explanation:The problem is asking us to work with addition. The bridge is 1,595 feet long and each cable is 1,983 feet longer than the bridge. To find the length of each cable, we add the length of bridge and the extra length of the cable. That is, we add 1,595 feet (length of bridge) to 1,983 feet (extra length of cable).
Add 1,595 and 1,983. The result is the length of each cable, which equals 3,578 feet.Learn more about Addition here:
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Drag each set of side lengths to show whether they can or cannot make a triangle, or if there is not enough information to tell.
A. 4cm, 6cm, 10cm
B. 2cm, 3cm, 10cm
C. 1cm, 1cm, 12cm
D. 5cm, 8cm, 10cm
E. 7cm, 7cm, 12cm
F. 6cm, 6cm, 12cm
Answer:
D and E
Step-by-step explanation:
because the rule to make triangle is
a<b+c with a, b and c is the side of the triangle
Answer:
Step-by-step explanation:
I just did it nothing to explain :D
Jack is driving from his house to the airport. At 9:00 AM, he is 150 miles from the airport. At 10:30 AM, he is 75 miles from the airport. What is Jack’s average driving speed between 9:00 AM and 10:30 AM?
______ miles/hour
Answer:
I b3live it is 50 miles/hour
Step-by-step explanation:
We need to know how many miles he drove from 9:00 to 10:30 so you do 150-75 which is 75. Then, you do 75÷1.5 because 9:00 and 10:30 are an hour and a half apart and then you get 50 mph.
Find the area of the shaded region in the polygon below.
Answer:
35
Step-by-step explanation:
I multiply 3 and 7 that give 35
Answer:
Step-by-step explanation:
The area of a pentagon given the radius is
Area = (5/2)r^2 * sin(72º)
r = 7
Area = (5/2)*7^2 * sin(72)
Area = 122.5 * 0.95106
Area = 116.5
=============
r = 5
Area = (5/2) * 5^2 * sin(72)
Area = 59.4
Area of the shaded area = 116.5 - 59.4
Area of the shaded area = 57.1
When you multiply a function by -1, what is the effect on its graph?
Answer:
The correct answer is C.
Step-by-step explanation:
When you multiply a real function by -1 you only change its sign in all the domain of definition. The positive part becomes negative, and the negative values becomes positive and the zeros are unaltered. So, it is no difficult to see that the multiplication by -1 is equivalent to make a reflection with respect to the x - axis.
Distance from origin
Answer:
Maybe 13
Step-by-step explanation:
Im not sure from the answer
Answer:
B
Step-by-step explanation:
Use the distance formula, that is
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = A(- 3, - 2) and (x₂, y₂ ) = (0, 0)
d = [tex]\sqrt{(0+3)^2+(0+2)^2}[/tex]
= [tex]\sqrt{3^2+2^2}[/tex] = [tex]\sqrt{9+4}[/tex] = [tex]\sqrt{13}[/tex]
PLZ HELP 25 POINTS
No Dumb Answers and Please tell me how u got the answer
How could the relationship of the data be classified?
scatter plot with points loosely scattered going down to the right
A positive correlation
A causation
A negative correlation
No correlation
Answer:
Negative Correlation
Explanation:
As the points progress by + x, the general pattern is to decrease in y.
Slope = m = rise/run = x/y
+x/-y = x/-y = -x/y. Negative correlation
which should I choose
To win a game you need at least 45 points.Each question is worth 3 points.Write and solve an inequality that represents the number of questions you need to answer correctly to win the game.
What is 7-(a-b)-4+(3a-2b)
Answer:
[tex]\boxed{2a+3-b}[/tex]
Step-by-step explanation:
Distributive property:
↓
A(B+C)=AB+AC
Remove parenthesis first.
7-(a-b)-4+3a-2b
(-a-b)=-a+b
7-a+b-4+3a-2b
Simplify, to find the answer.
7-a+b-4+3a-2b
Group like terms:
↓
-a+3a+b-2b+7-4
Add numbers from left to right.
-a+3a=2a
2a+b-2b+7-4
b-2b=-b
2a-b+7-4
Adding and subtracting numbers from left to right.
7-4=3
2a+3-b
[tex]2a+3-b[/tex], which is our answer.
Answer:
3 +2a -b
Step-by-step explanation:
7-(a-b)-4+(3a-2b)
Distribute the minus
7 -a +b -4 +3a-2b
Combine like terms
7-4 -a +3a +b-2b
3 +2a -b
Alina spent no more than $45 on gas for a road trip. The first gas station she used charged $3.50 per gallon and the second gas station charged $4.00 per gallon. Which inequality relates the number of gallons of gas she bought at the first station, x, the number of gallons of gas she bought at the second station, y, and the total amount she paid? What are the possible values of y?
Answer: 3.50x + 4.00y ≤ 45
0 < y < 11.25
Step-by-step explanation:
[tex]3.50x + 4.00y \leq 45\\\\\\\text{Subtract 3.50x from both sides:}\\4.00y\leq -3.50x+45\\\\\\\text{Divide everything by 4.00 (to isolate y):}\\\dfrac{4.00y}{4.00}\leq \dfrac{-3.50x}{4.00}+\dfrac{45}{4.00}\\\\\\y\leq-0.875x+11.25\\\\\\\text{Both x and y must be greater than zero, so:}\\0<y<11.25[/tex]
Two parallel lines are crossed by a transversal.What is the value of m?
Same side interior angles are supplementary, which means together they add up to 180 degrees.
In order to find the value of angle m, subtract 180 from the supplement.
180 - 78 = 102
The value of m is 102 degrees
Answer:
C.m=102
Step-by-step explanation:
The two angles are alternate interior angle, those angles add up to 180, 180-78=102. The answer is c
Veronique found the difference of a number and 8.
Which expression models the situation?
n-8 8/n 8-n
Answer:
n-8
Step-by-step explanation:
Let
n ----> the number
we know that
To find the difference of a number and 8, subtract 8 from the number
so
n-8
Find all the values of x that make 0.1x + 0.25(102 - x) < 17.10 true.
Answer:
x > 560
Step-by-step explanation:
0.1x + 0.25(102 - x) < 17.10
simplify
0.1x + 25.5 - 0.25x < 17.10
subtract 25.5 from both sides
0.1x + 25.5 - 25.5 - 0.25x < 17.10 - 25.5
0.1x - 0.25x < - 84
- 0.15x < - 84
divide both sides by - 0.15
x < -84/-0.15 = 560
When you divide or multiply by a negative, the sign changes
x > 560
Hope this helps!
Please mark as brainliest.
To solve the inequality 0.1x + 0.25(102 - x) < 17.10, distribute, combine like terms, and isolate x to find that the values for x that make the inequality true are x > 56.
Explanation:To find the values of x that make the inequality 0.1x + 0.25(102 - x) < 17.10 true, we need to solve the inequality. First, we distribute 0.25 to get 0.1x + 25.5 - 0.25x < 17.10. Then, combining like terms gives -0.15x + 25.5 < 17.10. Next, we subtract 25.5 from both sides to get -0.15x < -8.4. Finally, dividing both sides by -0.15 gives x > 56.
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What is an expression for the amount of money you can save if you use 5/6 Of your wages for spending money?
Evaluate your expression for weekly wages of $60, $120 , $180 and $300.
Answer:
Step-by-step explanation:
If you spend 5/6 of your wages, you'll have 1/6 of your wages left, hopefully to be placed into your savings account.
If your wages are $60, you'd have 1/6 of that, or $10, left.
$120, $20.
$180, $30
$300, $50
Combine like terms.
48y + 21y = ??
Hello There!
We’re just using addition for this.
Image Attached below.
69y is your Answer
Which lines are parallel if m 3 = m 6?
Justify your answer.
Answer:
[tex]r \parallel s[/tex] by the Converse of the Alternate Interiors Angles Theorem.
Step-by-step explanation:
Remember that two lines are parallel if their angle of direction is the same.
So, in this case we know that [tex]m\angle 3 = m\angle 6[/tex], where [tex]\angle 3[/tex] is the direction of [tex]r[/tex] and [tex]\angle 6[/tex] is the direction of [tex]s[/tex].
Therefore, [tex]r \parallel s[/tex] by the Converse of the Alternate Interior Angles Theorem, which states that if two lines are cut by a transversal and the alternate interior angles are congruent, then those lines are parallel.
If f(x) = 27 +3 and g(x) = x - 7, find (f - g)(x).
Answer:
(f - g)(x) = 37 - x
Step-by-step explanation:
(f - g)(x) = (27 +3) - (x - 7)
= 27 + 3 - x + 7
= 37 - x
Answer:
(f - g)(x) = 26x + 10Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
We have f(x) = 27x + 3 and g(x) = x - 7. Substitute:
(f - g)(x) = (27x + 3) - (x - 7)
(f - g)(x) = 27x + 3 - x - (-7)
(f - g)(x) = 27x + 3 - x + 7 combine like terms
(f - g)(x) = (27x - x) + (3 + 7)
(f - g)(x) = 26x + 10
Please help! Will mark brainliest, thank, and rate to the best answer!This is easy math!ASAP!
_____________________________________________
This week, 300 tickets were sold to the school play. This is 120 percent of the number of tickets sold last week. How many tickets were sold last week for the school play?
_________ tickets sold
Answer:
250 tickets
Step-by-step explanation:
This week, the tickets sold was 300.
The # of tickets sold this week was 120% of last weeks ticket sales.
To find out the number of tickets sold last week, first convert 120% into a decimal.
120% = 1.2
Now, divide 300 [tickets sold this week] by 1.2.
If you do this, you get 250.
That means 250 tickets were sold last week.
To double check our answer, break down 120% again, but this time, differently.
100% + 20% = 120%
100% = 1
20% = 0.2
Now, multiply 250 by 1.
250 x 1 = 250.
Now multiply 250 by 0.2
250 x 0.2 = 50.
250 + 50 = 300
So, the amount of tickets sold last week is 250. I hope this helps! :)
What is the gcf of 45 and 9?
Answer:
9
Step-by-step explanation:
The factors of 9 are: 1, 3, 9
The factors of 45 are: 1, 3, 5, 9, 15, 45
Then the greatest common factor is 9.
The GCF of 45 and 9 is 9.
To find the greatest common factor we need to prime factorize 9 and 45 and then find the product of the factors common between the two. This can be represented mathematically as follows:
[tex]45 = 3 \times 3 \times 5\\9 = 3 \times 3[/tex]
Thus we can see that two pair of 3 are common factors between 9 and 45. Thus the GCF [tex]= 3 \times 3 = 9[/tex]
Therefore, the GCF of 45 and 9 is 9.
amon is graphing the function f(x) = 3(4)x. He begins by plotting the initial value. Which graph represents his initial step?
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]f(x)=3(4)^{x}[/tex]
This is a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
a is the initial value
b is the base
Remember that
The initial value is the value of the function when the value of x is equal to zero (y-intercept of the function)
In this problem
The y-intercept is the point (0,3)
therefore
using a graphing tool
The initial step is plot the point (0,3)
see the attached figure
please can someone answer this quickly. 50 points!!
Answer:
Step-by-step explanation:
Distribute...
6x^2-3x-6x+3
6x^2-9x+3 is the expanded equation
The solution....
(3x-3)=0
(2x-1)=0
3x=3
2x=1
x=1
x=1/2
How to rationalize the denominator of sqrt(a)/sqrt(a)-2
Step-by-step explanation:
√a / (√a - 2)
To rationalize the denominator, you need to multiply the fraction by the conjugate:
√a / (√a - 2) × (√a + 2) / (√a + 2)
√a (√a + 2) / ((√a - 2) (√a + 2))
(a + 2√a) / (a - 4)
Can the set of lengths be the side lengths of a right triangle?
7ft, 12ft, 17 ft
Answer:
No
Step-by-step explanation:
For a right triangle, a^2+b^2=c^2 EVERY time.
a and b are always smaller than c, so 7 and 12 are a and b, and 17 is c:
7^2+12^2 ?= 17^2
49+144 ?= 289
193 != 289
Therefore, these can't be the set of lengths for a right triangle
Answer:
These set of lengths cannot be the side lengths of a right angled triangle.
Step-by-step explanation:
Pythagoras Theorem is always followed by a right angled triangle. According to which the sum of squares of the two shorter legs is equal to the square of the longest leg.
[tex]a^2=b^2+c^2[/tex]
So here, 17 is the longest leg and 7 and 12 the shorter ones.
Applying Pythagoras Theorem to these lengths to find out.
[tex]17^2=7^2+12^2[/tex]
[tex]289\neq 193[/tex]
Therefore, these set of lengths cannot be the side lengths of a right angled triangle.