If x² = y³ , for what value of z does [tex]x^{3z}[/tex] = [tex]Y^{9}[/tex] ?
Answer:
z= 2
Step-by-step explanation:
To solve the question given, we will follow the steps below;
[tex]X^{3z}[/tex] = [tex]Y^{9}[/tex] -----------------------------------------------------------------(1)
but applying the law of indices mᵃᵇ = (mᵃ)ᵇ
then
[tex]Y^{9}[/tex] = [tex](Y^{3})^{3}[/tex]
replace [tex]Y^{9}[/tex] by [tex](Y^{3})^{3}[/tex] in equation (1)
[tex]X^{3z}[/tex] = [tex]Y^{9}[/tex]
[tex]X^{3z}[/tex] = [tex](Y^{3})^{3}[/tex] --------------------------------------------------------------------(2)
but from the question x² = y³
replace y³ by x² in equation (2)
[tex]X^{3z}[/tex] = [tex](Y^{3})^{3}[/tex]
[tex]X^{3z}[/tex] = [tex](X^{2})^{3}[/tex]
[tex]X^{3z}[/tex] = [tex]X^{6}[/tex]
3z = 6
divide both-side of the equation by 3
3z/3 = 6/3
On the left-hand side of the equation, 3 at the numerator will cancel-out 3 at the denominator leaving us with just z while on the right-hand side of the equation 6 will be divided by 3
z= 2
Which algebraic expressions are polynomials
Answer:
2,3,5,6
Step-by-step explanation:
which set of angles has the same terminal arm as 70 degrees?
Answer: B = B ∈ {70° + n*360° I n ∈ Z } where Z is the set of the integer numbers.
Step-by-step explanation:
If we have an angle A, the other angles that have the same terminal arm than A can be written as:
B = A + n*360°
Here B is a "coterminal" angle to A. (they have the same terminal side)
where n can be any integer number (if n = 0 we have A = B, which is trivial, this means that any angle can be coterminal with itself.)
So we can write the set as:
B = B ∈ {70° + n*360° I n ∈ Z }
The set of angles that has the same terminal arm as 70 degrees is B = B ∈ {70° + n*360°, n ∈ Z}.
We have to determine, which set of angles has the same terminal arm as 70 degrees.
According to the question,
Let, The angle A and other angle B that have the same terminal arm as A can be written as,
B = A + n × 360°
Where the value of angle A is 70 degrees.
B is the coterminal angle, and they have the same terminal,
And n is the number of integers.
Substitute the value of A in the equation,
B = 70 + n × 360°
Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.
Since the value of n is equal to 0 then A = B,
Therefore, The angles coterminal with itself is called trivial.
Hence, The set of angles that has the same terminal arm as 70 degrees is B = B ∈ {70° + n*360°, n ∈ Z}.
To know more about Terminal Arm click the link given below.
https://brainly.com/question/20333574
what type of solutions does this equation have
Answer:
two imaginary numbers
Step-by-step explanation:
What is the value of y when x= 2.5
Answer:
The value of y is unknown bas there is no equation
True or False. When graphing the inequality y>3x+2 the line drawn would be a solid line.
Answer:
False
Step-by-step explanation:
Since the inequality uses the greater than symbol >
Then the line drawn should be a broken line.
If the inequality had ≥ ( greater than or equal to )
Then the line would be solid.
the guy above is correct
The answer is: False
If x =√63 and y = √24, what is the approximate value of x + y2?
Find the point-slope equation for the line
that passes through the points (5, 19) and
(-5, -1). Use the first point in your equation. please help :/
y- [?]=[?](x-[?])
Answer:
work is shown and pictured
The point-slope form of the line is [tex]y-19=2(x-5)[/tex].
Important information:
A line passes through the two points [tex](5,19)[/tex] and [tex](-5,-1)[/tex].Use the first point in the equation.We need to find the point-slope equation for the line
Point-slope equation:The point-slope form of a line that passes though the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Substitute [tex]x_1=5,y_1=19,x_2=-5,y_2=-1[/tex].
[tex]y-19=\dfrac{-1-19}{-5-5}(x-5)[/tex]
[tex]y-19=\dfrac{-20}{-10}(x-5)[/tex]
[tex]y-19=2(x-5)[/tex]
Thus, the point-slope form of the line is [tex]y-19=2(x-5)[/tex].
Find out more about 'point-slope form' here:
https://brainly.com/question/12743204
Please help it’s geometry
find the values for a and b.
Answer:
the value of a and b is 68
Step-by-step explanation:
the other half is 224 so you minus 360 from 224 which will give us 136 then you divide by 2 to get a and b.
Answer:
a = 68, b = 136
Step-by-step explanation:
The angle in the circle = 360°, thus
b = 360 - 224 = 136
The inscribed angle a between a tangent- chord is equal to half the measure of its intercepted arc, so
a = 0.5 × 136 = 68
BIg Points big answer and explanations
Answer:
1/10
Step-by-step explanation:
We are hoping for 2 of the 20, and 2/20 simplified equals 1/10
C: 1/5 chance.
There are 20 possible outcomes, with 4 involving chicken and 4 involving ribs.
However, only 2 of each of those involves red sauce.
So the possibilities of getting a red sauce with chicken or ribs is 4.
4/20 = 1/5.
Match each function with its domain. 1. S(x) = √x 2. H(x) = √2+x 3. Z(x) = √x-2 4. Q(x) = √2-x 5. V(x) = √-x 6. N(x) = ^3√2-x x ≤ 2 x ≥ -2 x ≥ 0 x ≥ 2 x ≤ 0 All real numbers
Answer:
1. x ≥ 0
2. x ≥ -2
3. x ≥ 2
4. x ≤ 2
5. x ≤ 0
6. All real numbers
Step-by-step explanation:
Domain of square function:
Suppose we have a square function in the following format:
[tex]f(x) = \sqrt[n]{g(x)}[/tex]
If n is even, the domain of f(x) is:
[tex]g(x) \geq 0[/tex]
Otherwise, if n is odd, the domain of f(x) is all real numbers.
1. S(x) = √x
If n does not appear is that it is 2.
g(x) = x
So the domain is:
[tex]x \geq 0[/tex]
2. H(x) = √2+x
g(x) = 2 + x
So
[tex]2 + x \geq 0[/tex]
[tex]x \geq -2[/tex]
3. Z(x) = √x-2
g(x) = x - 2
[tex]x - 2 \geq 0[/tex]
[tex]x \geq 2[/tex]
4. Q(x) = √2-x
g(x) = 2 - x
[tex]2 - x \geq 0[/tex]
[tex]-x \geq -2[/tex]
Multiplying by -1, everything
[tex]x \leq 2[/tex]
5. V(x) = √-x
g(x) = -x
Then
[tex]-x \geq 0[/tex]
Multiplying by -1
[tex]x \leq 0[/tex]
6. N(x) = ^3√2-x
Cubic root(odd number), so all real numbers.
Write this equation c + 25/ 100c as a coefficient fraction PLZ HELP !!! Really Apreciate
Answer: 5/4c
Step-by-step explanation:
Hi, to answer this question we simply have to solve the equation given:
Coefficients are the numbers next to the variable; in this case, the variable is c.
c + 25/ 100c
1/1 c +25/100c
100/100c +25/100 c
125/100 c
5/4c
Feel free to ask for more if needed or if you did not understand something.
Write in standard form
iii)
0.0000574
Answer:
Forest are going up
Step-by-step explanation:
Because leeds will bottle it
On January 1st, the temperature at noon was 10.2℉. By midnight, the temperature had decreased by 13.5 degrees. What was the temperature at midnight?
Answer:
-3.3 degrees
Step-by-step explanation:
10.2-13.5+ -3.3
what is the value of the expression 2(×+4) -(y×8) A. 11/4 B. 65/2 C. 21/4 D. 27/4
Answer:
27/4
Step-by-step explanation:
2x + 8 - 8y
2x - 8y + 8
2 * (1/8) - [ 8 * (3/16)] +8
(1/4) - (3/2) + 8
[tex]\frac{1 - 6 + 32}{4} = \frac{27}{4}[/tex]
Janice already has $65 dollars in her savings account. If she puts $5 per week in her account, write an equation to find out how many weeks she must save to have at least $200 in her account.
2 points
Your answer
Answer: 65 + 5x ≥200
Step-by-step explanation:
Hi, to answer this question we have to write an inequality with the information given:
Janice's savings (65) plus the product of the amount she saves per week (5) and the number of weeks (x) must be higher or equal to $200.
Mathematically speaking:
65 + 5x ≥200
If we solve it for x:
5x ≥200-65
5x ≥135
x ≥ 135/5
x ≥ 27 weeks
Feel free to ask for more if needed or if you did not understand something.
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!
Answer:
C. Add the equations
Step-by-step explanation:
Adding both the equations will help eliminating 5y.
Two Parallel lines are cut by a transversal and form a pair of alternate exterior angles. One angle measures (6x+5) and other measures (7x+4). Explain how to determine what those other angles actually measure.
Answer:
The other angles will measure 83.9° and 96.1°Step-by-step explanation:
If two parallel lines are cut by a transversal and form a pair of alternate exterior angles, then the sum of the two exterior angles will be equal to 180° as shown;
If one angle measures (6x+5) and other measures (7x+4), then;
(6x+5)+(7x+4) = 180° (sum of two exterior angles)
Firstly, lets get the value of x from the equation.
6x+7x+9 = 180°
13x= 180-9
13x = 171
x = 171/13
x = 13.15°
The first angle 6x+5 will measure 6(13.15)+5 = 83.9°
The other angle 7x+4 will mesure 7(13.15)+4 = 96.1°
Answer:
Since the lines are parallel, the alternate exterior angles are congruent. Therefore you can set the expressions equal to each other and solve for x. Then you can substitute the value of x back into either expression to find the angle measure.
Step-by-step explanation: exact answer
Gracie is making 2 and 1/2 batches of chocolate chip cookies for her school bake sale. If one batch of cookies requires 1 and 1/4 cups of flour, how many cups of flour will she need?
Answer:
Step-by-step explanation:
What you just have to do is multiply 2 1/2 and 1 1/4, but i can still do it. 2 1/2 is the same as 5/2 , and 1 1/4 is the same as 5/4, so just multiply the top and the bottom and you will get 25/8 whicxh is basically 3 and 1/8
Translate (11, 3) 8 units up and 14 units left
What’s the answer
Answer: 3, 11
Step-by-step explanation:
Y= 3+8 = 11
X= 11-14=3
Can someone help me with my online homework please!!!
Answer:
26cm^2
Step-by-step explanation:
To calculate area of a triangle we multiply height with base and that divided by two
13 × 4 ÷ 2 = 26cm^2
Which is a simplified form of the expression -6a + 2(2a + 2)? A. -2a + 4 B. -2a – 4 C. 2a + 4 D. 2a – 4
Answer:
A
Step-by-step explanation:
-6a+2(2a+2)
-6a+4a+4
-2a+4
Answer:
-2a+4 is the answer
we need to follow BODMAS rule
Sung borrowed money from his parents over the last three days. This is represented by the negative values in the table. What is the total of the values? What is the average of the values?
Answer:
-9 and -3
Step-by-step explanation:
I hope this helps!
Answer:
-9 -3 because -2+-3= -5+-4= -9 and the number in the middle of -2 and -4 is -3
Step-by-step explanation:
Can someone answer this i need help
All that is needed to do is to simplify the expression.
The answer to your question is:
[tex]6 x^{6}[/tex] - [tex]10 x^{3}[/tex] + [tex]8x^{2}[/tex]
Hope I helped!
A circular flower bed is 15 m in diameter and has a circular sidewalk around it that is 3 m wide. Find the area of the sidewalk in square meters. Use 3.14 for pi π.
Answer:
346.19 m²
Step-by-step explanation:
The diameter of the circular flower bed is 15 m and the length of the sidewalk round the flower bed is 3 m.
This means that an extra length of 3 m is added on each side.
The joint diameter of the flower bed and sidewalk is:
15 + 3 + 3 = 21 m
The radius is half of the diameter, that is 10.5 m
The area of the sidewalk is therefore:
A = pi * r²
Where r = radius
A = 3.14 * 10.5²
A = 346.19 m²
How can I solve this problem?
a) 108°
Answer:
b) 54°
Step-by-step explanation:
a) By arc sum property of a circle.
[tex] m\widehat {AEB} + m\widehat {AB} = 360°\\
252° + m\widehat {AB} = 360°\\
m\widehat {AB} = 360°- 252°\\
\huge \red {\boxed {m\widehat {AB} = 108°}} \\[/tex]
b) In the given figure, DC is tangent to the circle with O at point A and AB is chord or secant. Therefore, by tangent secant theorem:
[tex] m\angle BAC = \frac{1}{2} \times m\widehat {AB}\\\\
\therefore m\angle BAC = \frac{1}{2} \times 108°\\\\
\huge \purple {\boxed {m\angle BAC = 54°}} [/tex]
Mel's Furniture received an invoice dated September 27 for 5 bedroom sets at $3,000 each. The invoice indicated a chain discount of 5/8/3. The seller of the furniture prepaid the freight of $200 (FOB Shipping Point). Terms were 2/10, EOM. Assuming that Mel pays within the discount period, what is the total payment amount?
Answer: $12,916.70
Step-by-step explanation:
Given the following:
Invoice received :
Bedroom set = 5
Cost per set = $3,000
Chain discount = 5/8/3
Freight cost = $200
If Mel pays within the discount period:
Chain discount given = 5/8/3
Therefore, net equivalent price rate equals:
(1 - 0.05) × (1 - 0.08) × (1 - 0.03) =
0.95 × 0.92 × 0.97 = 0.84778
Net price = total cost × 0.84778
($3000 × 5) × 0.84778
$15000 × 0.84778 = $12,716.7
Net equivalent price + FOB Shipping
$12,716.7 + $200 = $12,916.70
Navid has $72 in her savings account. Each week she saves $24. When will navid have the total savings of $288
write an equation you can use to solve the problem.
[tex]x - 15 = - 6[/tex]
Answer:
The value of [tex]x[/tex] :
[tex]x = 9[/tex]
Step-by-step explanation:
-Solve for [tex]x[/tex] :
[tex]x =- 15 = -6[/tex]
-Add both sides by 15:
[tex]x - 15 + 15 = -6 + 15[/tex]
[tex]x = 9[/tex]
Now, you have found the answer.
The length of a window in Andrew's house is 4 feet and its height is 3 feet.
What is the diagonal length of the window?
O A) 2 ft
O C 8 ft
O B) 5 ft.
O D) 12 ft.
The solution for this problem is:
To get the diagonal length of a square, multiply the length of one side by the square root of 2:If the length of one side is x.
length of diagonal = x √2
length of a diagonal = 4√2
length of a diagonal = 5.6569 feet
Use the Pythagorean theorem
Diagonal = sqrt(4^2 + 3^2)
Diagonal = sqrt( 16 + 9)
Diagonal = sqrt(25)
Diagonal = 5