Answer:
n = -5
Step-by-step explanation:
Given:
[tex]\dfrac{y^4 \cdot y^n}{y^2}=y^{-3}[/tex]
Multiply both sides by y²:
[tex]\implies \dfrac{y^4 \cdot y^n}{\diagup \!\!\!\!\!y^2} \cdot \diagup \!\!\!\!\!y^2=y^{-3}\cdot y^2[/tex]
[tex]\implies y^4 \cdot y^n=y^{-3} \cdot y^2[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies y^{4+n}=y^{-3+2}[/tex]
[tex]\implies y^{4+n}=y^{-1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]
[tex]\implies 4+n=-1[/tex]
Solve for n by subtracting 4 from both sides:
[tex]\implies 4+n-4=-1-4[/tex]
[tex]\implies n=-5[/tex]
Answer:
n = - 5
===========
Given equation:
[tex]\dfrac{y^4*y^n}{y^2} =y^{-3}[/tex]Solve it for n:
[tex]y^{4+n-2}=y^{-3}[/tex] [tex]y^{2+n}=y^{-3}[/tex][tex]2+n=-3[/tex][tex]n=-3-2[/tex][tex]n=-5[/tex]===========
Used properties:
[tex]a^b*a^c=a^{b+c}[/tex] product of exponents with same base[tex]a^b/a^c=a^{b-c}[/tex] division of exponents with same baseIf [tex]a^b=a^c[/tex] then [tex]b = c[/tex] equal exponents with same basePlease help me I need this for exam tomorrow and can u please show the working
Answer:
46,57/4
Step-by-step explanation:
area = π.r^2 = π.(d^2)/4
d^2 = AB^2= 5,6^2+3,9^2 =46,57
----> area = π.46,57/4
The graph of y=x^2-4x by drawing the line y=x-4
Answer:
the graph of y=x^2-4x is parabola as shown in the image
Step-by-step explanation:
The graph of [tex]y = x^{2} -4x[/tex] by drawing the line y=x-4
so this gives us that the line y=x-4 satisfies the equation [tex]y = x^{2} -4x[/tex]
To get points put y = x - 4 in the equation [tex]y = x^{2} -4x[/tex]
so we get x -4 = x( x- 4)
x =1 and x - 4 = 0
from here we get x = 1,4
now put these values in y = x -4
From here we get y = -3,0
so the points are (1 , -3) and ( 4 , 0)
Plot these on graph and we get the straight line .
For equation [tex]y = x^{2} -4x[/tex]
As we know it is of type of parabola with shifted centre.
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Let a population consist of the values cigarettes, cigarettes, and cigarettes smoked in a day. Show that when samples of size 2 are randomly selected with replacement, the samples have mean absolute deviations that do not center about the value of the mean absolute deviation of the population. What does this indicate about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a population?.
Based on the given mean absolute deviations, the sample mean absolute deviation will be 2 and the population mean absolute deviation will be 3.8.
What is the sample mean absolute deviation?= Sum of sample mean absolute deviation / Number
= (0 + 0.5 + 4.5 + 0.5 + 0 + 4 + 4.5 + 4 + 0) / 9
= 2
What is the population mean absolute deviation:First find the population mean:
= (10 + 11 + 19) / 3
= 13.3
Population mean absolute deviation:
= 1/3 x ( (10 - 13.67) + (11 - 13.3) + (19 - 13.3))
= 3.8
We can therefore see that the sample mean deviations is a biased estimate of the population mean absolute deviation.
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Solve 1 2 1 2x = x2 − 7x 10 4x by rewriting the equation as a proportion. which proportion is equivalent to the original equation?
The proportion that is equivalent to the original equation is [tex]\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]
Rational expressionsGiven the following expression
[tex]\frac{1}{2} + \frac{1}{2x} =\frac{x^2-7x+10}{4x}[/tex]
In order to find the equivalent proportion, we will find the LCM of the right side expression to have:
[tex]\frac{1}{2} + \frac{1}{2x} =\frac{x^2-7x+10}{4x}\\\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]
Hence the proportion that is equivalent to the original equation is [tex]\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]
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Answer: For the next part
✔ x = 1 and x = 8
✔ x = 0
if a/b and c/d are rational expressions, then: a/b / c/d = a*b/c*d
if a/b and c/d are rational expressions,a/b / c/d = a*b/c*d is false.
What is the definition of a fraction number?A fraction number is a number that represents a portion of a larger number, where the larger number might be any integer. It has the shape of a numerator and a denominator.
The given rational expression is;
a/b and c/d
Given relation;
[tex]\rm \frac{\frac{a}{b}}{\frac{c}{d}}\\\\ \frac{a d}{bc}[/tex]
When two fractions are divided the number got reversed and multiplied by the fraction.
Hence the given calculation is false.
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Answer: false
Step-by-step explanation: .
21 added to a number is the same as 37
Answer:
Step-by-step explanation:
Hi, let me help you out.
First I'm going to turn the verbal phrase into an algebraic phrase...
21+n=37. here n is the unknown number
Next, I believe you need to find what n equals.
This can be done by subtracting 21 from both sides.
n=37-21
n=16
Thus the number we need is 16.
_________________
Hope I helped. Best wishes.
Section B, Q5
please answer, it is urgent
Write 3x^2+12x+20 in the form a(x+b)^2+c
The equation is written as 3(x+12)²+20.The formula for ax² + bx + c is (Ax + B)² + C.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
3x^2+12x+20
The equation is compared the equation with,ax²+bx+c
After comparing the equation we get;
a=3
b=12
c=20
The equation is written in the form as;
⇒a(x+b)^2+c
⇒3(x+12)²+20
The formula for ax² + bx + c is (Ax + B)² + C.
Hence the equation is written as 3(x+12)²+20.
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What are the coordinates for point b?
a. (7, 0)
b. (0, 7)
c. (0, 8)
d. (1, 7)
The coordinates for point B are (a) (7,0)
Complete QuestionPoint B is located 7 units right of the origin. What are the coordinates for point b?
How to determine the coordinates?The origin is located as:
(0,0)
From the question, we understand that:
B ⇒ 7 unit right of origin
This means that:
B = (0 + 7, 0)
Evaluate the sum
B = (7,0)
Hence, the coordinates for point B are (a) (7,0)
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Answer:a
Step-by-step explanation:
On January 1, 2023, One of Mr. Cutter’s chickens flies away and lands on a Hawaiian Island. She
immediately begins laying and hatching eggs. The chicken population on the island begins to
triple every year. Write and graph a function that represents this situation. How many chickens
will be on the island on January 1, 2033?
Answer:
Step-by-step explanation:
Do you have any options or a graph?
If Bob sells each fish at a profit of $1.25, how much money will he have after selling all 24 fish? Show your calculation.
Best answer receives brainliest
Answer: $30
Step-by-step explanation:
So if Bob sells his fish at a profit of $1.25 and he has 24 fish to sell then 1.25*24= 30
(I'm assuming what you mean by "how much money he will have" is profit)
Answer:
The answer is $30. remove the decimal from the price and multiply it by the amount of fish. then when you finish multiplying add the decimal back in.
Step-by-step explanation:
125
× 24
--------
500
+ 2500
-----------
30.00
Decrease 80g by 12.5%
Find a the shortest distance from d to b
Please helppppppp????
The volume of the spherical ball will be 4 · π · 3² · 10⁶ cubic cm. Then the correct option is A.
The complete question is attached below.
What is the volume of the sphere?Let r be the radius of the sphere.
Then the volume of the sphere will be
V = 4/3 πr³ cubic units
The radius of the sphere is 3·10² cm.
Then the volume of the spherical ball will be
V = 4/3 πr³
V = 4/3 π(3 x 10²)³
V = 4/3 · π · 3³ · 10⁶
V = 4 · π · 3² · 10⁶ cubic cm
Then the correct option is A.
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Pleaseee hurry and answer
HELP ME!! FIND X AND Y.
Answer:
x = 26
y = 72°
Step-by-step explanation:
Finding x:Alternates angles are equal.(4x - 16)° = (3x + 10)°
Subtract 3x to both sides
4x - 3x - 16 = 10
x - 16 = 10
Add 16 to both sides
x = 10 + 16
x = 26
Finding y:Angles on a straight lines add up to 180 degrees.(4x - 16)° + y° = 180°
4x - 16 + y = 180
4(26) - 16 + y = 180
104 - 16 + y = 180
88 + y = 180
Subtract 88 to both sides
y = 180 - 88
y = 72°
[tex]\rule[225]{225}{2}[/tex]
georgia drew a scale model of one of the stepping stones in her garden. the two shapes are similar, and the ratio of the lengths of the sides is 4:1. if the length of side dc equals twelve inches, what is the length of side ut in the scale drawing?
The length of the UT is 3 inches if the ratio of the lengths of the sides is 4:1. if the length of side DC equals 12 inches,
What is a scale factor?The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.
We have:
Georgia drew a scale model of one of the stepping stones in her garden. the two shapes are similar, and the ratio of the lengths of the sides is 4:1.
The length DC = 12 inches
DC/UT = 4/1
12/UT = 4/1
UT = 12/4 = 3 inches
Thus, the length of the UT is 3 inches if the ratio of the lengths of the sides is 4:1. if the length of side DC equals 12 inches,
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Answer:
3 in.
Step-by-step explanation:
Keep it simple :)
This circle is centered at the origin, and the length of its radius is 8. What is
the circle's equation?
or +
5
8
5
OA. x+y=8
OB.x²2² +2²=8
OC. x + y = 64
OD. x² + y² = 64
4
Answer:
D
Step-by-step explanation:
x² + y² = 64, because when x is 0, y = ± 8, when y is 0, x = ± 8, that is the radius r
The equation of a circle with center at the origin and radius 8 is,
⇒ x² + y² = 64
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
This circle is centered at the origin, and the length of its radius is 8.
Since, The equation of a circle with center at the origin and radius r is,
⇒ x² + y² = r.
Hence, for this circle, the equation would be;
⇒ x² + y² = 8²,
or simplified,
⇒ x² + y² = 64
Thus, The equation of a circle with center at the origin and radius 8 is,
⇒ x² + y² = 64
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PLEASE HELP RNNN HELPPPPPPPPPPPP
Answer:
I think favorable outcomes are just the outcomes
which is 6
SR, SB, MR, MB, LR, LB
Step-by-step explanation:
a car travels along the highway to little rock a steady speed. when it begins it is 280 miles after 4 hours it 100
The function that describes the car's distance from little rocks would be option A; y = 45x + 280
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Point 1:
(x, y) = (0, 280)
Since we are told the car's initial position is 280 miles in the time 0 h
Point 2:
(x, y) = (4, 100)
Since we are told the car's final position is 100 miles after 4h.
Let's find the Slope :
m = 45
Now, the equation of the line is:
y = mx + b
y = 45x + 280
Then, The function that describes the car's distance from little rocks would be option A; y = 45x + 280
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1. Given the points A (2, 14) and B (17, -6).
(a) Find the distance of the line AB.
(b) Find the midpoint of the line AB.
(c) Find the gradient of the line AB.
(d) Find the equation of the line AB.
(e) Find the equation of the line parallel to AB passing through the point (3,5).
(f) Find the equation of the line perpendicular to AB passing through point (4,-2).
(g) Draw the above 3 lines on a graph.
Answer:
Step-by-step explanation:
the nth term of the sequence is 3n + 2. Find the first three terms of the sequence
Answer:
5, 8, 11, ...
Step-by-step explanation:
f(n)=3n+2
the first three terms will be f(1), f(2), and f(3).
f(1)=3(1)+2=5
f(2)=3(2)+2=8
f(3)=3(3)+2=11
Hope this helps!
If not, I am sorry.
Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph. What are the coordinates of pre-image point H?
(2, 3)
(–2, 3)
(3, 2)
(3, –2)
The coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a trapezoid GHJK that was rotated 180° about the origin.
The rule for 180-degree rotation about the origin:
(x, y) → (-x , -y)
From the graph:
Coordinate of H' is (-3, -2)
(-3, -2) → (3, 2)
Thus, the coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.
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8.
36.2
22.3
- 30-
33
Find the value of x.
(Round answer to the nearest tenth when necessary)
44.6
33.2
Answer:
36.2
Step-by-step explanation:
Assuming that the dotted line is a perpendicular bisector, we can say that it splits the side that is 30 units long into 2 sets of 15 units. Then, we can use the pythaogrean theorem to solve (Leg A is 33 and Leg B: 15). a^2+b^2=c^2
33^2+15^2=c^2
1089+225=c^2
1314=c^2
Square root of 1314 = square root of c^2
36.2 aapproximately c
Can someone help me out with this problem
From the given options the options B and C are correct for the given equation.
we have given the equation,
70=10+12r
We have to determine the correct option
What is the equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.
Therefore from the given options the options B and C are correct for the given equation.
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point-slope equation for perpendicular lines y=-2x-7 that passes through (-2,-3)
Answer: below! ^^
Step-by-step explanation:
Hii, do you need an answer to your question? Let me help you out! (;
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Part 1 ⚜Perpendicular lines have slopes that are opposite inverses of each other.
The slope (m) of the line that is perpendicular to y=-2x-7 is [tex]\sf -\cfrac{1}{2}[/tex].
Part 2 ⚜⚜ Point slope formula[tex]\boldsymbol{y-y1=m(x-x1)}[/tex]
⚜Stick in the known values[tex]\boldsymbol{y-(-3)=-\cfrac{1}{2}(x-(-2)}[/tex]
⚜ Simplify[tex]\boldsymbol{y+3=-\cfrac{1}{2}(x+2)}[/tex]
Voila! There's our answer, cheers! (:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Hope I helped! Best wishes!
Reach far. Aim high. Dream big.
[tex]\underbrace[/tex]
Solve for x.
Use the quadratic formula.
2x² - 9x + 8 =0
Answer:
x = 9/4 + 1/4 √17 or x = 9/4 + −1/4 √17
/ = over
Step-by-step explanation:
a = 2, b=-9, c=8
x = −b±√b2−4ac/2a
x = −(−9)±√(−9)2−4(2)(8)/2(2)
x = 9±√17/4
x = 9/4 + 1/4 √17 or x = 9/4 + −1/4 √17
On a number line, 6.3 would be located ______. Choose all answers that make a true statement.
6.3
《--|----|----|----|----|----|----|----|----|----|--》
A. between 6.2 and 6.4
B. to the left of 6.42
C. to the right of 6.45
D. to the right of 6.5
Answer:
A).
Step-by-step explanation:
The numbers should be in consecutive order e.g. - 6.2 6.3 6.4
For f(x)=3x+1 and g(x)=x²-6, find (f-g)(x)
Answer:
-x² + 3x + 7
Step-by-step explanation:
(f-g)(x) = f(x) - g(x) = (3x+1)-(x²-6) = -x² + 3x + 7
The value of (f - g)(x) is -x² + 3x + 7.
What is Function?The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, the given functions are;
f(x) = 3x + 1
g(x) = x² - 6
Now,
(f - g)(x) = f(x) - g(x)
= (3x + 1) - (x² - 6)
= 3x + 1 - x² + 6
(f - g)(x) = -x² + 3x + 7
Thus, the value of (f - g)(x) is -x² + 3x + 7.
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Which of the following terms best describes a vertical line that the graph of a
function approaches but never intersects?
A Horizontal asymptote
B Proportion
C Vertical asymptote
D Inverse variation
