Answers
Answer: [tex]\frac{1}{9}[/tex]
Step-by-step explanation:
When any number has a negative exponent, all the negative exponent is doing is flipping the sides.
When we plug -3 in for x we get [tex]-3^{-2}[/tex].
Now just imagine the -3 in fraction form as [tex]\frac{-3}{1}[/tex]. And all you do now is just flip the sides to get [tex](\frac{1}{-3} )^{2}[/tex]
And now apply the exponent 2 to the 1 and negative 3.
1 to the power of 2 is just 1
-3 to the power of 2 is 9.
So your answer is [tex]\frac{1}{9}[/tex]
Related Questions
What else would need to be congruent to show that ABC= A DEF by SAS?
B
E
Given:
AC DF
ZCZE
А
O A. BC = EF
O B. ZCEF
O C. ZAŁ ZD
O D. AC = DF
Answers
Answer:
A.
Step-by-step explanation:
BC ≅ EF
BC needs to be congruent to EF to show that ΔABC ≅ ΔDEF by SAS(Side -Angle-Side) Postulate.
how many times do you need to add 5 to 17 to reach the product of 6 and 7
Answers
Answer:
5
Step-by-step explanation:
The product of 6 and 7 is 42.
Let x be the number of times needed to add 5 to 17 to reach 42.
17 + 5x = 42
5x = 42 - 17
5x = 25
x = 5
Answer: I’m pretty sure it’s 5
Step-by-step explanation:
if four points are collinear, they are also coplanar
Answers
Answer:
Hi there!
The correct answer is: True
Step-by-step explanation:
If there is a line, there are infinite planes that pass through that line, therefore since the 4 points are in a line, they are coplanar .
A student walk 60m on a bearing of 028 degree and then 180m due east. How is she from her starting point, correct to the nearest whole number?
Answers
Answer: she is 215m from her starting point
Step-by-step explanation:
The diagram representing the situation is shown in the attached photo. Triangle ABC is formed with AC representing her distance from her starting point.
Angle B = 28 + 90 = 118°
To determine AC, we would apply the law of Cosines which is expressed as
a² = b² + c² - 2abCosA
Where a,b and c are the length of each side of the triangle and B is the angle corresponding to b(AC). Likening the expression to the given triangle, it becomes
AC² = AB² + BC² - 2(AB × BC)CosAC
AC² = 60² + 180² - 2(60 × 180)Cos118
AC² = 3600 + 32400 - 21600Cos118
AC² = 36000 - 21600(-0.46947156)
AC² = 36000 + 10140.59
AC² = 46140.59
AC = √46140.59
AC = 215 m
write h(x)=x2-6x + 3 in vertex form
Answers
Answer: The vertex form is h(x)=(x-3)^2-6
Step-by-step explanation:
Using the complete the square method, first complete any squares
X^2-6x+(-3)^2-(-3)^2+3
Use the binomial formula
(x-3)^2 - (-3)^2 +3
Simplify
(x-3)^2-6
Please help help❤️help me it would mean a lot
Answers
Answer:
B. points C, F and G
Step-by-step explanation:
B. Points G C F
Change each algebraic expression to a verbal expression.
1. A+B = 10
2. 4x - y = a
Answers
Answer:
1. A letter, A, added to a letter, B, equals ten.
2. A letter, x, which is multiplied by 4, then has a number, y, subtracted from it to equal a letter, a.
If you try write these out, I'm sure you'd get the algebraic expression given.
Can I have some help please? Thanks!
Answers
Answer:
(22/7)/6=0.523809
Step-by-step explanation:
V=4/3πr^3
V=4/3π(1/2)^3=π/6
or (22/7)/6=0.523809
Please help with answers A and B :)
Answers
b. 9
64 to 49 is -15, 49 to 36 is -13, 36 to 25 is -11, 25 to 16 is -9, so the next number is 16-7=9
Gretta created some figures that she calls reebs What attribute do these reebs have in common?
Answers
Answer:
Reebs have 1 right angle
Step-by-step explanation:
Look at all the reebs. They all have 1 right angle!
Answer:
C
Step-by-step explanation:
find the smallest square number that is divisible by each of the number 8,12,18 and 30
Answers
Answer:
3600.
Step-by-step explanation:
8 = 2*2*2
12= 2*3
18= 2*3*3
30 = 2*3*5
The lowest common multiple of the these is
2 * 2 * 2 * 3*3* 5 = 360.
So the smallest square number = 2*2*2*2*3*3*5*5
(We make all the sets of factors a square).
So it's 16 * 9 * 25 = 3600.
Answer:
3600
Step-by-step explanation:
PLEASEEEE.. MY TEACHER IS ASKING FOR THE ANSWER
Answers
See attached graph: v is on the y-axis and t is on the x-axis
cereal is on sale for $3.60 for a 9-ounce box. what is the price per ounce?
Answers
Answer:
$0.40 per oz
Step-by-step explanation:
given that the cereal is $3.60 for a 9 oz box
i.e
9 oz ----> costs $3.60
1 oz ----> costs $3.60 ÷ 9 = $0.40
hence the unit rate is $0.40 per oz
Answer:
0.40 per ounce
Step-by-step explanation:
The question asks is to find the unit rate, or price per ounce.
To find this, we need to divide the price by the number of ounces.
price/ ounces
It costs $3.60 for 9 ounces of cereal.
$3.60/9 ounces
Divide $3.60 by 9 (3.60/9=0.4)
$0.4/ounce
It costs $0.40 per ounce of cereal.
7th grade math I needs some help
Answers
Answer:
Step-by-step explanation:
To find 5e. El change, find the difference between week 1 and 1.
56.92-(-16.54) = 56.92+16.54 = -73.46.
Note: this is negative, because we are calculating the difference.
Hope this helps
Change the unit of length. 6 ft 2 in. = _____ ft Answer Choices A. 6 1/3 B. 6 1/6 C. 6 1/12 D .6 2/3
Answers
Answer:
6 1/6 ft
Step-by-step explanation:
12 inches = 1 ft
So 2 inches is 2/12 of a foot
2/12 = 1/6
6 ft 2 inches = 6 1/6 ft
plz help iam new i rlly need help
Answers
[tex]42 \times 48=2016[/tex]
[tex]24 \times 84 = 2016[/tex]
The answer is 42 × 48 because even when we switch the digits, the product remains the same.
A particle is moving along a projectile path at an initial height of 96 feet with an initial speed of 16 feet per second. This can be represented by the function H(t) = −16t2 + 16t + 96. What is the maximum height of the particle?
Answers
Answer:
The maximum height the projectile reaches is 100 feet
Step-by-step explanation:
Notice that the given equation representing the height of the projectile is a quadratic equation which negative leading coefficient (-16). Such type of equations would have a parabola that branches downwards as its graph.
therefore, what we need to find is the coordinates of the top vertex of that parabola. We can use for such the typical formula for the x-position of the vertex of a parabola with standard equation:
[tex]f(x)=ax^2+bx+c[/tex]
with x-position of the vertex given by:
[tex]x_v=\frac{-b}{2a}[/tex]
Then in our case ([tex]H(t)=-16t^2+16t+96[/tex]) we have:
Horizontal position of the vertex given by:
[tex]t_{vertex}=\frac{-16}{2(-16)} =\frac{1}{2}[/tex]
and now we can find the maximum height plugging this value into the height expression:
[tex]H(t)=-16(\frac{1}{2}) ^2+16\,(\frac{1}{2})+96=-4+8+96=100\,\,ft[/tex]
Four lines extend from point K. The space between lines K J and K N is 58 degrees. The space between lines K N and K M is 61 degrees. The space between lines K M and K L is 61 degrees. Which statement must be true about the diagram? Point K is a midpoint of Line segment J L. mAngleJKN = One-halfmAngleJKM Ray KM is an angle bisector of AngleNKL. JK = One-halfKL
Answers
Answer:
Ray KM is an angle bisector of [tex]\angle NKL[/tex].
Step-by-step explanation:
Given that there are 4 lines that are extended from a point K.
Angle between KJ and KN is [tex]58^\circ[/tex] i.e. [tex]\angle JKN =[/tex] [tex]58^\circ[/tex]
Angle between KN and KM is [tex]61^\circ[/tex] i.e. [tex]\angle NKM =[/tex] [tex]61^\circ[/tex].
Angle between KM and KL is [tex]61^\circ[/tex] i.e. [tex]\angle MKL =[/tex] [tex]61^\circ[/tex]
Please refer to the attached image for the conditions and dimensions of angles given in the question statement.
Now, let us have a look at the options given:
1. Point K is a midpoint of Line segment JL
JL is not a straight line first of all, and secondly there is no condition given about the line segments.
So, it is incorrect.
2. [tex]m \angle JKN = \dfrac{1}{2}m \angle JKM[/tex]
[tex]\angle JKN =[/tex] [tex]58^\circ[/tex] and
[tex]m \angle JKM =58+61=139^\circ\\\Rightarrow \dfrac{1}{2} m \angle JKM = 64.5^\circ[/tex]
So, it is also incorrect.
3. Ray KM is an angle bisector of [tex]\angle NKL[/tex].
Ray KM divides the [tex]\angle NKL[/tex] into two equal angles [tex]\angle NKM =[/tex] [tex]61^\circ[/tex] and [tex]\angle MKL =[/tex] [tex]61^\circ[/tex] so it is correct.
Determine whether the geometric series 25 − 5 + 1 − 0.2 ... converges or diverges, and identify the sum if it exists.
Answers
Answer:
Converges
Sum = 20.8333
Step-by-step explanation:
A geometric series has a general formula of:
[tex]\sum ar^n[/tex]
Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.
In this particular case, the initial term is a=25, and each term is being divided by -5, or multiplied by -0.2, so the general form would be:
[tex]\sum 25*(-0.2)^n[/tex]
Since 0.2 < 1.0, the series converges.
The sum of the series is given by:
[tex]S=\frac{a}{1-r}\\S=\frac{25}{1-(-0.2)}\\S=20.8333[/tex]
The sum is 20.8333.
The geometric series converges and the sum is equal to 20.83.
What is a Geometric Series ?A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms .
A geometric series has a general formula of:
∑arⁿ
Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.
In this particular case, the initial term is a=25 and each term is divided by -5 or multiplied by (-0.2)
Therefore r = -0.2 and as it is <1 therefore the series converges
The sum of a convergent series is
S = a/(1-r)
S = 25/(1-(-0.2))
S= 25/1.2
S = 20.83
Therefore the sum of the series is 20.83
To know more about Geometric Series
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The water from a fire hose follows a path described by y equals 2.0 plus 0.9 x minus 0.10 x squared (units are in meters). If v Subscript x is constant at 10.0 m/s, find the resultant velocity at the point left parenthesis 9.0 comma 2.0 right parenthesis .
Answers
Answer:
The resultant velocity is 12.21 m/s.
Step-by-step explanation:
We are given that the water from a fire hose follows a path described by y equals 2.0 plus 0.9 x minus 0.10 x squared (units are in meters).
Also, v Subscript x is constant at 10.0 m/s.
The water from a fire hose follows a path described by the following equation below;
[tex]y=2.0 + 0.9x-0.10x^{2}[/tex]
The velocity of the [tex]x[/tex] component is constant at = [tex]v_x=10.0 \text{ m/s}[/tex]
and the point at which resultant velocity has to be calculated is (9.0,2.0).
Let the velocity of x and y component be represented as;
[tex]v_x=\frac{dx}{dt} \text{ and } v_y=\frac{dy}{dt}[/tex]
Now, differentiating the above equation with respect to t, we get;
[tex]y=2.0 + 0.9x-0.10x^{2}[/tex]
[tex]\frac{dy}{dt} =0 + 0.9\frac{dx}{dt} -(0.10\times 2)\frac{dx}{dt}[/tex]
[tex]\frac{dy}{dt} = 0.9\frac{dx}{dt} -0.2\frac{dx}{dt}[/tex]
[tex]v_y = 0.9v_x -0.2v_x[/tex]
[tex]v_y = 0.7v_x[/tex]
Now, putting [tex]v_x=10.0 \text{ m/s}[/tex] in the above equation;
[tex]v_y = 0.7 \times 10.0[/tex] = 7 m/s
Now, the resultant velocity is given by = [tex]v=\sqrt{v_x^{2}+v_y^{2} }[/tex]
[tex]v=\sqrt{10^{2}+7^{2} }[/tex]
= [tex]\sqrt{149}[/tex] = 12.21 m/s
If 96 out of 200 pet owners own cats, what fraction and what percentage of
pet owners do not own cats?
Check all that apply.
A. 52%
104
IL B.
200
C. 48%
D. 0.52%
E 96 help ASAP plz
200
Answers
Answer:
A. 52% and B. 104/200
Step-by-step explanation:
To find the answer, we first have to find how many pet owners own cats. As percentages are x/100, when we have x/200 we divide the numerator and denominator by 2 to bring the fraction to 48/100. (96/200 divided by 2 equals 48/100). Now that we have the percentage of pet owners that own cats (48%), we need to find how many do not own cats. To do so, we just subtract 100-48 to get 52. Then, we do the same to the fraction of 96/200. (200-96 = 104). This brings our answers to A. 52% and B. 104/200
The percentage of owners that do not own cat is 52%
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Given here, 96 out of 200 pet owners own cats then the owners who do not own cat are 104
Therefore the number of non cat owners in percentage terms is
= (104/200) ×100
= 52.5%
Hence, the answer is 52.5%
Learn more about percentages here:
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4x= 2y + 38; 2 - 3y=x
Simultaneous equation please help
Answers
Answer:
x = 59/7, y = -15/7
Step-by-step explanation:
4x= 2y + 38;
2 - 3y=x
We can substitute for x in the first equation since the second equation is solved for x
4(2-3y) = 2y+38
Distribute
8 - 12y = 2y+38
Add 12y to each side
8-12y+12y = 2y+12y+38
8 = 14y+38
Subtract 38 from each side
-30 = 14y
Divide by 14
-30/14 = y
-15/7 = y
Now solve for x
2 - 3y = x
2 - 3*-15/7 = x
2 +45/7 = x
14/7 + 45/7 = x
59/7 =x
A package of 3 pairs of insulated socks costs $20.67. What is the unit price of the pairs of socks?
The unit price is $ per pair of socks.
Please quickly
Answers
Answer:
$6.89
Step-by-step explanation:
To find unit price divide the dollar by the amount. The dollar is 20.67. The amount of socks are 3. The equation would then be 20.67/3. Then solve and the answer would be $6.89.
Explanation:
Set up a proportion.
3/20.67=1/x
3x=20.67
x=6.89
what is the solution to the following inequality? x/-3 ≤ 3 A) x ≥ 6 B) x ≤ -9 C) x ≥ 1 D)x ≥ -9
Answers
Answer:
option D
Step-by-step explanation:
x/-3≤3
multiply by (-1) on both sides
x/3≥-3
x>=-9
Answer:
Letter D
Step-by-step explanation:
What is the range of this function?
Answers
Explanation: the range is the set of all possible resulting values of the dependent variable ( y )
The given line passes through the points (-4, -3) and (4.
1)
What is the equation, in point-slope form of the line that is
perpendicular to the given line and passes through the
point (-4, 3)?
V-3 -2(x+4)
3-
2-
+
Oy-3 =-{(x+4)
Ov-3 = {(x + 4)
-2
y-3 =2(x + 4)
-3
(-3)
Answers
9514 1404 393
Answer:
y -3 = -2(x +4)
Step-by-step explanation:
The slope of the given line is ...
m = (y2 -y1)/(x2 -x1)
m = (1 -(-3))/(4 -(-4)) = 4/8 = 1/2
The perpendicular line will have slope -1/(1/2) = -2.
__
The point-slope equation of the line with slope m through point (h, k) is ...
y -k = m(x -h)
For point (-4, 3) and slope -2, the equation is ...
y -3 = -2(x +4)
The congruence theorem that can be used to prove △LON ≅ △LMN is SSS. ASA. SAS. HL.
Answers
Answer:
The correct option is SSS (Side-Side-Side) Theorem
Step-by-step explanation:
The question is incomplete because the diagrams of ΔLON and ΔLMN are not given. I have attached the diagram of both triangles below for better understanding of the question.
Consider the diagram attached below. We have to find the congruence theorem which can be used to prove that ΔLON ≅ ΔLMN
We can see in the diagram that both triangle have a common side that is LN. It means 1 side of both triangles is congruent because LN≅LN
Consider the sides ON and MN. Both side have a single bar on them, which means that it is given that both of these side are congruent. Hence ON≅MN
Consider the sides LO and LM. Both side have a double bars on them, which means that it is given that both of these side are also congruent. Hence LO≅LM
SSS theorem states that if all sides of the triangles are congruent, then the triangles themselves are also congruent, which is the same case in this question
Answer:
D. SSS
Step-by-step explanation:
I hope this helps.
Please help thank you
Answers
Answer:
D
Step-by-step explanation:
subsitute each of the x and y values for each of the equations and if they both equal each other It is correct.
Answer:
x = 2, y= -1
Step-by-step explanation:
12x - y = 25
9x + y = 17
add both equations to eliminate y
21x = 42
divide by 21
x = 42/21
x = 2
sub x in equation i to find y
12(2) - y = 25
24 - y = 25
-y = 1
therefore y = -1, x = 2
An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated. (a) Draw the possibility diagram of the product of the two numbers appearing on the die in each throw (b) Use the possibility diagram to calculate the probability that the product of the two numbers is (i) A prime number (ii) Not a perfect square (iii) A multiple of 5 (iv) Less than or equal to 21 (v) Divisible by 4 or 6
Answers
Answer:
this question is roung
Which of the following choices is the x intercept of the equation 2y-x=-6
Answers
Answer:
[tex]x = 6[/tex]
Step-by-step explanation:
Given
[tex]2y-x=-6[/tex]
Required
Determine the x intercept
To get the value of x intercept; we simply substitute 0 for y;
i.e. y = 0
[tex]2y-x=-6[/tex] becomes
[tex]2(0)-x=-6[/tex]
[tex]0-x=-6[/tex]
[tex]-x=-6[/tex]
Multiply both sides by -1
[tex]-1 * -x=-6 * -1[/tex]
[tex]x=-6 * -1[/tex]
[tex]x = 6[/tex]
Hence, the x intercept is 6