To solve the negative exponents , we have to apply the negative exponent rule or the fractional exponent rule.
How are negative exponent calculated?To calculate the negative exponent we need to remember about the negative exponent that the base is on the opposite side of the fraction. Here , We need to flip the fraction so that the base will be on the other side.
Negative exponent Rule :-
[tex]a^{-n} = \frac{1}{a^{n} }[/tex]
Now , we will solve a fraction with negative exponent
For example ; Simplify the fraction [tex]\frac{3^{-2} }{9^{-2} }[/tex]
Solution : [tex]\frac{3^{-2} }{9^{-2} } = \frac{9^{2} }{3^{2} }= \frac{81}{9}[/tex]
= 9
Here, 9 is the answer of the above example.
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Find the area of the triangle ABC with the coordinates of A(10, 15) B(15, 15) C(30, 9).
A= units^2
Check the picture below. so, that'd be the triangle's sides hmmm so let's use Heron's Area formula for it.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{15}) ~\hfill a=\sqrt{[ 15- 10]^2 + [ 15- 5]^2} \\\\\\ ~\hfill \boxed{a=\sqrt{125}} \\\\\\ (\stackrel{x_1}{15}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{9}) ~\hfill b=\sqrt{[ 30- 15]^2 + [ 9- 15]^2} \\\\\\ ~\hfill \boxed{b=\sqrt{261}}[/tex]
[tex](\stackrel{x_1}{30}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill c=\sqrt{[ 10- 30]^2 + [ 5- 9]^2} \\\\\\ ~\hfill \boxed{c=\sqrt{416}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{125}\\ b=\sqrt{261}\\ c=\sqrt{416}\\ s\approx 23.87 \end{cases} \\\\\\ A\approx\sqrt{23.87(23.87-\sqrt{125})(23.87-\sqrt{261})(23.87-\sqrt{416})}\implies \boxed{A\approx 90}[/tex]
Mrs cunningham wants to use rubber tiles to cover the floor of an indoor playground
what is the unit cost per ruber tile
Answer:
the unit cost per rubber tile is $$$$$$$$$$$$$6
Step-by-step explanation:
..
PLS HELP ASAP !!!!!!!!!!
Answer:
Alice
Step-by-step explanation:
14$ the amount he had - X the amount he lost (the unknown) is what is described by Alice
12. Calculate. a) - (-/-)²2 c) 49
Answer:
write your questions very well
If a female student is selected at random, find the probablility that the student is a senior.
Add all the females together: 3 + 4 + 6 + 3 = 16
Female seniors = 3
Probability of picking a senior = 3/16 = 0.1875 x 100 = 18.75%
Rounded to the nearest whole number = 19%
Answer: 19%
Not sure how to do this
Answer:
[tex]\underline{\boxed{\sf{2(x - 11)(x + 11)}}}[/tex]
Step-by-step explanation:
[tex]\sf{2x^2 - 242}[/tex]
Common factor :
[tex]\sf{2x^2 - 242}[/tex]
[tex]\sf{2(x^2 - 121)}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Use the sum-product pattern :
[tex]\sf{2(x^2-121)}[/tex]
[tex]\sf{2(x^2 + 11x-11x - 121)}[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Common factor from the two pairs :
[tex]\sf{2(x^2 + 11x-11x - 121)}[/tex]
[tex]\sf{2(x(x+11) -11(x + 11))}[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Rewrite in factored form :
[tex]\sf{2(x(x+11)- 11(x + 11))}[/tex]
[tex]\sf{2(x - 11)(x + 11)}[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Solution :
[tex]\sf{2(x - 11)(x + 11)}[/tex]
Jerome solved a system of equations and found that it had an infinite number of solutions. Which system could be the system that Jerome solved
One example of a system of equations that has infinite solutions is given by:
x + y = 2.
2x + 2y = 4.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
A system will have infinite solutions when the two equations are multiples, hence one example is given by:
x + y = 2.
2x + 2y = 4.
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Round 4/15 to the nearest thousandth
Answer:
0.267
Step-by-step explanation:
4/15 as a decimal is 0.26 repeating so rounded to the nearest thousandth would be 0.267
How long does it take $500 to double at a simple interest rate of 24%?
Answer:
4 years and 2 months
Step-by-step explanation:
Simple interest formula
A = P(1 + rt)
where:
A = final amountP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
A = $500 × 2 = $1,000P = $500r = 24% = 0.24Substitute the given values into the formula and solve for t:
[tex]\implies \sf 1000 = 500(1 + 0.24t)[/tex]
[tex]\implies \sf \dfrac{1000}{500}=(1 + 0.24t)[/tex]
[tex]\implies \sf 2=1 + 0.24t[/tex]
[tex]\implies \sf 1 = 0.24t[/tex]
[tex]\implies \sf t=\dfrac{1}{0.24}[/tex]
[tex]\implies \sf t=4 \frac{1}{6} \:years[/tex]
[tex]\implies \sf t=4\:years\:2\:months[/tex]
Therefore, it takes 4 years and 2 months for the initial investment of $500 to double at a simple interested rate of 24%.
Find the greatest common factor of 15x2y³ and -18x³yz.
Answer:
GCF=3[tex]x^{2}y[/tex]
Step-by-step explanation:
First, take a look at the numbers.
GCF of 15 and -18 = 3
Then, look at the variables.
GCF of (x^2)(y^3) and (x^3)(y)(z) = (x^2)(y)
Lastly, combine the two expressions
GCF = 3(x^2)(y)
Answer: 3(x^2)(y)
Hope this helps!
If A = (-2, -4) and B = (-8, 4), what is the length of AB?
A.) 14 units
B.) 10 units
C.) 16 units
D.) 12 units
Please helpppp!
Answer:
10
Step-by-step explanation:
Using the distance formula,
[tex] \sqrt{ {( - 2 - ( - 8))}^{2} + { (- 4 - 4)}^{2} } = 10[/tex]
What is the value of x in the figure?
X
40⁰
OA. 40°
OB. 70°
OC. 80°
OD. 120°
OE. 150°
70⁰
Answer:
E 150
Step-by-step explanation:
The coordinates of the mid - point of the line AB is (-1, -5).
What is mid - point?A midpoint is a point that divides a given line into two equal parts.
Given is that AB has endpoints at A(4, -8) and B(-6, -2). It is asked to find the coordinates of the midpoint of AB.
We can write the coordinates of the midpoint of AB as -
{x} = (x₁ + x₂)/2
{x} = (4 - 6)/2
{x} = - 2/2
{x} = -1
{y} = (y₁ + y₂)/2
{y} = (-8 - 2)/2
{y} = - 10/2
{y} = - 5
Therefore, the coordinates of the mid - point of the line AB is (-1, -5).
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Point QQQ is located at (-4, 6)(−4,6)left parenthesis, minus, 4, comma, 6, right parenthesis. Point RRR is located at (8, 6)(8,6)left parenthesis, 8, comma, 6, right parenthesis.
What is the distance from point QQQ to point RRR?
=========================================================
Explanation:
Points Q and R have the same y coordinate of 6.
This means they're on the same horizontal level and we can form a number line through these points. Think of Q and R being on the x axis.
Going from -4 to 8 is a distance of 12 units because either
-4-8 = -12 which flips to +12 or 12
8-(-4) = 8+4 = 12
Effectively I used absolute value for the first part to go from -12 to 12. Distance cannot be negative.
Alternatively, you can count out the number of horizontal spaces from -4 to 8 and you should count out 12 units.
--------------------------------
If you need to use the distance formula, then this is what the steps may look like:
[tex]Q = (x_1,y_1) = (-4,6) \text{ and } R = (x_2, y_2) = (8,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-4-8)^2 + (6-6)^2}\\\\d = \sqrt{(-12)^2 + (0)^2}\\\\d = \sqrt{144 + 0}\\\\d = \sqrt{144}\\\\d = 12\\\\[/tex]
In my opinion, the distance formula is overkill because we can simply apply subtraction or count out the number of spaces. It's up to you which you prefer you like better. Of course be sure to follow all instructions your teacher mentions.
If the two points weren't on the same horizontal level, then we would have no choice and have to use the distance formula. Or you could use the pythagorean theorem which is effectively what the distance formula is derived from.
Question 3 of 10
Theresa has a credit card that uses the average daily balance method. For the
first 12 days of one of her billing cycles, her balance was $350, and for the
last 19 days of the billing cycle, her balance was $520. If her credit card's APR
is 14%, which of these expressions could be used to calculate the amount
Theresa was charged in interest for the billing cycle?
The amount that Theresa was charged in interest for the billing cycle is $5.30
How to calculate the interest?By using the average daily balance, the amount will be:
= (350 × 12) + (520 × 19) / (12 + 19)
= (4200 + 9880)/31
= 454.19
Therefore, the interest will be:
= (454 × 0.14)/12
= $5.30
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I totally don't understand this I will give you 20 points if you help me with it
Answer:
-4.25
Step-by-step explanation:
Solve system of equation using elimination by addition.
Will give brainliest!!
Answer:
[tex]x = 2, y = -1[/tex]
Step-by-step explanation:
We can add the 2 equations together to solve for y.
[tex](-3x + 5y) + (3x + 7y) = (-11) + (-1)\\-3x + 3x + 5y + 7y = -11 -1\\12y = -12\\y = -1[/tex]
Now we can solve for x by substituting y in one of the original equations.
[tex]3x + 7y = -1\\3x + 7(-1) = -1\\3x - 7 = -1\\3x = 6\\x = 2[/tex]
Those are the answers
- Kan Academy Advanced
Sara sells aloe vera plants and barrel cacti at the local street fair. Each aloe vera plant is $3 and each barrel cactus is $2.
On Monday she sold a total of 12 plants for $31. How many of each type of plant did Sara sell?
x:# aloe vera y : # barrel cacti
HELP ASAP
Find the volume of the sphere. Round your answer to the nearest tenth.
Answer:
V = 3053.63 mm^3
Step-by-step explanation:
radius : 9mm
V = 4/3 * pi * r^3
V = 4/3 * (3.1415926535898...) * 9^3
V = 3053.63 mm^3
Please help me with this
Answer:
point B
Step-by-step explanation:
Answer:
It's Point B.
Go to 5 on the x-axis and then go up 3
The 5 is the x-axis and 3 is the y-axis
Which equations and/or functions represent the graphed line? Select three options.
A coordinate plane with a line passing through the points, (negative 4, 0), (negative 2, 1), (0, 2), and (2, 3).
The equations of the graphed line and function can be written as:
f(x) = 1/2x + 2
y - 3 = 1/2(x - 2)
y - 1 = 0.5(x + 2)
What is the Equation of a Graphed Line?Equation of a graphed line can be expressed in:
Slope-intercept form as y = mx + b, where m = slope, b = y-intercept; or
Point-slope form as y - b = m(x - a), where (a, b) is a point and m = slope.
Find the slope (m) of the line:
Slope (m) = change in y / change in x = 1/2 = 0.5
y-intercept (b) = 2
To express the graphed line in slope-intercept form, substitute m = 1/2 and b = 2 into f(x) = mx + b:
f(x) = 1/2x + 2.
Using the point-slope form, write the equation by substituting m = 1/2 and (a, b) = (2, 3) into y - b = m(x - a):
y - 3 = 1/2(x - 2)
Or substitute m = 0.5 and (a, b) = (-2, 1) into y - b = m(x - a):
y - 1 = 0.5(x - (-2))
y - 1 = 0.5(x + 2)
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help meeee i need 100
8 out of 15
Select the graph that represents the inequality.
2x+3y>6
Answer:
3rd graph
Step-by-step explanation:
Since the inequality has a greater than symbol (>) and not a greater than or equal to symbol ([tex]\geq[/tex]), the graph will have a dotted line, meaning only the third and fourth graphs could be the one.
Since 2x+3y is GREATER THAN 6 and not LESS THAN 6, we know that the shaded part of the graph will be above (or more) than the line. Therefore, the third graph is the graph that represents the inequality.
The attached picture proves it :)
Hope this helps!
0/1
What is the equation of
the line in y=mx+b form?
(Photo)
Answer:
y=-15x+100
Step-by-step explanation:
i need help to find the square units of this triangle
Answer:
24square unit
Step-by-step explanation:
triangle area=1/2.b.h
=1/2.8.6=24
4 in.
4 in.
What is the volume of this container?
1 in.
2 in.
4 in.
56 in²
64 ins
64 in²
56 ins
Answer:
64in
Step-by-step explanation:
for a four sided figure, you do base x height. volume isn't squared in Math.
helpp asapp please due soonn
Answer:
A.
Step-by-step explanation:
1.5m + 6.5q > 100
✨♥️
geometry problem please help!
Answer:
x = 3
Step-by-step explanation:
the midsegment XW is half the sum of the parallel bases , that is
7x + 10 = [tex]\frac{1}{2}[/tex] (46 + 16 ) = [tex]\frac{1}{2}[/tex] × 62 = 31 ( subtract 10 from both sides )
7x = 21 ( divide both sides by 7 )
x = 3
Is (x+5) a factor of f(x)=x^3 - 4x^2 + 3x + 7? use either the remainder theorem or the factor theorem to explain your reasoning.
Answer:
No
Step-by-step explanation:
Use synthetic division
-5 | 1 -4 3 7
____-5 45 -240
1 -9 48 | -233
Since the remainder is not 0, then x+5 is not a factor of the polynomial
Find the volume.
Area = 16.4 cm²
8.1 cm
cm³
Answer:
132.84 is the answer as volume is area times length
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