By using properties for exponents, we will see that the equivalent expression is:
[tex]2x^{-4}y^6[/tex]
Which is the equivalent expression?Here you need to remember the property:
[tex]a^n/a^m = a^{n - m}[/tex]
We have the expression:
[tex]\frac{-4x^{-3}y^4}{-2xy^{-2}}[/tex]
We can separate the fraction to:
[tex]\frac{-4x^{-3}y^4}{-2xy^{-2}} = \frac{-4}{-2}*\frac{x^{-3}}{x} *\frac{y^4}{y^{-2}}[/tex]
Now we can simplify by using the above relation, we will get:
[tex]\frac{-4x^{-3}y^4}{-2xy^{-2}} = \frac{-4}{-2}*\frac{x^{-3}}{x} *\frac{y^4}{y^{-2}} = 2*x^{-3-1}*y^{4 - (2)} = 2*x^{-4}*y^6[/tex]
So the correct option is the last one.
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[tex]\\ \rm\Rrightarrow (-4x^{-3}y^4)\div(-2xy^{-2})[/tex]
a^m÷a^n=a^m-n[tex]\\ \rm\Rrightarrow 2x^{-3-1}y^{4+2}[/tex]
[tex]\\ \rm\Rrightarrow 2x^{-4}y^6[/tex]
Option D
Find the distance between the points ( – 4,8) and ( – 4, – 5)
Answer:
they are 13 points away from eachother
Step-by-step explanation:
count up or down then left or right
Answer:
13 units.
Step-by-step explanation:
Distance = √[(x2-x1)^2 + (y2-y1)^2] where (x1,y1) and (x2,y2) are the 2 points
So here the distance = √(-4 - -4)^2 + (8 - -5)^2)
√(0 + 13^2)
= 13
Which statement is true about the factorization of 30x2 40xy 51y2? the polynomial can be rewritten after factoring as 10(3x2 4xy 5y2). the polynomial can be rewritten as the product of a trinomial and xy. the greatest common factor of the polynomial is 51x2y2. the greatest common factor of the terms is 1.
The statement that is true about the trinomial is the greatest common factor of the terms is 1.
What is a trinomial?A trinomial is a polynomial with three terms or monomials.
To know which statements about the polynomial are true, let's check each of the statements individual.
A.) The polynomial can be rewritten after factoring as [tex]10(3x^2+4xy+5y^2)[/tex]
Since the product of 5 and 10 is equal to 50, the third term is 51. Therefore, the statement about the polynomial is false.
B.) The polynomial can be rewritten as the product of a trinomial and xy.
All the terms in the polynomial are completely different therefore, can not be written as the product of a trinomial and xy.
C.) The greatest common factor of the polynomial is 51x2y2.
All the terms in the polynomial are completely different therefore, can not be written as the product of a trinomial and xy.
D.) The greatest common factor of the terms is 1.
As all the greatest common factors of the terms are completely different, therefore, the only common factor between the three terms will be 1.
Hence, the statement that is true about the trinomial is the greatest common factor of the terms is 1.
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Answer:
Step-by-step explanation:The statement that is true about the trinomial is the greatest common factor of the terms is 1.
What is a trinomial?
A trinomial is a polynomial with three terms or monomials.
To know which statements about the polynomial are true, let's check each of the statements individual.
A.) The polynomial can be rewritten after factoring as
Since the product of 5 and 10 is equal to 50, the third term is 51. Therefore, the statement about the polynomial is false.
B.) The polynomial can be rewritten as the product of a trinomial and xy.
All the terms in the polynomial are completely different therefore, can not be written as the product of a trinomial and xy.
C.) The greatest common factor of the polynomial is 51x2y2.
All the terms in the polynomial are completely different therefore, can not be written as the product of a trinomial and xy.
D.) The greatest common factor of the terms is 1.
As all the greatest common factors of the terms are completely different, therefore, the only common factor between the three terms will be 1.
Hence, the statement that is true about the trinomial is the greatest common factor of the terms is 1.
Pls help I need this
Step-by-step explanation:
I hope this helps, you take the substitution and put it in where the variable once was in parenthesis, then you let them interact as the vaiable onece was but now you can solve because you know the value.
A pan from the oven is sitting out to cool to room temperature. If the temperature difference between the pan and room temperature is currently 197°C and is decreasing by 6% every minute, how much above room temperature will the pan be in 15 minutes? If necessary, round your answer to the nearest tenth.
The temperature difference between the pan and room temperature would be 77.9⁰C in the next 15 minutes,
How to solve an exponential function?Let y represent the temperature difference after x minutes.
The difference between the pan and room temperature is currently 197°C and is decreasing by 6% every minute, hence:
y = 197(100% - 6%)ˣ
y = 197(0.94)ˣ
The temperature in the next 15 minute is:
y = 197(0.94)¹⁵ = 77.9⁰C
The temperature difference between the pan and room temperature would be 77.9⁰C in the next 15 minutes.
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A dryer and washer cost $936 combined the washer cost $86 more than the dryer what is the cost of the dryer
By definition, theoretical probability is equal to:
A.
No. Of favorable outcomes
Total no. Of possible outcomes
B.
No. Of total outcomes
Total no. Of impossible outcomes
No. Of total outcomes
C.
Total no. Of possible outcomes
D.
No. Of possible outcomes
Total no. Of favorable outcomes
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
The Correct choice is A
Theoretical probability is defined as number of favorable outcomes out of Total possible outcomes.
That is :
[tex]\qquad \tt \dashrightarrow \: \dfrac{ \texttt{No. of favorable outcomes}}{ \texttt{Total number of possible outcomes}}[/tex]
By definition, Theoretical probability is equal to,
⇒ Number of favorable outcomes / Total no. of possible outcomes.
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
To find the definition of Theoretical probability.
Now, We know that;
Theoretical probability can be defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
Hence, By definition, Theoretical probability is equal to,
⇒ Number of favorable outcomes / Total no. of possible outcomes.
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3. A square pyramid has a base with a side length
of 3 ft and lateral faces with heights of 2 ft. What
is the lateral area of the pyramid?
The lateral area of the pyramid is 15!
The product of two rational numbers is 6 If one of them is 8 find the other numbers
Answer:
3/4
Step-by-step explanation:
8x = 6
x = other number = 6/8 = 3/4
oder number to least to greatest 1/8 ; 2/5 ; 3/4
Answer:1/8, 2/5 3/4
Step-by-step explanation: you can turn each into decimal
0.125, 0.4 and 0.75
Answer:
[tex]\dfrac{1}{8} < \dfrac{2}{5} < \dfrac{3}{4}[/tex]
Step-by-step explanation:
[tex]\text{You can rewrite the fractions as}\\\\\dfrac 18=\dfrac{5}{40}\\\\\\\dfrac 25 = \dfrac{16}{40}\\\\\\\dfrac 34 = \dfrac{30}{40}\\\\\\\text{So,} ~\dfrac{5}{40} < \dfrac{16}{40} < \dfrac{30}{40}[/tex]
2/5+7/20 can y’all help me
Answer:
3/4
hope this helps. have a nice day :>
I need this answered please
Answer:
80 yds^2
Step-by-step explanation:
A=2(wl+hl+hw)=2·(2·2+9·2+9·2)=80
Delta math: Angle Terminology with Equations
Answer:
m∠A = 139°
Step-by-step explanation:
First we must know that
Supplementary angles equal to 180 degree.
Since we know that supplementary angles equal to 180 degree we can solve now:
Putting m ∠A and m ∠ B together and put the = 180
( 7x - 15 ) + ( 2x - 3 ) = 180
Now solving for x:
( 7x - 15 ) + ( 2x - 3 ) = 180
9x - 18 = 180
9x - 18 + 18 = 180 + 18
9x = 198
9x/9 = 198/9
x = 22
Hence, Angle A will have a measure of 7x - 15 which means 7 × 22 -15 = 154 - 15 = 139°
m∠A = 139°
The measure of Angle B will be 2x - 3 = 2 • 22 - 3 = 44 - 3 = 41°
m∠ B = 41°
139 + 31= 180
[RevyBreeze]
Supplementary angles have sum 180°
7x-15+2x-3=1809x-18=1809x=198x=198/9x=22m<A
7(22)-15=154-151397th grade math escape room: geometry Math in the Midwest 2019
An example of 7th grade geometry Math in the Midwest 2019 is Puzzle: Simplify -5 + 8 - 7.
What is geometry ?Geometry is known to be an aspect of mathematics that deals with the study of sizes, positions of angles, and others.
To simply the above, -5 + 8 - 7, follow the rule of BODMAS. and thus: we solve for addition before subtraction.
= -5 + 8 = 3
3 - 7 = -4
Therefore the simplified form of -5 + 8 - 7 is -4
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What is x and y? 2x-2y=-4 2x+y=11 Is there infinitely many solutions, 1 solution, or no solution? solve by elimination.
Let's solve your system by substitution.
2x−2y=−4;2x+y=11
Rewrite equations:
2x+y=11;2x−2y=−4
Step: Solve2x+y=11for y:
2x+y=11
2x+y+−2x=11+−2x(Add -2x to both sides)
y=−2x+11
Step: Substitute−2x+11foryin2x−2y=−4:
2x−2y=−4
2x−2(−2x+11)=−4
6x−22=−4(Simplify both sides of the equation)
6x−22+22=−4+22(Add 22 to both sides)
6x=18
6x/6 = 18/6
(Divide both sides by 6)
x=3
Step: Substitute3forxiny=−2x+11:
y=−2x+11
y=(−2)(3)+11
y=5(Simplify both sides of the equation)
Answer:
x=3 and y=5
Please help me with this!!! (Please no scams or fake answers)
Step-by-step explanation:
maybe if i reply I'll get points or whatever
See the picture below.
Answer:
in photo
Step-by-step explanation:
remember you still need to round it to 2 decimal places!!
Which number is equivalent to 3.4/3.2?
A. 2
B. 9
C. 81
D. 729
Answer:
1.0625
Step-by-step explanation:
3.4 divided by 3.2 = 1.0625 Did you enter your Q and A correctly ?
rewrite the function in an equivalent form the would reveal the vertex of the function f(x)=x^2+8x+6
Answer:
f(x)=(x+4)-10
Step-by-step explanation:
Since the function f(x)=x^2+8x+6 is in standard form, you need to find the axis of symmetry using the formula -b/2a, and then plug the value back into the original equation to find the vertex.
The vertex is (-4, -10)
Using this information, we can rewrite the equation in vertex form (f(x=a(x-h)+k), where (h, k) is the vertex.
The equation we rewrite is f(x)=(x+4)-10
What is 112.491 written in word form?
Answer:
112.491 = one hundred twelve and four hundred ninety-one
thousandths.
Step-by-step explanation:
Nicole bought a meal in a town that has no sales tax. She tips 20%. Select all meals Nicole could buy with less than $16 total.
A-$12. 36
B-$12. 50
C-$13. 00
D- $14. 79
E- $14. 99
Answer:
I'm missing some information... but I'll answer the question regardless
x=the cost of the meal
1.2x≤$15
divide both sides by 1.2
x≤$12.5
In short, this means that Nicole can buy anything that costs $12.50 or less.
120 students were surveyed about which vegetable is their favorite.
Answer:
48 Students
Step-by-step explanation:
It is given that the total number of students is 120, and to find the amount of students that chose carrots or potatoes as their favorite vegetable multiply the percentage by 120 and add. 120 * .1 = 12. 120 * .3 = 36. 36 + 12 = 48.
Answer:
48 Students
Step-by-step explanation:
4. Romeo paid $380.75 in car repairs. The sales tax rate is 8%. What is the
total Romeo paid to repair his car?*
[tex][text]\orange{ \rule{100pt}99999pt}[/tex]
help with this questions please!
math
Step-by-step explanation:
[tex]area \: of \: rectangle = length \times \: width[/tex]
Given
[tex]l = 2w - 3[/tex]
using this
[tex]area = l \times w = (2w - 3)(w) = 27[/tex]
[tex]2 {w}^{2} - 3w = 27[/tex]
[tex]2 {w}^{2} - 3w - 27 = 0[/tex]
[tex]2 {w}^{2} - 9w + 6w - 27 = 0[/tex]
[tex]2w(w - 4.5) + 6(w - 4.5) = 0[/tex]
[tex](2w + 6)(w - 4.5) = 0[/tex]
[tex]w = - 3 \: \: or \: \: w= 4.5[/tex]
Since size cannot be negative therefore
[tex]w = 4.5cm[/tex]
[tex]l = 2w - 3 = 9 - 3 = 6[/tex]
Hence length of the rectangle=6m
width of the rectangle=4.5m
Answer:
Let length and breadth of rectangle be x metres and y metres respectively.
xy = 27 ---- eqn 1
x = 2y-3 ---- eqn 2
Sub eqn 2 into eqn 1:
(2y-3) × y = 27
2y² - 3y = 27
2y² - 3y - 27 = 0
(y+3)(2y-9) = 0
y+3=0 or 2y-9=0
y=-3 (rejected) 2y=9
y=4.5
Sub y=4.4 into eqn 2:
x = 2(4.5) - 3
= 6
Hence,
length of rectangle = x metres
= 6m
breadth of rectangle = y metres
= 4.5m
Please, Please, Please Help MEE!! ASAP!
1a. 35
b. 17.5
c. 3.5d
2. $4.5
Two times the sum of four times a number plus six is the same as five less than twice the same number what is the number?
Answer:
[tex]\frac{-17}{6}[/tex]
Step-by-step explanation:
Let x be the number we want to find.
First we analyze the given informations
Info 1 : Two times the sum of four times a number plus six
We translate this statement (info 1) mathematically as : 2×(4x + 6)
Info 2 : five less than twice the same number
We translate this statement (info 2) mathematically as : 2x - 5
Info 1 is the same as Info 2 ⇔ 2×(4x + 6) = 2x - 5
2×(4x + 6) = 2x - 5
⇔ 8x + 12 = 2x - 5
⇔ 8x - 2x = -5 - 12
⇔ 6x = - 17
⇔ x = -17/6
What is the measure of the missing angle?
Points R(-6,-5),S(-2,-5) and T(-2,n) are plotted in the coordinate plane. The distance between points R and S is half the distance between points S and T. The value of n could be blank or blank.
The square of the distance between two points is the sum of the squares of the difference between two coordinates. The value of n can be -13 or 3.
What is the distance between two points?The distance between two points is given by the formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
As it is given that the distance between points R and S is half the distance between points S and T.
[tex]2(RS) = ST[/tex]
Now, the distance between RS can be written as,
[tex]RS=\sqrt{[-6-(-2)]^2+[-5-(-5)]^2}\\RS = \sqrt{(-6+2)^2+(0)^2}\\RS = \sqrt{16}\\RS = \pm 4[/tex]
Further, we can write,
[tex]2(RS) = ST\\\\2(\pm 4) = \sqrt{[-2-(-2)]^2+[-5-n]^2}\\\\\pm 8 = \sqrt{(0)^2+(-5-n)^2}\\\\\pm 8^2=(-5-n)^2\\\\\pm8=(-5-n)\\\\[/tex]
When the value of 8 is positive,
[tex]+8+5=-n\\\\13=-n\\\\n=-13[/tex]
When the value of 8 is negative,
[tex]-8+5=-n\\\\-3=-n\\\\n=3[/tex]
Hence, the value of n can be -13 or 3.
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Find the volume of the prism.
7.5m
8m
4m
Sarah deposited $920 into a savings account 6 years ago. The account earns 7 --% interest, compounded annually. How much 3 interest has she earned? Answer in dollars and round to the nearest cent.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$920\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &6 \end{cases}[/tex]
[tex]A=920\left(1+\frac{0.07}{1}\right)^{1\cdot 6}\implies A\approx 1380.67~\hfill \underset{earned~interest}{\stackrel{1380~~ - ~~920}{\approx 460.67}}[/tex]
How do I solve 20x + 21??
Answer:
Step-by-step explanation:
20x+21=0
20x=-21
x=-1.05