Answer:
[tex] {a}^{6} {b}^{2} [/tex]
solution
[tex] {a}^{3} \times b \times {a}^{3} \times b \\ = {a}^{3 + 3} \times {b}^{1 + 1} \\ = {a}^{6} {b}^{2} [/tex]
hope this helps...
Good luck on your assignment..
Answer:
[tex]a^{6}b^{2}[/tex]
Step-by-step explanation:
[tex]a^3 \times b \times a^3 \times b[/tex]
If there are no exponents written, then the exponent is 1.
[tex]a^3 \times b^1 \times a^3 \times b^1[/tex]
When multiplying two powers that have the same base, you can add the exponents.
[tex]a^{3+3} \times b^{1+1}[/tex]
[tex]a^{6} \times b^{2}[/tex]
Can someone plz help me
Answer:
33%
Step-by-step explanation:
- The area of the inner white circle is π4² = 16π
- The area of the blue "band" is π7² - π4² = 33π
- The total area is π10² = 100π
The ratio of the blue band and the total area is 33π/100π ×100% = 33%
Use the Factor Theorem to examine the polynomial p(x)=6x4+x3−45x2+26x+24. Which binomial is a factor of p(x)?
2x+3
(3x-2)
(2x-1)
(3x−4)
Answer:
(D) 3x−4
Step-by-step explanation:
Factor Theorem
Given a polynomial P(x) and a linear function x-a, If P(a)=0, then the linear function x-a is a factor of P(a).
In Option A:
[tex]L$inear Function =2x+3\\Set 2x+3=0$\\x=-\frac{3}{2} \\p(x)=6x^4+x^3-45x^2+26x+24\\p(-\frac{3}{2})=6(-\frac{3}{2})^4+(-\frac{3}{2})^3-45(-\frac{3}{2})^2+26(-\frac{3}{2})+24\\\\p(-\frac{3}{2})=-89.25[/tex]
In Option B
[tex]L$inear Function =3x-2\\Set 3x-2=0$\\x=\frac{2}{3} \\p(x)=6x^4+x^3-45x^2+26x+24\\p(\frac{2}{3})=6(\frac{2}{3})^4+(\frac{2}{3})^3-45(\frac{2}{3})^2+26(\frac{2}{3})+24\\\\p(\frac{2}{3})=22.8[/tex]
In Option C
[tex]L$inear Function =2x-1\\Set 2x-1=0$\\x=\frac{1}{2} \\p(x)=6x^4+x^3-45x^2+26x+24\\p(\frac{1}{2} )=6(\frac{1}{2} )^4+(\frac{1}{2} )^3-45(\frac{1}{2} )^2+26(\frac{1}{2} )+24\\\\p(\frac{1}{2} )=26.25[/tex]
In Option D
[tex]L$inear Function =3x-4\\Set 3x-4=0$\\x=\frac{4}{3} \\p(x)=6x^4+x^3-45x^2+26x+24\\p(\frac{4}{3} )=6(\frac{4}{3})^4+(\frac{4}{3} )^3-45(\frac{4}{3} )^2+26(\frac{4}{3})+24\\\\p(\frac{4}{3} )=0[/tex]
We can see that only Option D: 3x−4 gives a result of 0. Therefore, by the factor theorem, it is a factor of the polynomial.
Mrs. Jackson made a line plot of the times it took students to complete a project.
She made a line plot to display the data.
Line plot named as ALTDCTime Spent Completing ProjectALTDC shows a number line from 0 to 5. The number line is divided into 10 equal parts. 1 dot on 1, 2 dots on one and half, 4 dots on 2, 3 dots on two and half, 2 dots on three and half, 1 dot on 4 and 1 dot on four and half is given.
Part A
What is the outlier in the data set?
A. 1
B. 2
C. 3
D. There is no outlier.
Part B
Which explains your reasoning in Part A?
A.
There is no value that is very different from the other values.
B.
This is the most common value in the data set.
C.
This value is very different from the other values.
D.
There are no data values above this number.
Answer: D
Step-by-step explanation: D
Mrs. Allen, a high school math teacher, is grading quizzes and tests this weekend. She has at most 4 hours, or 240 minutes, to spend
grading, and she would like to get at least 60 quizzes and tests graded. On average, it takes her 3 minutes to grade each quiz and
8 minutes to grade each test,
If x represents the number of quizzes and y represents the number of tests Mrs. Allen grades this weekend, which graph represents
the solution set?
Answer:
(55,9)
Step-by-step explanation:
^
compare: 5/12 to 1/12 which one is greater
Answer:
5/12 is greater
Answer:
5/12 is greater than 1/12
Step-by-step explanation:
when you compare 2 fractions with the same denominator, greater is the one with bigger numerator so 5/12
AOV is a right angle and the ratio AOB: BOC= 2:3 what is the size of angle BOC ?
Help someone please cuhhhhhhhhhh!!!!!
Answer:
6^10
Step-by-step explanation:
2+11=13
13-3=10
What is the value of SZT?
Answer:
[tex] \boxed{m \angle SZT = 121 \degree } [/tex]
Given:
[tex]m \angle RZT = 137 \degree \\ m\angle RZS = 56 \degree [/tex]
Step-by-step explanation:
[tex]= > m \angle RZT = m\angle RZS + m \angle SZT \\ \\ = >157 \degree = 36 \degree+ m \angle SZT \\ \\ = > 157 \degree - 36 \degree = m \angle SZT \\ \\ = > 121 \degree = m \angle SZT \\ \\ = > m \angle SZT = 121 \degree [/tex]
the scale on a map is 1 : 15000 how many kilometers on the ground would be represented by 12 cm on the map?
Answer:
1.8 km
Step-by-step explanation:
The scale on the map is 1 : 15000.
This means that every 1 cm on the map is equal to 15000 cm on the ground.
12 cm on the map will therefore be:
12 * 15000 = 180000 cm
Let us convert to kilometres:
100000 cm = 1 km
180000 cm = 180000 / 100000 = 1.8 km
12 cm on the map will be 1.8 km on the ground.
Same-side interior angles form when a transversal intersects with two parallel lines, making the same-side interior angles supplementary.
O True
O False
PLZ HELP :) 10 PTS
Justify whether matrix A is invertible.
A.
Yes, because its determinant is not equal to zero.
B.
Yes, because its determinant is greater than zero.
C.
No, because its determinant is zero.
D.
No, because its determinant is less than zero.
E.
No, because its determinant is not equal to zero.
We have that
The Matrix A is a singular square matrix and because its determinate is zero. No the Matrix A is inveritible because its determinant is not equal to zero.
Option E is correct
From the question we are Given the matrix:
[tex]A= \begin{bmatrix}6 & -4 \\-9 & 6\end{bmatrix}[/tex]
Invertible Matrix
In linear algebra, an n-by-n square matrix A is called invertible if there exists an n-by-n square matrix B such that
[tex]AB=BA=I_n[/tex]
where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.
Invertible Matrix characteristics does not apply to singular square matrix, A square matrix is singular if and only if its determinant is zero
Generally the determinate of Matrix A is given as
[tex]A= \begin{bmatrix}6 & -4 \\-9 & 6\end{bmatrix}[/tex]
[tex]D=(6*6)-(-4*-9)\\\\D=0[/tex]
In conclusion
The Matrix A is a singular square matrix and because its determinate is zero.
So, No the Matrix A is inveritible because its determinant is not equal to zero.
Option E is correct
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factorize x^2/16+xy+4y^2
Answer:
[tex]\frac{x^2}{16} +xy+4y^2[/tex] can be factored out as: [tex](\frac{x}{4} +2\,y)^2[/tex]
Step-by-step explanation:
Recall the formula for the perfect square of a binomial :
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Now, let's try to identify the values of [tex]a[/tex] and [tex]b[/tex] in the given trinomial.
Notice that the first term and the last term are perfect squares:
[tex]\frac{x^2}{16} = (\frac{x}{4} )^2\\4y^2=(2y)^2[/tex]
so, we can investigate what the middle term would be considering our [tex]a=\frac{x}{4}[/tex], and [tex]b=2y[/tex]:
[tex]2\,a\,b=2\,(\frac{x}{4}) \,(2\,y)=x\,y[/tex]
Therefore, the calculated middle term agrees with the given middle term, so we can conclude that this trinomial is the perfect square of the binomial:
[tex](\frac{x}{4} +2\,y)^2[/tex]
Angelina wants to put $4,550 in a bank account that earns 5.6% interest compounded quarterly, how much interest will she earn in 8 years?
Answer:
7,035.95
Step-by-step explanation:
If your Current Principal Is 4,550.00, and your interest rate is 5.6%, then in 8 years you would have 7,035.95 if your interest rate is anually.
I need help urgently factorise :a squared divided by 8 minus b squared divided by 50.
Answer: 1/200 * (5a-2b)(5a+2b)
Step-by-step explanation:
a^2/8 - b^2/50
Factor out 1/200,
1/200 * (25a^2 - 4b^2)
Using a^2 - b^2 = (a-b)(a+b),
1/200 * (5a-2b)(5a+2b)
Answer:
1/2(a/2+b/5)(a/2-b/5)
Step-by-step explanation:
a²/8- b²/50= 1/2(a²/4- b²/25)= 1/2(a/2+b/5)(a/2-b/5)
Can someone help? Thanks :D
Answer:
[tex]y\leq -x+4[/tex]
Step-by-step explanation:
The first thing that we can do is look at the equation of the line and then worry about the inequality afterwards.
This line has a y-intercept of 4 and a slope of -1.
This means that the equation of this line would be [tex]y=-x+4[/tex]
Now that we have the equation of the line, we just need to determine which inequality sign to use.
As the shaded region is BELOW the line, we will use a less than (<) sign.
As the line is fully shaded, I can only assume that it is meant to include the line, which would mean that [tex]y\leq -x+4[/tex] would be the equation for this inequality.
I'M BEING TIMED HELP
The acceleration due to gravity is the constant of variation. What is the acceleration due to gravity of a falling object?
Answer:
acceleration = 9.8 m/s^2
Step-by-step explanation:
The problem expects the user to do the rate of change between any two pairs of (time, velocity) from the table, and see that they all render the same value. Notice as well that the rate of change of a difference in velocities divided a difference in time, will render units of acceleration (in this case [tex]\frac{m}{s^2}[/tex]
Let's use for example (0 s ,0 m/s) and the following point: (1 s, 9.8 m/s)
the rate of change is: [tex]acceleration= \frac{9.8-0}{1-0} \frac{m}{s^2} =9.8 \, \frac{m}{s^2}[/tex]
In fact you can use any two pairs of the table, and will get the same result.
So this is the acceleration is [tex]9.8 \, \frac{m}{s^2}[/tex]
The acceleration due to gravity is 9.8 m/s^2.
c 21/
D 101
2
Ms. Gartland bought x number of shirts for the new members of her chorus. The cost
for x number of shirts, including $3.99 shipping, was $77.49. Each shirt cost $12.25.
There was no sales tax on this purchase. Which equation could be used to find x?
2.5(2z + 5) = 5(z + 2.5)
Answer:
z is any real number
Step-by-step explanation:
2.5(2z + 5) = 5(z + 2.5)
Distribute
5z + 12.5 = 5z +12.5
Subtract 5z from each side
5z -5z + 12.5 = 5z-5z +12.5
12.5 = 12.5
This is always true so z can be any real number
Answer:
All Real Numbers
Step-by-step explanation:
We are considering the following equation - 2.5(2z + 5) = 5(z + 2.5),
[tex]2.5 * (2z + 5) = 5 * (z + 2.5) - Apply Distributive Property,\\\\2.5 ( 2z ) + 2.5 ( 5 ) = 5z + 5 ( 2.5 ) - Multiply Like Terms,\\5z + 12.5 = 5z + 12.5 - Subtract Terms From Either Side,\\\\0 = 0,\\Conclusion ; z - All Real Numbers[/tex]
Solution; All Real Numbers
find the average of the first 4 prime numbers greater than 10
Answer:
The average is mean
Mean is the sum of all the numbers divided by the total so the first prime numbers which are grater than 10 are 11, 13, 17, 19.
So we will add these
11+13+17+19=60
60/4= 15
SO 15 is the answer
I don’t know which one it is I dint get it?
Answer:
5,5,5
Step-by-step explanation:
an equilateral triangle
Billy invests £800 for 5 years in savings account By the end of the years he has received a total of £96 simple interest Work out the annual rate of simple interest
Answer: 2.4%
Step-by-step explanation:
SI = prt / 100
96 = ( 800 x r x 5) / 100
96 = 40r
r = 96 / 40 = 2.4%
I really need help with this question
Step-by-step explanation:
∠1 = ∠4 = 57° (vertical angles)
∠6 = 123° (same side interior angles are supplementary)
Answer:
The answer is 123
Step-by-step explanation:
Angle 5 is the same measure as angle one, and a straight line measures 180 degrees. Subtract 57 from 180, and you get the remaining angle. 123 degrees.
i need help, i would appreciate it a lot !!
How do outliers affect data analysis? A.They may significantly affect the mean of the data. B.Not enough information. I would need to know what the data points are. C.They afect the mode of the data. D.They do not, just calculate them with the data the same as all the other data. PLEASE HELPPP!!!!!!
Answer:
A.They may significantly affect the mean of the data.
Step-by-step explanation:
The outliers may significantly affect the mean of the data.
What is outlier?The extreme values in the data are called outliers.
Example: For a data set containing 2, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 84.
In the above number line, we can observe the numbers 2 and 84 are at the extremes and are thus the outliers.
The outliers are a part of the group but are far away from the other members of the group.
For example:
Consider the data: 70, 73, 77, 71, 7, 73, 72, and 78
Let's calculate the mean to understand how the outlier affects the results.
Here, the datapoint 7, is an outlier.
Mean (with outlier)
=70+73+77+71+7+73+72+78/8
=521/8
=65.1
Mean (without an outlier) = 70+73+77+71+73+72+78/7 = 514/ 7 =73.4.
the outlier creates a variation in the mean value of the data.
As, from the example discussed above we have seen that outliers depends on mean of the data.
Hence, outliers may significantly affect the mean of the data.
Learn more about outliers here:
https://brainly.com/question/26958242
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as an estimation we are told 5 miles is 8km convert 84km to miles
Step-by-step explanation:
84 km to miles is 52.195 miles
POR FA AYUDA URGENTEMENTE Dado los puntos A(-1;3) , B(2;5) y C(3;-1). Calcule 3(BA)VECTOR - 4 (CB)VECTOR
Answer:
the answer should be c
Step-by-step explanation:
The Retained earnings account has a credit balance of $54,000 before closing entries are made. Total revenues for the period are $72,200, total expenses are $48,300, and dividends are $15,800. What is the correct closing entry for the revenue accounts?
Answer: $62100
Step-by-step explanation:
The following can be deduced from the information given in the question:
Credit balance = $54000
Total revenues = $72,200
Total expenses = $48,300
Dividends = $15,800
Closing entry= Credit balance + Total revenues - (Total expenses + Dividends)
= $54000 + $72,200 - ($48300 + $15800)
= $126200 - $64100
= $62100
Find the zero of the function f(x)=x-3
When you look at the equation it's basically in slope-intercept form
.[tex]f(x)=x-3[/tex] = [tex]y=x-3[/tex]
which mean that your coordinates would be (0, -3) and (3,0)
Given quadrilateral RSTU, determine if each pair of sides (if any) are parallel and which are perpendicular for the
coordinates of the vertices.
R(0,0), 5(6,3), T(5,5), U(-1,2)
Answer:
US is parallel to RT, and UR is parallel to ST
ST is perpendicular to US and UR is perpendicular to RT
Basically anywhere that there's lines that make right angles are perpendicular to each other
I hope this helps
Step-by-step explanation:
Write down the value of angle y
Answer:
y= 71 Reason: alternate angle to 71 degrees
z = 44
Step-by-step explanation:
You already solve for x.
y = 71 because it is alternate to 71 degrees you see up there.
For z:
all angles inside a triangle sum upto 180
z=180-(71+65) = 44
