Answer:
Multiplying polynomials is a bit more challenging than adding and subtracting polynomials. We must use the distributive property to multiply each term in the first polynomial by each term in the second polynomial. We then combine like terms. We can also use a shortcut called the FOIL method when multiplying binomials. Certain special products follow patterns that we can memorize and use instead of multiplying the polynomials by hand each time. We will look at a variety of ways to multiply polynomials.
The dot plot below shows 6 data points with a mean of 16.
A dot plot going from 11 to 20. 1 dot is above 12, 13, 15, 17, 19, 20.
What is the absolute deviation at 19?
Answer:I think its C
Step-by-step explanation:
Answer: the answer is c
Step-by-step explanation:
Prove the divisibility of 16^5+2^15 by 33
Answer:
Both terms have a common factor of 2^15
Step-by-step explanation:
Make use of prime factorizations:
16^5+2^15=(2^4)^5+2^15=2^20+2^15
Both terms have a common factor of 2^15.
16^5+2^15=2^15(2^5+1)=2^15 x 33
The term [tex]16^5+2^{15}[/tex] is divisible by 33
We have to given [tex]16^5+2^{15}[/tex] is divisible by 33.
What is the meaning of prime factorization?Prime factorization is a way of expressing a number as a product of its prime factors
Make use of prime factorization
[tex]16^5+2^{15}=(2^4)^5+2^{15}[/tex]
[tex]=2^{20}+2^{15}[/tex]
factor out the term [tex]2^{15}[/tex] we get,
[tex]16^5+2^{15}=2^{15}(2^5+1)=2^{15} * 33[/tex]
Therefore the term [tex]16^5+2^{15}[/tex] is divisible by 33
Hence proved.
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Use the relationship between the angles in the
figure to answer the question.
Which equation can be used to find the value
of x?
Drag and drop the equation into the box.
Answer:
Depends on what x represents.
Step-by-step explanation:
Can you provide more details?
Answer:
x = 180 - (67 + 52)
Step-by-step explanation:
Had it wrong the first time ;)
Calculate the length of AB using Sine rule
Answer:
Approximately [tex]22.2\; \rm m[/tex].
Step-by-step explanation:
By sine rule, the length of each side of a triangle is proportional to the sine value of the angle opposite to that side. For example, in this triangle [tex]\triangle ABC[/tex], angle [tex]\angle A[/tex] is opposite to side [tex]BC[/tex], while [tex]\angle C[/tex] is opposite to side [tex]AB[/tex]. By sine rule, [tex]\displaystyle \frac{BC}{\sin{\angle A}} = \frac{AB}{\sin \angle C}[/tex].
It is already given that [tex]BC = 22.4\; \rm m[/tex] and [tex]\angle A = 58^\circ[/tex]. The catch is that the value of [tex]\angle C[/tex] needs to be calculated from [tex]\angle A[/tex] and [tex]\angle B[/tex].
The sum of the three internal angles of a triangle is [tex]180^\circ[/tex]. In [tex]\triangle ABC[/tex], that means [tex]\angle A + \angle B + \angle C = 180^\circ[/tex]. Hence,
[tex]\begin{aligned}\angle C &= 180^\circ - \angle A - \angle B \\ &= 180^\circ - 58^\circ - 65^\circ \\ &= 57^\circ\end{aligned}[/tex].
Apply the sine rule:
[tex]\begin{aligned} & \frac{BC}{\sin{\angle A}} = \frac{AB}{\sin \angle C} \\ \implies & AB = \frac{BC}{\sin{\angle A}} \cdot \sin \angle C \end{aligned}[/tex].
[tex]\begin{aligned}AB &= \frac{BC}{\sin{\angle A}} \cdot \sin \angle C \\ &= \frac{22.4\; \rm m}{\sin 58^\circ} \times \sin 57^\circ \\ &\approx 22.2\; \rm m\end{aligned}[/tex].
solve -5 + w/3 = -1
12
-12
2
-2
Answer:
Option A, 12
Step-by-step explanation:
Step 1: Add 5 to both sides
-5 + w/3 + 5 = -1 + 5
w / 3 = 4
Step 2: Multiply both sides by 3
w/3 * 3 = 4 * 3
w = 12
Answer: Option A, 12
Each cube represents 1 cubic inch. What is the volume if the prism?
Answer:
12 in³
Step-by-step explanation:
Its made up of 12 (4×3 = 12) cubes of 1 in³ each
So 12 × 1 = 12 in³
If f(x) = 3x5 - 5x4 + 29, find f(-1).
f(-1) = 3((-1)^5)-5((-1)^4)+29 = -3-(5)+29 = 21
answer: 21
Answer:
The value of f(-1) is 21
Step-by-step explanation:
Given:
[tex]f(x) = 3x^5 - 5x^4 + 29[/tex]
Finding f(-1)
[tex]f(-1)=3(-1)^5-5(-1)^4+29\\\\[/tex]
Multiplying '-1' odd times gives -1 and even times gives '1'
[tex]f(-1)=3(-1)-5(1)+29\\\\f(-1)=-3-5+29\\\\f(-1)=-8+29\\\\f(-1)=21\\[/tex]
The value of f(-1) is 21
What is the value of the expression 3 ^ 3 - 2 ^ 3
Answer:
27 - 8 = 19
The answer is 19.
Step-by-step explanation:
Karla had $138.72 in her checking account. She wrote checks for $45.23 and $18. Then she made a deposit for 75.85 into her account.what is the best estimate for how much money is in karla’s account now
Answer:
$151.34
Step-by-step explanation:
First, Karla starts with $138.72.
Then Karla writes checks for $45.23 and $18.00. This means the money will be withdrawn, so let's subtract these from the total.
$138.72 - $45.23 - $18.00 = $75.49
Now, Karla has $75.49 in her account.
However, a $75.85 deposit is made to her account. So let's add this back to the total.
$75.49 + $75.85 = $151.34
So after all the transactions, Karla has $151.34 in her checking account.
Un observador se acerca con una velocidad de 15m/s a un parlante estático que está emitiendo un sonido con una frecuencia de 297 Hz. ¿Cuál es la frecuencia percibida por el observador?
Answer:
310 Hz
Step-by-step explanation:
This is a spanish language mathematical question.
We translate this to english:
An observer approaches a static speaker at 15 meters per second. The speaker is emitting a sound with a frequency of 297 Hz. What is the frequency perceived by the observer?
Solution:
This can be solved using doppler effect formula. Which is:
[tex]f=(\frac{c}{c+V_s})f_0[/tex]
Where
f is the observed frequency (297 Hz)
c is the speed of sound (343 m/s)
[tex]V_s[/tex] is the velocity of source (given as 15)
[tex]f_0[/tex] is what we want to find
Now, substituting, we solve:
[tex]f=(\frac{c}{c+V_s})f_0\\297=(\frac{343}{343+15})f_0\\297=(0.9581)f_0\\f_0=309.99[/tex]
Rounding,
We can say the perceived frequency would be around 310 Hz
What is the inverse of f(x)= 9x-8
Answer:
f^-1(x) = (x + 8) / 9
Step-by-step explanation:
Step 1: Set y to x and x to y
y = 9x - 8
x = 9y - 8
Step 2: Solve for y
x + 8 = 9y - 8 + 8
(x + 8) / 9 = 9y / 9
(x + 8) / 9 = y
Step 3: Rename y to f^-1(x)
f^-1(x) = (x + 8) / 9
Answer: f^-1(x) = (x + 8) / 9
The inverse of the function f(x) = 9x - 8 is f^-1(x) = (x + 8) / 9.
To find the inverse of the function f(x) = 9x - 8, follow these steps:
First, replace f(x) with y. So, we have y = 9x - 8.
Next, solve for x. To do this, swap x and y to get x = 9y - 8.
Now, isolate y by adding 8 to both sides, resulting in x + 8 = 9y.
Finally, divide both sides by 9 to solve for y, giving y = (x + 8) / 9. This is the inverse function.
To denote the inverse, we replace y with f-1(x), resulting in f-1(x) = (x + 8) / 9.
What is 5y-4x =-7
2y+4x=14
X=?
Y=?
Answer:
X=3
Y=1
Step-by-step explanation:
In solving simultaneous equations, there are three methods, we have the elimination method, substitution method or graphical method. But for the purpose of this question, we would be using Elimination method.
5y-4x =-7 Equation 1
2y+4x=14 Equation 2
Since x has the same coefficient, it's easy to eliminate by adding up the two equations
5y+2y=7y
-4x+(+4x)=0
-7+(+14)=7
We have 7y=7
Divide both sides by 7,
y=7/7
y=1
Substituting for y in equation 2.
2(1)+4x=14
2+4x=14
4x=14-2
4x=12
x=12/4
x= 3
Suppose William and Donald both drive the same car, and have the same
deductible for car insurance. If William drives an average of 12,000 miles a
year and Donald drives an average of 15,000 miles a year, who is most likely
to pay a higher annual premium?
Answer: William
Step-by-step explanation: This is true because whichever has a better gas mileage pays less, so the bigger number per year has better mileage, so 15,000 would have better which is Donald, and William has 12,000 which is worse, so he would have to pay more.
Answer: Donald
Step-by-step explanation:
Write an equation that represents the volume V as a function of the height h
Answer:
h=V/b
Step-by-step explanation:
The volume V can be represented as a function of height h by the equations V = lwh for a rectangular prism or V = πr²h for a cylinder. If other dimensions are constants, this can be simplified to V=k*h, where k represents the base area.
Explanation:To represent the volume V as a function of the height h, we typically consider the volume of a rectangular or cylindrical shape. The volume V of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height. If we consider a cylinder, the volume is given by the equation V = πr²h, where r is the radius of the base circle and h is the height. However, if we simplify this formula assuming only the height can vary and all other dimensions are constants, the function could be simplified to V=k*h, where k represents the area of the base.
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Y=5x+20
Y=-7x-16
Solve each system by substitution
Answer:
x=3
y=35
Step-by-step explanation:
5x+20=-7x-16
-16+20=4
5x=-7x+4
5x+7x= 12x
12x=4
12/4=3
Answer: x = -3 ; Y = 5
Step-by-step explanation:
Y=5x+20
Y=-7x-16
5x+20 = -7x-16
5x+ 7x = -16 - 20
12x = - 36
x = -36 / 12
x = -3
Y=5x+20
Y = 5.(-3) + 20
Y = - 15+20
Y = 5
What is 6x729 and how would u do the math in the best way ?
6x729 equals 4374 and you get that by using a calculator that's how i would do it
Solve for X, and graph
8. - 6x + 14 <-28 OR 9x + 15 <- 12
For this case we must indicate the solution set of the given inequalities:
[tex]-6x + 14 <-28[/tex]
Subtracting 14 from both sides of the inequality we have:
[tex]-6x <-28-14\\-6x <-42[/tex]
Dividing by 6 on both sides of the inequality:
[tex]-x <- \frac {42} {6}\\-x <-7[/tex]
We multiply by -1 on both sides, taking into account that the sense of inequality changes:
[tex]x> 7[/tex]
Thus, the solution is given by all values of x greater than 7.
On the other hand we have:
[tex]9x + 15 <-12[/tex]
Subtracting 15 from both sides of the inequality we have:
[tex]9x <-12-15\\9x <-27[/tex]
Dividing between 9 on both sides of the inequality we have:
[tex]x <- \frac {27} {9}\\x <-3[/tex]
Thus, the solution is given by all values of x less than -3.
Finally, the solution set is:
(-∞, - 3) U (7,∞)
Answer:
(-∞, - 3) U (7,∞)
350 is what percentage of 50?
Answer:
175
Step-by-step explanation:
Answer:
175%
Step-by-step explanation:
Divide 50 by 100 then multiply it by 350
50 ÷ 100 × 350 = 175
What is the area of this trapezoid
Answer:
[tex]A = 80[/tex] [tex]units^{2}[/tex]
Step-by-step explanation:
Given Data:
a = 7+3+7 =17 units
b = 3 units
h = 8 units
To Find Out:
Area of trapezoid = ?
Formula:
[tex]A = \frac{a+b}{2}h[/tex]
Solution:
[tex]A = \frac{a+b}{2}*h[/tex]
[tex]A = \frac{17+3}{2}*8[/tex]
[tex]A = \frac{20}{2}*8[/tex]
[tex]A =10*8[/tex]
[tex]A = 80[/tex] [tex]units^{2}[/tex]
Find the value of the expression. x2 + y for x = 5 and y = 6
Answer:
31
Step-by-step explanation:
[tex] {x}^{2} + y \\ = {5}^{2} + 6 \\ = 25 + 6 \\ = 31 [/tex]
Answer:
31
Step-by-step explanation:
25+6=31
Find the sizes of the angles marked with a letter.
Why is my answer wrong?
Answer:
29.28 degrees.
Step-by-step explanation:
sin x / 16.2 = sin 49 / 25
Cross multiply:
25 sin x = 16.2 * sin 49
sin x = (16.2 * sin 49) / 25
sin x = 0.48905
x = 29.28 degrees.
In the last election, Candidate C received 15,000 fewer votes than candidate B. If a total of 109,000 votes were cast, how many votes did candidate B receive? What is the equation for this problem and what is the answer to it?
Answer:
B receives 62000 votes
C receives 47000 votes
Step-by-step explanation:
Let C be the vote for candidate C
Let B be the vote for candidates D
Let the total vote be T. Therefore,
C + B = T (1)
But C receives 15000 votes fewer than B ie
C = B —15000 (2)
Total votes, T = 109000
Substituting the value of C and T into equation 1
C + B = T
B — 15000 + B = 109000
Collect like terms
B + B = 109000 + 15000
2B = 124000
Divide both side by the coefficient B i.e 2
B = 124000/2
B = 62000
Putting the value of B into equation 2;
C = B —15000
But B = 62000
C = 62000 — 15000
C = 47000
B receives 62000 votes
C receives 47000 votes
Which of the following is a statistical question?
A.
How many hours do students in Mr. Brown's class typically spend on homework?
B.
What is Andy’s shoe size?
C.
What is the room temperature of Charlie's house?
D.
How much did Ashley pay for her smart phone?
Tiffany answered 80% of the questions on her math test correctly. There were 40 questions. How many questions did Tiffany get correctly
The lengths of the three sides of a triangle are given. Classify each triangle as acute, right or
obtuse.
30, 40, 50
1)
Triangle with side lengths 30, 40, and 50 is a right triangle.
To classify the triangle based on the lengths of its sides, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
For the given lengths of sides:
[tex]\(a = 30\)[/tex]
[tex]\(b = 40\)[/tex]
[tex]\(c = 50\)[/tex]
We can check if the triangle is a right triangle:
[tex]\[c^2 = a^2 + b^2\][/tex]
Substituting the values:
[tex]\[50^2 = 30^2 + 40^2\][/tex]
[tex]\[2500 = 900 + 1600\][/tex]
[tex]\[2500 = 2500\][/tex]
Since [tex]\(2500 = 2500\)[/tex], the Pythagorean theorem holds true, meaning this triangle is a right triangle.
So, the given triangle with side lengths 30, 40, and 50 is a right triangle.
Tom has three pieces of wood. The length of the longest piece is 3/4 foot. The length of the shortest piece is 3/8 foot. What might be the length of the third piece of wood.
Answer:
[tex]\dfrac{3}{8}\text{ foot}<x<\dfrac{3}{4}\text{ foot}[/tex]
Step-by-step explanation:
We are given the following in the question:
There are three pieces of a wood.
Length of longest piece =
[tex]\dfrac{3}{4}\text{ foot}[/tex]
Length of shortest piece =
[tex]\dfrac{3}{8}\text{ foot}[/tex]
Let x be the length of the third piece.
Since the length of third piece lies between the length of the longest and the shortest piece of wood, thus, we use the following inequality to represent the length of the third piece.
Inequality:
[tex]\dfrac{3}{8}\text{ foot}<x<\dfrac{3}{4}\text{ foot}[/tex]
Write 6 powered 0 in positive exponents
Answer:
1
Step-by-step explanation:
Anything to the power 0 is 1
Therefore, 6^0 is 1
Answer: 1
Answer:
6^0 = 1
Step-by-step explanation:
"6 to the power 0" is 6^0 = 1
LaTanya says that the growth factor of f(x) = 100(1.25) is 25%. What mistake did LaTanya make?
Answer:
The first error consists in the multiplication of f (x) = 100 * (1.25), the value she mentions is incorrect since it is 125.
It would be a 125% increase really.
In order for LaTanya's phrase to have no error she had to mention that it was a 25% increase over the original amount, in this way, the phrase would make sense and be valid.
Answer:
LaTanya confused growth factor with growth rate. The growth factor is 1.25. The growth rate is 25%.
Step-by-step explanation:
In the exponential growth model,
f(x)=a(1+r)x
a is the inital amount, r is the growth rate, and (1+r) is the growth factor. Hence, the growth factor of the given function is 1.25.
circle E, and are diameters. Angle BCA measures 53°.
Circle E is shown. Line segments A C and B D are diameters. Lines are drawn to connect points B and C and points A and D. Angle B C A is 53 degrees.
What is the measure of arc AD?
53°
74°
106°
180°
Answer:
74°
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
Triangle EBC is an isosceles triangle (because has two equal sides EB=EC)
so
[tex]m\angle BCA=m\angle BCE=m\angle EBC=53^o[/tex]
Find the measure of angle BEC
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]m\angle BCE+m\angle EBC+m\angle BEC=180^o[/tex]
substitute the given values
[tex]53^o+53^o+m\angle BEC=180^o[/tex]
[tex]m\angle BEC=180^o-106^o=74^o[/tex]
Find the measure of angle AED
we know that
[tex]m\angle AED=m\angle BEC[/tex] ----> by vertical angles
so
[tex]m\angle AED=74^o[/tex]
Find the measure of arc AD
we know that
[tex]m\ arc\ AD=m\angle AED[/tex] -----> by central angle
therefore
[tex]m\ arc\ AD=74^o[/tex]
Answer:
The answer is B on Edge 2020`
Step-by-step explanation:
I did the exam
Maricela was recently approved for an $18,000 loan for 5 years at an interest rate of 6.2%. Use the monthly payment formula to complete the
statement
M= (1 + 5* - 1
M= monthly payment
P= principal
r=interest rate
= number of years
Maricela's monthly payment for the loan iss
Answer:
top is wrong my teacher told me the answer its
349.67
Maricela's monthly payment for the loan using the monthly payment formula is; $349.67
What is the monthly payment?
We are given;
Principal; P = $18000
Interest Rate; r = 6.2% = 0.062
Number of years; t = 5 years
The formula to find the monthly payment is;
M = P[(r/n) * (1 + (r/n))^(nt)]/[((1 + (r/n))^(nt)) - 1]
Plugging in the relevant values gives;
M = 18000[(0.062/12) * (1 + (0.062/12))^(12 * 5)]/[((1 + (0.062/12))^(12 * 5)) - 1]
Solving this with a calculator gives us;
M = $349.67
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