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The standard form of the monomial expression is -1x¹⁰
Monomial expression:
A monomial is an algebraic expression with a single term but can have multiple variables and a higher degree too.
Given,
Here we have the expression
(-2x³)².(-1/4 x⁴)
Now, we have to convert the expression into standard form.
To convert the expression into standard monomial form,
First we have to expand the terms, then we get,
=> (-2²x⁶).(-1/4x⁴)
Then we have to divide the variables and constants separately.
=> (4 x -1/4).(x⁶⁺⁴)
=> -1 . x¹⁰
=> -1x¹⁰
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Related Questions
Find the equation of the linear function represented by the table below in slope-intercept form. Answer: y=
Answers
Answer:
y = 2x + 6
Explanation:
The slope-intercept form of a linear equation can be found as:
[tex]y=m(x-x_1)+y_1[/tex]Where m is the slope and it is calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]And (x1, y1) and (x2, y2) are values from the table. So, we can replace (x1, y1) by (0,6) and (x2, y2) by (1, 8):
Then, the slope is:
[tex]m=\frac{8-6}{1-0}=\frac{2}{1}=2[/tex]Therefore, the equation of the line is:
[tex]\begin{gathered} y=2(x-0)+6 \\ y=2x+6 \end{gathered}[/tex]So, the answer is y = 2x + 6
Determine the functions value when x= -1?a. g(-1) = -3b. g(-1) = 0c. g(-1) = 1d. g(-1) = 27
Answers
Problem
Determine the functions value when x= -1?
a. g(-1) = -3
b. g(-1) = 0
c. g(-1) = 1
d. g(-1) = 27
Solution
For this case we just need to find the value of g when x= -1 and if we look at the table we got:
g(-1)= (-1)^3 + 6(-1)^2 +12(-1) +8
g(-1)= -1 +6 -12+8 = 5-12+8= 1
And then the solution for this case would be:
c. g(-1) = 1
Pls help with my hw pls
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A radio tower is located 250 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 31∘ and that the angle of depression to the bottom of the tower is 29∘
How tall is the tower? ____________ feet.
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Given a radio tower of 250 feet and angles of 31 and 29 degrees, the height of the tower is given as 308.58 ft
What is angle of depression?This is the term that is used to refer to the angle that lies between the horizontal line and the object that would be observed from the horizontal line.
In the question we have the following data
b = 250 feet
angles = 31 degrees, 29 degrees
for the top α = 31 degrees, β = 59
For the bottom α = 29 degrees, β = 61 degrees
We have the formula as
a /sin α = b / sin β = c
tan ∅ = opp / adj
for ΔOCA
h1 = 250 x tan 39 degrees
= 250 x 0.8098
= 202.45
h2 = OCB
= 250 x tan 23
= 250 x 0.4245
= 106.125
The height h = h1 + h2
= 202.45 + 106.125
= 308.58
The height of the tower is 308.58 ft
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11) What is the area of the composite figure? *7 points6 ftT T2 ft5 ft3ft220O 212223
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Answer: 22
Step-by-step explanation:
I need the slope the y intercept is -2 and the x intercept is -1
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The x intercept is the value of x when y = 0
Given that x intercept = - 1, the coordinate is (- 1, - 0)
The y intercept is the value of y when x = 0
Given that y intercept = - 2, the coordinate is (0, - 2)
Slope = (y2 - y1)/(x2 - x1)
x1 = - 1, y1 = 0
x2 = 0, y2 = - 2
Slope = (- 2 - 0)/(0 - - 1)
slope = - 2/1
slope = - 2
The table shows the cost for a clothing store to buy jeans and khakis. The total cost for Saturday's shipment, $1,800, is represented by the equation 15x + 20y = 1,800. Use the x- and y-intercepts to graph the equation. Then interpret the x- and y-intercepts.
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I have a practice problem that I need help on.These are included in the problem as well Where did Arjun make errors?Explain his errors and the properties of logarithms that leads to the answer. State the correct answer.
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Arjun applied the wrong laws of logarithms.
The question can be solved as shown below:
[tex]\log _7x+\log _7y+\log _7z[/tex]Step 1: Apply the addition rule of logarithm given as
[tex]\log _am+\log _an=\log _a(m\cdot n)[/tex]Thus, we have:
[tex](\log _7x+\log _7y)+\log _7z=\log _7(x\cdot y)+\log _7z[/tex]Step 2: Apply the subtraction rule of logarithm given as
[tex]\log _am-\log _an=\log _a(\frac{m}{n})[/tex]Thus, we have:
[tex]\log _7(x\cdot y)+\log _7z=\log _7(\frac{x\cdot y}{z})[/tex]Therefore, the correct answer is:
[tex]\log _7x+\log _7y+\log _7z=\log _7(\frac{xy}{z})[/tex]I'm trying to simplify negative 5/8 divided by negative 3/4 how do I do that?
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Solve the inequality and write the solution using:
the inequality
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Looking to receive assistance on the following problem, thank you!
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Given:
[tex]\begin{gathered} v=3i-4j \\ u=-2i-7i \\ w=5j \end{gathered}[/tex]So the value is:
(a)
[tex]\begin{gathered} u=-2i-7j \\ 2u=2(-2i-7j) \\ 2u=-4i-14j \end{gathered}[/tex][tex]\begin{gathered} 2u-v=-4i-14j-(3i-4j) \\ =-4i-14j-3i+4j \\ =-7i-10j \end{gathered}[/tex](b)
[tex]\begin{gathered} w=5j \\ 3w=3\times5j \\ 3w=15j \end{gathered}[/tex][tex]\begin{gathered} u=-2i-7i \\ 4u=4(-2i-7j) \\ 4u=-8i-28j \end{gathered}[/tex][tex]\begin{gathered} 3w+4u=15j+(-8i-28j) \\ =15j-8i-28j \\ =-8i-13j \end{gathered}[/tex](c)
The dot product of v and u.
[tex]\begin{gathered} v=3i-4j \\ u=-2i-7i \end{gathered}[/tex]dot product is:
[tex]\begin{gathered} vu=(3i-4j)\cdot(-2i-7j) \\ =-6(i\cdot i)-21(i\cdot j)+8(j\cdot i)+28(j\cdot j) \end{gathered}[/tex]The doat product (i.i = 1) and ( j.j=1) and ( i.j=0) and ( j.i = 0)
[tex]\begin{gathered} =-6(1)-21(0)+8(0)+28(1) \\ =-6+28 \\ =22 \end{gathered}[/tex]Here are the exam scores for the 15 students in Mr. Kirk's statistics class:
72 75 75 78 81 83 85 89 90 90 90 91 95 95 98
Karen was at the 20th percentile of the distribution. What score did Karen earn on the exam?
(A) 75
(B) 78
(C) 81
(D) 83
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The stock price for dgy was $38.21. In June. In July the stocked had in by 7 percent, but in August the price fell by 7 percent. What was the price of dgy stock in august . Round your answer to nearest cent , if necessary
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The initial price is $38.21, and it got an increase of 7%, so the new price is the old one multiplied by 1.07:
[tex]38.21\cdot1.07=40.88[/tex]Then, the new price decreased by 7%, so let's multiply it by 0.93 (that is, 1 minus 0.07):
[tex]40.88\cdot0.93=38.02[/tex]So the price in August is $38.02.
IF G and R denote the grade and the radian measure of an angle, then prove that G/200 = R/pie
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Solution:
Given;
IF G and R denote the grade and the radian measure of an angle, i.e.
Where
[tex][/tex]In how many ways can 3 students from a class of 23 be chosen for a field trip?aYour answer is:
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SOLUTION:
This is a combination problem.
The number of ways 3 students from a class of 23 be chosen for a field trip is;
[tex]23C_3=\frac{23!}{(23-3)!3!}=1771\text{ }ways[/tex]I need help question
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Solution
- The first integral is bounded by the x-values of [6, 22]
- The second integral is bounded by the x-values of [6, 14]
- When we are asked to find the difference between the two integrals, since, they both begin at 6, it implies that, when the second integral is taken away from the first integral, there must be some extra x-values.
- The extra values are from 14 to 22.
- Thus, we have:
[tex]\int_6^{22}f(x)-\int_6^{14}f(x)=\int_{14}^{22}f(x)[/tex]Final Answer
[tex]\begin{gathered} b=22 \\ a=14 \end{gathered}[/tex]in a recent year the annual salary of the governor of New York was 1790000 during the same year the annual salary of the governor of Tennessee was 940000 less write and solve an equation to find the annual salary of the government of Tennessee in that year
Answers
Step 1 : Let's review the information given to us to answer the problem correctly:
• Annual salary of the governor of New York = $ 1,790,000
,• Annual salary of the governor of Tennessee = $ 940,000
Step 2: Let x to represent the annual salary of the governor of New York
and let's find the ratio of the salary of the governor of Tennessee, as follows:
940,000/1,790,000 = 0.525
Step 3: Now, let's write the equation for calculating the salary of the governor of Tennessee for any given year, this way:
• 0.525x = Annual salary of the governor of Tennessee
,•
Step 4: If the salary of the governor of New York for the next year is 2,000,000, then we can calculate the salary of the governor of Tennessee, this way:
0.525x = 0.525 * 2,000,000 = 1,050,000
The annual salary of the governor of Tennessee woudl be 1,050,000
Use the graph of the function y= f(x) below to answer the questions
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a)
We need to find the value of f(-3), that means we need to find the value of the y-coordinate when the x-coordinate is -3
As we can see in the graph
f(-3)=-5
Therefore f(-3) is negative
The answer for this part is NO
b)
if f(x)=0, that means that we are looking for the x-intercepts
x=-2
x=1
x=4
The answer is -2,1,4
c)
We need to know for what values of x f(x)<0
In this case in interval notation
[tex]\lbrack-3,2)\cup(1,4)[/tex]A lighthouse beacon will illuminate to a distance of 12 km. If the lighthouse is located at (-5,2) on a grid, find the equation of the location of the furthest points lit the beacon.
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Light house is located at (-5,2)
Lighthouese beacon will illuminate a distnce =12 km
Use the distance formula to find the equation :
Distance formula is expressed as :
[tex]\begin{gathered} (x-a)^2+(y-b)^2=c^2 \\ \text{where (a,b) \& (x,y) are the coordinates and c is the distance} \end{gathered}[/tex]Substitute the given values :
[tex]undefined[/tex]find the area of the composite figures by either adding and subtracting regions
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Explanation:
This figure is a rectangle and a quarter of a circle. We can find their areas and add them to find the total area of the figure.
The area of the rectangle is:
[tex]A_{\text{rectangle}}=17cm\times10\operatorname{cm}=170\operatorname{cm}^2[/tex]The area of a circle is:
[tex]A_{\text{circle}}=\pi\cdot r^2[/tex]Where r is the radius of the circle. In this case we have a quarter of a circle, so its area is a quarter of the area of the circle:
[tex]A_{1/4\text{circle}}=\frac{A_{\text{circle}}}{4}=\frac{\pi\cdot r^2}{4}[/tex]The radius of this circle is 8cm:
[tex]A_{1/4\text{circle}}=\frac{\pi\cdot8^2}{4}=\frac{\pi\cdot64}{4}=\pi\cdot16\approx50.27\operatorname{cm}^2[/tex]The total area of the figure is:
[tex]A_{\text{figure}}=A_{\text{rectangle}}+A_{1/4\text{circle}}=170\operatorname{cm}+50.27\operatorname{cm}=220.27\operatorname{cm}^2[/tex]Answer:
The area is 220.27 cm²
Lisa played 42 of thepossible 60 minutes of asoccer game. Whatpercent did she notplay?
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Lisa played 42 minutes of a 60 minutes match. This means that she didn't play 18 minutes of the game; to find what percent this represents we can use the rule of three:
[tex]\begin{gathered} 60\rightarrow100 \\ 18\rightarrow x \end{gathered}[/tex]Then:
[tex]\begin{gathered} x=\frac{18\cdot100}{60} \\ =30 \end{gathered}[/tex]Therefore, Lisa didn't play 30% of the game.
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BRAINLIEST!!!!! AND 100
POINTS!!!!!
Answers
the rriangle is 3 4 5 triangle so 5×5 is 25
In triangle XYZ, | XZ | = | YZ | ∆YXZ = 40⁰ and ∆XZY = (13x - 20)⁰. Find the value of x.
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Given the triangle XYZ with the following parameters
[tex]\begin{gathered} |XZ|=|YZ| \\ \measuredangle YXZ=40^0 \\ \measuredangle XZY=(13x-20)^0 \\ \text{Therefore} \\ \measuredangle ZYX=40^0 \end{gathered}[/tex]The diagram of the triangle is shown below
To find the value of x, we will apply sum of interior angle of triangle theorem
[tex]\begin{gathered} 40^0+40^0+(13x-20)^0=180^0(\text{ sum of angles in a triangle)} \\ 80^0+13x-20^0=180^0 \\ 13x+60^0=180^0 \\ 13x=180^0-60^0 \\ 13x=120^0 \\ x=\frac{120^0}{13} \\ x=9.2308^0 \end{gathered}[/tex]Hence, the value of x is 9.2308°
HelppppppFunction f is a(n)functionThe graph is a reflection in thewith a verticaland atranslationunits:The domain of f isThe domain of the parent function is;The range of f isThe range of the parent function is
Answers
Answer:
In order of appearance of boxes
quadraticx-axisstretch3 (units)upall real numbersall real numbersy ≤ 3y ≥ 0Step-by-step explanation:
The given function f(x) = -2x² + 3 belongs to the quadratic family of equations. A quadratic equation has a degree of 2. The degree is the highest power of the x variable in the function f(x)
The parent f(x) = x²
Going step by step:
2x² ==> graph x² is vertically stretched by 2. For any value of x in x², the new y value is twice that the old value. For example, in the original parent function x², for x = 2, y = 4. In the transformed function 2x², for x = 2, y = 2 x 4 = 8 so it has been stretched vertically. It becomes skinnier compared to the original
-2x² => graph is reflected over the x-axis. It is the mirror image of the original graph when viewed from the x-axis perspective
-2x² + 3 ==> graph is shifted vertically up by 3 units
Domain is the set of all x-input values for which the function is defined. For both x² and -2x² + 3 there are no restrictions on the values of x. So the domain for both is the set of all real numbers usually indicated by
-∞ < x < ∞
The range is the set of all possible y values for a function y = f(x) for x values in domain.
The range of f(x) = x² is x≥ 0 since x² can never be negative
Range of -2x² + 3 is x ≤ 3 : Range of -2x² is y ≤ 0 since y cannot be negative and therefore range of -2x² + 3 is y ≤ 3
Figure 2 is a scaled copy of Figure 1.B.Figure 1AsADMYColJFigure 2MYHKProIdentify the side in Figure 2 that corresponds to side BC in Figure 1.
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Figure 1 was enlarged to figure 2
Hence the side |AB| is corresspounding to the side |PQ|
Use the table to find the slope of the line.Round your answer out to two decimal places
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Given:
The points are (8, -3) and (-5, 1).
To find the slope of the line:
The slope formula is,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{1-(-3)}{-5-8} \\ =\frac{1+3}{-13} \\ =-\frac{4}{13} \\ =-0.30769 \\ \approx-0.31 \end{gathered}[/tex]Hence, the slope of the line is -0.31 (rounded to the nearest two decimal places).
Which equation shows a proportional relationship? options: O y = x O y + 1 = 7x O y - 2 = x + 8 O x = y + 5
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A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:
y = kx
for some constant k , called the constant of proportionality . This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.
From the given options, the baove property is satisfied by,
[tex]y=\frac{2}{3}x[/tex]Thus, the correct option is A.
An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an airplane located at that point. Express the bearing using both methods.(-8,0)
Answers
Given,
The coordinates of the point is (-8, 0).
There are two methods of bearing is:
Compass bearing
True bearing.
The figure of the point is,
The bearing of the point with respect to anticlockwise from north is,
[tex]\begin{gathered} \tan \theta=\frac{y}{x} \\ \tan \theta=\frac{0}{-8} \\ \theta=\tan ^{-1}0 \\ \theta=0^{\circ} \\ \text{Bearing from north=(90}^{\circ}-0^{\circ})=90^{\circ} \end{gathered}[/tex]The bearing of point from west is 0 degree and from anticlockwise north is 90 degree.
The true bearing is,
[tex]\begin{gathered} \theta=0^{\circ} \\ B=(360^{\circ}-90^{\circ}) \\ B=270^{\circ} \end{gathered}[/tex]The points (-6, -10) and (23, 6) form a line segment.
Write down the midpoint of the line segment.
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A line segment has the endpoints at (-6, -10) and (23, 6) then the midpoints of the line segment will be (17, -2).
What is meant by line segment?An area or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be estimated by utilizing either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.
A line segment has the endpoints at (-6, -10) and (23, 6).
Mid point of the line segment is given by [tex]$\left(\frac{x_1+x_2}{2}\right),\left(\frac{y_1+y_2}{2}\right)$[/tex]
The midpoints of the line segment will be
= [tex]$\frac{23+-6}{2}[/tex], [tex]$\frac{-10+6}{2}}[/tex]
= 17, -2
Therefore midpoints of the line segment will be (17, -2).
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you can make pancakes with just bananas and eggs : serves 4 people with 6 eggs 2 bananas. how many eggs and bananas do u need to serve 6 people?
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Given:
To prepare a pancake that serves 4 people, we need 6 eggs and 2 bananas.
Required:
The number of eggs and bananas that serves 6 people
By comparison,
If we need 6 eggs to prepare a pancake that serves 4 people, the number of people that 1 egg would serve is:
[tex]\begin{gathered} k\text{ = }\frac{4\text{ people}}{6\text{ eggs}} \\ =\text{ }\frac{2}{3}\text{ people/ egg} \end{gathered}[/tex]Similarly, If we need 2 bananas to prepare a pancake that serves 4 people, the number of people that 1 banana would serve is:
[tex]\begin{gathered} k_2\text{ = }\frac{4\text{ people}}{2\text{ bananas}} \\ =\text{ 2 people/banana} \end{gathered}[/tex]The number of eggs that serves 6 people:
[tex]\begin{gathered} =\text{ 6 people }\times\frac{3}{2}\text{ egg/people} \\ =\text{ 9 eggs} \end{gathered}[/tex]The number of bananas that serves 6 people:
[tex]\begin{gathered} =\text{ 6 people }\times\text{ }\frac{1}{2}\text{ banana/ people} \\ =\text{ 3 bananas} \end{gathered}[/tex]Answer:
9 eggs are needed
3 bananas are needed