Explanation
When two expressions are not equivalent, you can use an inequality symbol
[tex]\begin{gathered} \leq\Rightarrow less\text{ or equal } \\ \ge\Rightarrow greater\text{ or equal } \\ >\Rightarrow greater\text{ than } \\ <\Rightarrow smaller\text{ than} \end{gathered}[/tex]
now, when comparing two expressions that are equivalent , WE CAN NOT USE an inequality simbol, instead of we need to use The equals sign or equal sign formerly known as the equality sign
[tex]=[/tex]for example
[tex]3x+19x=30x-8x[/tex]the = symbold indicates that both sides have the same value ( rigth and left)
I hope this helps you
See attached for the problem
The areas and volumes are given as follows:
a) Area of the four sides to be painted: 2448 m².
b) Area to be covered with shingles: 1140 m².
c) Volume of concrete needed to pour a floor 16 cm deep: 174.72 m³.
d) Total surface area: 5878.4 m².
Area -> Four sides paintedThe sides painted are divided as follows:
Two rectangles of dimensions 26 m and 18 m.Two rectangles of dimensions 42 m and 18 m.Hence the total area to be painted is found as follows:
Total area = 2 x 26 x 18 + 2 x 42 x 18 = 2448 m².
(Area rectangle = base x height)
Area to be covered with shinglesThis part of the problem seems incomplete, however the answer is correct.
Volume of concreteThe volume is given by:
Volume = base area x height.
Hence:
The base area is a rectangle of dimensions 26 m and 42 m.The height is of 16 cm = 0.16 m.Hence the volume is given by:
V = 26 x 42 x 0.16 = 174.72 m³.
Surface areaThe base is a rectangular prism of dimensions 26 m, 42 m and 18m, hence:
Surface area base = 2 x (26 x 42 + 26 x 18 + 42 x 18) = 4632 m².
The top is composed by:
Two rectangles of dimensions 13.6 m and 42 m.Two triangles of base 26 m and height 4 m.Hence:
Surface area top = 2 x 13.6 x 42 + 2 x 0.5 x 26 x 4 = 1246.4 m².
Then the total surface area is:
Total surface area = 4632 + 1246.4 = 5878.4 m².
More can be learned about areas and volumes at https://brainly.com/question/22070273
#SPJ1
(a) The perimeter of a rectangular parking lot is 340 m.If the width of the parking lot is 77 m, what is its length?Length of the parking lot: 0m(b) The area of a rectangular pool is 7410 m².If the length of the pool is 95 m, what is its width?Width of the pool: Im
Part a)
Perimeter = 340 = 2•77 + Length doubled
then
Length x 2 = 340 - 154 = 186
Length= 186/2 = 93
ANSWER IS Length of parking lot is= 93 meters
Part b)
Area = 7410 = Width x Length
. 7410 = Width x 95
. 7410/95 = Width
THEN Width of the pool IS
78 square meters
I need help with this practice problem If you can, show your work step by step so I can take helpful notes
The given geometric series is
[tex]120-80+\frac{160}{3}-\frac{320}{9}+\cdots[/tex]In a geometric series, there is a common ratio between consecutive terms defined as
[tex]r=\frac{-80_{}}{120_{}}=-\frac{2}{3}[/tex]The sum of the first n terms of a geometric series is given by
[tex]S_n=\frac{a(1-r^n)}{1-r},r<1[/tex]Where a is the first term.
From the given series
a = 120
Hence, the sum of the first 8 terms is
[tex]S_8=\frac{120(1-(-\frac{2}{3})^8)}{1-(-\frac{2}{3})}[/tex]Simplify the brackets
[tex]S_8=\frac{120(1-\frac{2^8}{3^8}^{})}{1+\frac{2}{3}}[/tex]Simplify further
[tex]\begin{gathered} S_8=\frac{120(1-\frac{256}{6561})}{\frac{3+2}{3}} \\ S_8=\frac{120(\frac{6561-256}{6561})}{\frac{5}{3}} \\ S_8=\frac{120(\frac{6305}{6561})}{\frac{5}{3}} \\ S_8=\frac{120\times6305}{6561}\div\frac{5}{3} \\ S_8=\frac{120\times6305}{6561}\times\frac{3}{5} \\ S_8=\frac{120\times6305}{6561}\times\frac{3}{5} \\ S_8=\frac{8\times6305}{729} \\ S_8=\frac{50440}{729} \end{gathered}[/tex]Therefore, the sum of the first 8 terms is
[tex]\frac{50440}{729}[/tex]Which relation below is not a function
Answer:
0,0
Step-by-step explanation:
Two numbers can not equal another number
uhh im stuck and im stressed .. and i dont understand area model math..
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
(5x + 6)(2x² + 3x + 8) = ?
Step 02:
Area Model
First, you must multiply the values in the rows by each of the values in the columns.
Then, you must add all the values resulting from the multiplications.
10x³
2x²
+ 12x²
15x²
18x
3x
40x
48
8
--------------------------------------------
10x³ + 29x² + 61x + 56
The answer is:
(5x + 6)(2x² + 3x + 8) = 10x³ + 29x² + 61x + 56
(b) The area of a rectangular painting is 5568 cm².If the width of the painting is 58 cm, what is its length?Length of the painting:
Step 1: Problem
The area of a rectangular painting is 5568 cm².
If the width of the painting is 58 cm, what is its length?
Length of the painting:
Step 2: Concept
Area of a rectangle = Length x Width
Step 3: Method
Given data
Area = 5568 cm square
Width = 58 cm
Length = ?
Area of a rectangle = Length x Width
5568 = 58L
L = 5568/58
L = 96cm
Step 4: Final answer
Length of the painting = 96cm
b) A survey on the nationality of the student in the St Thomas international school is conducted and the results are shown below:i) if two students are randomly selected, what is the probability that both of them are European (correct to 4 decimal places)ii) if one student is randomly selected, what is the probability that a student is not Asian. (correct to 4 decimal places)
Given:-
A survey on the nationality of the student in the St Thomas international school is conducted and the results are shown.
To find if two students are randomly selected, what is the probability that both of them are European and if one student is randomly selected, what is the probability that a student is not Asian.
So now the total number of students are,
[tex]230+110+85+25=450[/tex]So now the probability of getting European is,
[tex]\frac{110}{450}=\frac{11}{45}[/tex]So the probability is,
[tex]\frac{11}{45}[/tex]So now the probability is asian is,
[tex]\frac{230}{450}=\frac{23}{45}[/tex]So the probability that it is not asian is,
[tex]1-\frac{23}{45}=\frac{45-23}{45}=\frac{22}{45}[/tex]so the required probability is,
If tan=21/20,0
a. sin a/2
b. cos a/2
c. tan a/2
Using trigonometry we can conclude that the value is sin a/2=7/58, cos a/2= -3/√58, tan a/2= -7/3.
What is Trigonometry?A branch of mathematics called trigonometry looks at how triangle side lengths and angles relate to one another. Applications of geometry to astronomical research led to the development of the field in Hellenistic civilization during the third century BC.We are aware:
x=tan(a/2)And,
tan(a)=2tan(a/2)/1-tan²(a/2)=21/20= 2x/1x2⇒21−21x²=40x⇒21x²+40x−21=0⇒21x²+49x−9x−21=0⇒7x(3x+7)−3(3x+7)=0⇒(3x+7)(7x−3)=0Thus, x=7/3 or x=3/7
It is now given:
180<a<270⇒ 90<a/2<135The a/2 second quadrant.
As a result:
x = tan(a/2)negativeTherefore,
x = tan(a/2)= -7/3sin(a/2) => +veThis means that:
sin(a/2) = 1/cos(a/2) = 1/(1+cot²(a/2))= 1/(1+1/tan(a/2))=1/√(1+9/49)=7/√58The formula is now:
cos(a/2)=sin(a/2)/tan(a/2)=7/√58/ -7/3cos(a/2) = -3/√58Therefore, using trigonometry we can conclude that the value is sin a/2=7/58, cos a/2= -3/√58, tan a/2= -7/3.
To learn more about Trigonometry click on the link
brainly.com/question/24349828
#SPJ13
In a certain fraction, the denominator is 3 less than the numerator. If 1 is added to both the numerator and denominator, the resulting fraction is equal to 10/7 Find the original fraction.
The original fraction has a denominator that is 3 less than the numerator. If we define the numerator as x, then the denominator is x-3, and the fraction can be written as x/(x-3).
If 1 is added both to the numerator and denominator, the resulting fraction is equal to 10/7.
Then, we can write:
[tex]\begin{gathered} \frac{x+1}{(x-3)+1}=\frac{10}{7} \\ \frac{x+1}{x-2}=\frac{10}{7} \\ 7(x+1)=10(x-2) \\ 7x+7=10x-20 \\ 7x-10x=-20-7 \\ -3x=-27 \\ x=\frac{-27}{-3} \\ x=9 \end{gathered}[/tex]With the value of x, we can replace it in the fraction and know the value of it:
[tex]\frac{x}{x-3}=\frac{9}{9-3}=\frac{9}{6}=\frac{3}{2}[/tex]Answer: The fraction is 9/6, that can be simplified to 3/2 or 1.5.
at what rate is the depth of the pool water increasing?
Given:
Find-:
Rate is the depth of the pool water increasing
Explanation-:
The rate of change is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Choose any two points is:
[tex]\begin{gathered} (x_1,y_1)=(2,1) \\ \\ (x_2,y_2)=(4,2) \end{gathered}[/tex]So, the rate of change is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{2-1}{4-2} \\ \\ m=\frac{1}{2} \end{gathered}[/tex]So, 1/2 ft per hour
a certain number was multiplied by 3. then, this product was divided by 10.2. finally, 12.4 was subtracted from this quotient, resulting in a difference of -8.4. what was this number
Answer:
13.6
Step-by-step explanation:
[tex] \frac{3x}{10.2} - 12.4 = - 8.4[/tex]
[tex] \frac{3x}{10.2} = 4[/tex]
[tex]3x = 40.8[/tex]
[tex]x = 13.6[/tex]
May I get help, I know I have to multiply the possibilities, but I keep getting stuck
First we obtain each probability
The land has no oil
is a 45% chance that the land has oli , then the chance that the land has not oil is 55%
55% can be represented like 0.55
then the probability to the land has no oil is 0.55
The test shows that there is no oil
Kit claims to have an 80% of idicating oil, then the percent that there is no oil is 20%
20% can be represented like 0.2
the tne probability to shows that theere is no oil is 0.2
Finally
Multiply the probabilities to find the probability that say the land has no oil and the test shows that there is no oil
[tex]0.55\times0.2=0.11[/tex]then irhg toption is B
Find all solutions of the equation in the interval [0,2pi). csc =7/4 If there is more than one solution, separate them with commas.Do not round any intermediate computations. Give your answer(s) in radians, and round your answer(s) to the nearest hundredth
Since the cosecant is the inverse of the sine, we can write the following:
[tex]\begin{gathered} \csc (\theta)=\frac{7}{4} \\ \sin (\theta)=\frac{1}{\csc(\theta)}=\frac{1}{\frac{7}{4}}=\frac{4}{7} \end{gathered}[/tex]Then, using a calculator, we can calculate the angle that has a sine of 4/7:
[tex]\begin{gathered} \theta=\sin ^{-1}(\frac{4}{7})_{} \\ \theta=34.85\degree \end{gathered}[/tex]There is one more angle between 0 and 2π that has the same value of 4/7 for the sine, and it's the supplementary angle to the one we found:
[tex]\theta_2=180-\theta_1=180-34.85=145.15\degree[/tex]Therefore the answers are 34.85° and 145.15°.
Converting to radians, we have:
[tex]\begin{gathered} 34.85\cdot\frac{\pi}{180}=0.61 \\ 145.15\cdot\frac{\pi}{180}=2.53 \end{gathered}[/tex]So the final answer is 0.61 and 2.53.
Q.Using triangle congruency theorems, justify why the triangles are similar.
4a)
Looking at the figure,
AD and BE are parallel lines
AE and BD are transversals
Thus,
angle DAE is congruent to angle BEA because they are alternate angles(They lie in similar positions but on alternate sides of the transversal
Also,
angle ADB is congruent to angle EBD because they are alternate angles(They lie in similar positions but on alternate sides of the transversal.
Angle ACD is congruent to angle BCE
Recall, 2 triangles are similar if at least, 2 of their corresponding angles are congruent. In this case, 3 corresponding triangles are congruent. Thus,
triangle ADC is similar to triangle EBC by AA(angle angle) postulate
4b) If 2 triangles are similar, it means that the ratio of their corresponding sides is equal. Thus,
AD/EB = DC/BC = AC/ CE
From the information given,
AD = 2
AC = 4
EB = 5
Thus,
2/5 = 4/CE
By cross multiplying,
2 * CE = 5 * 4
2CE = 20
CE = 20/2
CE = 10
a janitor had 2/3 of a cleaning solution. he used 1/4 of the solution in an day. how much of the bottle did he use?
Answer:
5/12 of the cleaning solution.
Step-by-step explanation:
2/3 – 1/4
------------------------------------------
2 × 4
= 8/12
3 × 4
------------------------------------------
1 x 3
= 3/12
4 x 3
------------------------------------------
8 – 3
12
= 5/12
------------------------------------------
Hopefully this makes sense!
a plant is already 44 cm tall, and will grow one cm every month. let H be height in cm and M months. write and equation relating H to M . then use equation to find plants height after 32 months
H = height in cm
M = months
The plant is already 44 cm tall
GRowth every month = 1 cm
Equation:
H (m) = 44 + m
The height after m months, will be equal to the initial height (44) plus the number of months.
For 32 months, replace m by 32 and solve:
H (32) = 44+32
H (32) = 76 cm
After 32 months, the plant will be 76 cm tall
Consider the following expression-x + 8x2 - 9x?Step 2 of 2: Determine the degree and the leading coefficient of the polynomial.
Solution
For this case we have the following polynomial:
[tex]-x+8x^2-9x[/tex]For this case the higher degree is 2 then the answer is:
Degree= 2
Leading Coefficient of the polynomial: 8
You might need:CalculatorHiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 squaremeters left to paint.Let y represent the area (in square meters) left to paint after chours.Which of the following information about the graph of the relationship is given?
The graph is that of area painted against the number of hours. Given that he painted 8 square meters per hour, the slope is 8 square meters per hour because slope is known as unit rate.
After 3 hours of painting, he would have painted 8*3 = 24 square meters.
Since he has 28 meters left to paint, it means that the total rea of the room that
Course ListScore! OU TUUTUTZu anisweredQuestion 11In A XYZ, the sum of the measures of ZX and Y are 55°. What is the measure of ZZ?ZZ=?
To solve that question we must remember that the sum of all internal angles of a triangle is 180°, we can say that
[tex]\angle X+\angle Y+\angle Z=180[/tex]That's a rule! it's always true.
The problem says that
[tex]\angle X+\angle Y=55[/tex]Then let's use it in our equation!
[tex]\begin{gathered} \operatorname{\angle}X+\operatorname{\angle}Y+\operatorname{\angle}Z=180 \\ \\ 55+\operatorname{\angle}Z=180 \end{gathered}[/tex]Now we can solve it for Z
[tex]\begin{gathered} 55+\angle Z=180 \\ \\ \angle Z=180-55 \\ \\ \angle Z=125° \end{gathered}[/tex]Therefore the measure of Z is 125°
Melanie went shopping and spent $18 on scarves. If she spent $77 total, what percentage did she spend on scarves? Round your answer to the nearest percent.
Answer:
23.4%
Step-by-step explanation:
[tex]\frac{18}{77} =\frac{x}{100}[/tex]
$18 divided by $77 is the equivalent of X(% spent on scarves) divided by 100. To find X you cross multiply and divide. [tex](18*100)/77=23.377...[/tex], rounded, X = 23.4
What is the explicit formula for the sequence?3,1,-1, -3, -5,...a,= -2n +5a, = 17-5an= 2n-5an= -2n + 3
We need the formula that gives us the values of the sequence
where n is the value of the position
using the formula
[tex]a_n=-2n+5[/tex][tex]\begin{gathered} a_1=-2(1)+5=3 \\ a_2=-2(2)+5=1 \\ a_3=-2(3)+5=-1 \\ a_4=-2(4)+5=-3 \\ a_5=-2(5)+5=-5 \end{gathered}[/tex]as we can see the formula is the correct formula because we obtain the values of the sequence
In a right triangle, the hypotenuse is the longest side?
Okay, here we have this:
The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle. The other two sides are called the opposite and adjacent sides.
This mean that the statement is true.
4. If line segment AB has coordinates A(-2,4) and B(2,0) and line segment
CD has coordinates C(3,4)and D(-3,-2), how would you describe these two
line segments?
These 2 lines perpendicular to each other on the graph.
What are perpendicular lines?The two different lines that meet at an angle of 90 degrees are called perpendicular lines. Do your walls' connecting corners—or the letter "L"—share any similarities? They are the straight lines, referred to as perpendicular lines, that intersect at the proper angle. An angle of 90 degrees between two straight lines is known as a perpendicular. The illustration depicts a little square in between two perpendicular lines to indicate the 90° angle, which is also known as a right angle. Here, a right angle between the two lines Two lines that cross each other at a 90° angle are referred to as perpendicular lines in mathematics. I
To know more about perpendicular lines ,visit:
brainly.com/question/18271653
#SPJ13
Write the equation of a quadratic in general form, given its solutions.x=4 ; x=-1
The given solutions of the quadratic equation:
x = 4 and x = -1
First we make them factors of the equation:
x= 4 becomes:
[tex]x-4\text{ = 0}[/tex]and x = -1 becomes:
[tex]x\text{ + 1 = 0}[/tex]So (x-4) and (x+1) are the factors.
To get the general quadratic equation, we would expand the factors
[tex]\begin{gathered} (x-4)(x+1)\text{ = 0 } \\ x(x+1)\text{ -4(x+1) = 0} \\ x^2+x\text{ -4x-4 = 0} \end{gathered}[/tex][tex]\begin{gathered} Adding\text{ like terms} \\ x^2-3x-4\text{ = 0} \end{gathered}[/tex]The general quadratic equation:
[tex]x^2\text{ - 3x - 4 = 0}[/tex]which of these is closest to the unit distance between points M and M' ?
the coordinate of M is (-3, -5)
it is given that M is translated 6 unit right , and 5 unit up.
so the coordinate of M' is (-3+6 , -5 + 5) = (3, 0)
so, the distance between M and M' is,
[tex]d=\sqrt[]{(3-(-3))^2+(0-(-5))^2}[/tex][tex]\begin{gathered} d=\sqrt[]{6^2+5^2} \\ d=\sqrt[]{36+25} \\ d=\sqrt[]{61} \end{gathered}[/tex]d = 7.81
so, the closest to the unit distance is 8
thus, the answer is option D
Write these numbers from least to greatest: 0, -6.1, 4, 10/2
Answer:
10/2, 4, 0, -6.1
Step-by-step explanation:
It is the only answer that makes sense.
pls mark brainliest
Answer: -6.1, 0, 4 , 10/2
Step-by-step explanation:
-6.1 is the only negative number, so it is the least. Zero comes next. 10/2 is 5, so 4 comes before it. Therefore 4 is the 3rd installment in these ordered numbers.
One factor of the polynomial x3 − 7x2 + 13x − 3 is (x − 3). What is the other factor of the polynomial? (Note: Use long or synthetic division.) A. (x2 + 4x − 1) B. (x2 − 4x + 1) C. (x − 4) D. (x + 4)
The other factor of the polynomial from what we have here is given as x² - 4x + 1 option B is correct.
How to solve the polynomialWe are required to divide x³ - 7x² + 13x - 3 by x -3
We have this as
x² - 4x + 1
-----------------
x-3 | x³ - 7x² + 13x - 3
we would have
x³ - 3x²
subtract this value by the one that we have above
then we would have
-4x² + 13x
-4x² + 12x
subtract these values from each other to get the value below.
x - 3
Hence the solution to the polynomial would be x² - 4x + 1.
Read more on polynomials here:
https://brainly.com/question/2833285
#SPJ1
Need help with this.. tutors have been a great help
Given the table in I which represents function I.
x y
0 5
1 10
2 15
3 20
4 25
• Graph II shows Item II which represents the second function.
Let's determine the increasing and decreasing function.
For Item I, we can see that as the values of x increase, the values of y also increase. Since one variable increases as the other increases, the function in item I is increasing.
For the graph which shows item II, as the values of x increase, the values of y decrease, Since one variable decreases as the other variable decreases, the function in item I is decreasing.
Therefore, the function in item I is increasing, and the function in item II is decreasing.
ANSWER:
A. The function in item I is increasing, and the function in item II is decreasing.
select the ordered pair that represent solutions of the system of inequalities A) (-1,3)B) (0,0)C) (-4,1)D) (0,2)E) (-5,0)F) ( -4,4)G) (-5,3)H) (-6,5)please answer fast
From the graph, the solution of the graph is given by the area of intersection of the two functions. The are under the area of the two functions are (-4, 1), (-5, 0), (-4, 4)
Trying to figure out this for my home work assignment
Given:
Choosing a even number from the numbers between 1 and 10.
The sample space is
[tex]\mleft\lbrace2,3,4,5,6,7,8,9\mright\rbrace[/tex]Let A be the event of choosing a even number.
There are 4 out comes in the experiment.
