The length of the diagonal of the square is 22.05 units
How to find the diagonal of a square?A square have all its sides equal to each other.
Therefore, using Pythagoras theorem,
c² = a² + b²
c² = (9√3)² + (9√3)²
c² = 81 × 3 + 81 × 3
c² = 243 + 243
c² = 486
square root both sides
c = √486
c = 22.045407685
c = 22.05 units
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How Do You Answer This Question
if a= (-3 -9 -3 -4 -3 9 7 9 -10) and b= (9 1 6 3 -10 5 -1 9 -9) find -7A -4B?
Answer: Choice A
[tex]\begin{pmatrix}-15 & 59 & -3\\16 & 61 & -83\\-45 & -99 & 106\end{pmatrix}[/tex]
===========================================================
Explanation:
In matrix A, the upper left corner is -3
Multiply this with -7 to get -7*(-3) = 21
So we'll have 21 in the upper left corner of matrix -7A. The other entries will be handled in a similar fashion.
Meanwhile, the upper left corner of matrix B is 9. Multiply this with -4 to get 9(-4) = -36 which is the upper left corner entry of matrix -4B
Combine those products: 21 + (-36) = -15
The number -15 is the upper left corner entry in matrix -7A-4B
This points us to choice A as the final answer.
A graph displays point A (5, 3, 4) and point B (−4, 2, 6). Calculate the approximate distance each point is from the origin. Round to the nearest tenth. Which point is farther from the origin, and by how much?
Distance from the origin to the points ≈ 0.41.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
D = √[(x-p)² + (y-q)²]
Point A (5, 3, 4) and point B (−4, 2, 6) are located away from the origin (0,0,0), and the points from the origin to this points are expressed as OB - OA where;
Let OB is the distance from the origin to the point B
Let OA is the distance from the origin to the point A
Using the formula for calculating the distance between two points;
OA = √(z2-z1)²+(y2-y1)²+(x2-x1)²
OA = √(4-0)²+(3-0)²+(5-0)²
OA = √(16)+(9)+(25)
OA = √50
OA = 7.071
Similarly;
OB = √(6-0)²+(2-0)²+(-4-0)²
OB = √(6)²+(2)²+(-4)²
OB = √36+4+16
OB = √56
OB = 7.4833
Distance from the origin to the points = 7.4833 - 7.071= 0.4123
Distance from the origin to the points ≈ 0.41
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What is the difference when estimating?
Answer:
1 1/6 = 1
5/9 = 45/99
Step-by-step explanation:
When rounding, make sure that anything that's above half will be rounded up if anything is below half it will be rounded down.
e.g. Round to the nearest half or whole
1. 5/9
Answer: 45/99
Why: 5/9 is 4 units to 9 while 5/9 is half of a unit closer to 45/99
2. 8/10
Answer: 10/10 or 1
Why: 8/10 is 2 units from 10 while 8/10 is 3 units from 5
Hopefully this helped!
Which function is the inverse of f(x)=1/2x+5?
click on the attachment below and please help me with the question
The value of the length of the scaled up rectangle is 12.8 unit.
What is a Rectangle ?A rectangle is a polygon with four sides , the opposites are parallel and equal.
It is given in the figure that
A rectangle 4* 8 is scaled up and a new rectangle is formed α * 25.6
Scale factor = 25..6/8 =3.2
The value of the length therefore will be
4 * 3.2 = 12.8 unit
Therefore the value of the length of the scaled up rectangle is 12.8 unit.
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Select the correct answer.
x
f(x)
2.0 2.8
2.5 1.1
3.0 –0.8
3.5 –1.2
4.0 –0.3
4.5 0.7
For the given table of values for a polynomial function, where must the zeros of the function lie?
A.
between 2.0 and 2.5 and between 4.0 and 4.5
B.
between 2.5 and 3.0 and between 4.0 and 4.5
C.
between 2.0 and 2.5 and between 3.5 and 4.0
D.
between 2.5 and 3.0 and between 3.5 and 4.0
Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The correct option is B.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication, and non-negative exponentiation of variables involved.
Example:
x² + 3x + 5
In order to find the values at which the given polynomial will have zeros of the function, we need to find the values at which f(x) changes from positive to negative or vice versa. Since this is the range at which the function must have crossed the x-axis on the graph.
As per the given table, the value of f(x) is changing from negative to positive and positive to negative are between 2.5 and 3.0 and between 4.0 and 4.5.
Hence, the correct option is B.
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considering the inequality -5x-4y<12 , the shaded area of its graph is described by
The shaded area for the inequality y > -3-(5/4)x is given below.
The inequality is the relation between two expressions showing the relationships such as greater than, lower than, greater than equals to, and lower than equals to.
The given inequality is -5x-4y<12
solving this inequality for y
-5x-4y<12
⇒ -4y<12+5x
⇒y > (12+5x)/(-4)
⇒y > -3-(5/4)x
the line y= -3-(5/4)x has y intersection at (0,-3) and x intersection at (-12/5,0).
The inequality y > -3-(5/4)x show that this will be above the straight line y = -3-(5/4)x as if we put (0,0) in the inequality, the inequality will be 0>-3 which is true that shows that the region contains (0,0).
Therefore the shaded area for the inequality y > -3-(5/4)x is given below.
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Question 3(Multiple Choice Worth 4 points)
Which expression is equivalent to (7³)-2?
1
7-7-7-7-7-7
07
01
7
-1
7-7-7-7-7-7
frm
This table represents a proportional relationship between x and y.
x 0.2 0.4 0.6 0.8
y 0.25 0.5 0.75 1.0
What is the constant of proportionality?
Enter your answer as a decimal in the box.
Answer:
x
Step-by-step explanation:
I got it right.........
Scott started his bank account with $150 and is spending $7 per day on lunch. The x-axis would be labeled:
The x axis is labeled as Number of days.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
let x be the number of days and y be money.
So, the equation is
y = -7x + 150.
Hence, the x axis is labeled as Number of days.
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A car is purchased for 28,000 after each year, the resale value decreased by 25% what will be the resale value be after 3 years?
Answer:
11,812.5
Step-by-step explanation:
25% = 0.25
(YEAR ONE)
[tex]28,000*0.25 -- > 21,000[/tex]
↓ (why?)
28,000 * 0.25 = 7,000
[tex]28,000 - 7,000 = 21,000[/tex]
(YEAR TWO)
[tex]21,000 * 0.25 -- > 15,750[/tex]
↓ (why?)
[tex]21,000 * 0.25 = 5250[/tex]
[tex]21,000 - 5,250 = 15,750[/tex]
(YEAR THREE)
[tex]15,750 * 0.25 -- > 11,812.5\\[/tex]
↓ (why?)
[tex]15,750 * 0.25 = 3,937.5\\15,750 - 3,937.5 = 11,812.5[/tex]
Answer = 11, 812.5
Please SHOW THE WORK. How many miles are in 10 kilometers?
A triangular pyramid has a triangular base with height of 1.5 inches and base length of 4 inches, and height of 9 inches. What is the volume?
18 cubic inches
27 cubic inches
3 cubic inches
9 cubic inches
Answer:
V = 9 in^3
Step-by-step explanation
Comment
The formula for a Pyramid of any B is V = B * h / 3. You have to be able to calculate the Base or just be given in it.
In this case the Base is a triangle. So the first thing needed is the area of the base.
Base
Area_triangle = base length * height / 2
Neither the Base length nor the height need to be the same as the B and h used for the volume of the Pyramid
Givens
b = 4 inches
h = 1.5 inches
Area_triangle = 4 * 1.5 / 2
Area_triangle = 2 * 1.5
Area_triangle = 3 inches^2
Solution
Base (triangle) Area = 3
h = 9
V = B * h / 3
V = 3 * 9 / 3
V = 9 cubic inches
Answer V = 9 in^3
Recently, a random sample of 2534 year olds was asked, "How much do you currently have in savings, not including retirement savings?" The data in the table represent the responses to the survey. Approximate the mean and standard deviation amount of savings.
Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3
The approximations of the mean and the standard deviation are 233.3 and 229.82, respectively
How to determine the mean?The table of values is given as:
Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3
Rewrite the table to include the class midpoint and the frequency
x f
99.5 345
299.5 97
499.5 52
699.5 21
899.5 9
1099.5 8
1299.5 3
The mean is calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{99.5* 345 + 299.5* 97 + 499.5* 52 + 699.5 * 21 + 899.5 * 9 + 1099.5 * 8 + 1299.5 * 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]
Evaluate
[tex]\bar x = 233.331775701[/tex]
Approximate
[tex]\bar x = 233.3[/tex]
Hence, the approximation of the mean is 233.3
How to determine the standard deviation?The standard deviation is calculated as:
[tex]\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]
So, we have:
[tex]\sigma= \sqrt{\frac{(99.5-233.3)^2* 345 + (299.5-233.3)^2* 97 +...... + (1299.5 -233.3)^2* 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]
Evaluate
[tex]\sigma = 229.82[/tex]
Hence, the approximation of the standard deviation is 229.82
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Which is not a solution of sin 20 = 1?
A = 90
B = 45
C = 225
D = - 135
NEED ASAP !!!!!
Which table represents a linear function?
Alana, Brianna and Carla divided $171 between them in the ratio 4 colon 7 colon 8. How much did Brianna receive?
Answer:
$63
Step-by-step explanation:
Alana has 4 units of the $171.
Brianna has 7 units of the $171.
Carla has 8 units of the $171.
Total units = 4 + 7 + 8 = 19
19 units = $171
1 unit [tex]\frac{171}{19} \\= $9[/tex]
Brianna has 7 units, so she receives 7 x $9 = $63.
()
8
What is 11 - 2³?
Answer:
[tex]11 - 2 {}^{3} [/tex]
[tex]11 - 8[/tex]
[tex]3[/tex]
A polynomial function has a root of -6 with multiplicity 3 and a root of 2 with multiplicity 4. If the function has a negative
leading coefficient and is of odd degree, which could be the graph of the function?
Answer:
Using the formula multiplicity, we find that the equation of the function will be [tex]f(x)=-(x+6)^{3} (x-2)^{4}[/tex]. The graph is in the attachment.
Step-by-step explanation:
Concept: Given that for -6, multiplicity is 3 and for 2 multiplicity is 4.
So, the equation of multiplicity is represented as:
[tex]f(x)=a(x-root)^{mutliplicity}[/tex]
This gives the following function
[tex]f(x)=a(x+6)^{3} (x-2)^{4}[/tex]
The equation has a negative leading coefficient.
This means that, the value of a is less than 0 i.e. a < 0
Assume any value of a (say a = -1), the equation becomes
[tex]f(x)=-(x+6)^{3} (x-2)^{4}[/tex]
The graph is in the attachment.
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Answer:
C
Step-by-step explanation:
trust bro
Part A: Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form
The expression that represents this inequality must relate both temperatures, then it would look like this: -40°F < x < 140°F.
How to write this situation with an inequality?To express this situation in an inequality we must include the temperature values. Additionally, we must include the greater than (>) or less than (<) symbols to relate the values.
According to the above, the expression would look like this:
-40°F < x < 140°FNote: This question is incomplete because some information is missing. Here is the information:
A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs to check the weather continuously to make sure the gas in his truck remains in liquid form. The gas he uses freezes at −40° F and evaporates at 140° F.
Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form.
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Are the two triangles congruent?
Answer:
yes.......................
Step-by-step explanation:
Solve each inequality and graph the solution set and a number lined, express the Solution set in interval notation. 6 < x + 3 < 8 Solve each inequality and graph the solution set and a number lined , express the Solution set in interval notation . 6 < x + 3 < 8
The solution set for the given inequality is 3<x<5.
The given inequality is 6<x+3<8.
What is the solution set?In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.
Now, solve the given inequality:
6<x+3<8⇒6<x+3 and x+3<8
6-3<x ⇒3<x
x+3<8⇒x<5
Thus, 3<x<5.
Therefore, the solution set is 3<x<5.
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Inequality and graph the solution set and a number line, express the Solution set in interval notation is 3 < x < 5
6<x+3<8
[tex]6 < x+3\quad \mathrm{and}\quad \:x+3 < 8[/tex]
What is the rule of inequality?[tex]\mathrm{If}\:a < u < b\:\mathrm{then}\:a < u\quad \mathrm{and}\quad \:u < b[/tex]
[tex]\mathrm{Combine\:the\:intervals}[/tex]
[tex]x > 3\quad \mathrm{and}\quad \:x < 5[/tex]
[tex]3 < x < 5[/tex]
Therefore the Inequality and graph of the solution set and a number line, express the Solution set in interval notation as 3 < x < 5.
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Curved surface area of a right circular cylinder is 4.4 m². If the radius of the base of the cylinder is 0.7 m, find its height. [Assume π = 22/7]
[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]
★ Curved surface area of right circular cylinder is 4.4 m².
★ Radius of base of the cylinder is 0.7 m.
★ [tex]\tt \pi = \dfrac{22}{7}[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}[/tex]
★ The height of cylinder.
[tex] {\large{\textsf{\textbf{\underline{\underline{Using \: Formula :}}}}}}[/tex]
[tex] \star \: \tt C.S.A \: of \: cylinder = \boxed{ \tt \pink{{ 2πrh}}}[/tex]
[tex] {\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]
Let,
❍ The height of circular cylinder be [tex]h[/tex]
❍ Radius [r] of base of cylinder be 0.7 m
We know,
[tex] \star \: \tt C.S.A \: of \: cylinder = 2πrh[/tex]
Putting,
☆ [tex]\tt \pi = \dfrac{22}{7}[/tex]
☆ r as 0.7
[tex] \longrightarrow \tt 4.4 {m}^{2} = 2πrh[/tex]
[tex] \longrightarrow \tt 4.4 {m}^{2} = \bigg( 2 \times \dfrac{22}{7} \times 0.07 \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{10} {m}^{2} = \bigg( {2 }\times \dfrac{22}{ \cancel{7}} \times \dfrac{ \cancel{7}}{10} \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{10} {m}^{2} = \bigg( 44 \times \dfrac{ {1}}{10} \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{ \cancel{10}} \times \cancel{10} \: m = \bigg( 44 \times 1 \times h \bigg)[/tex]
[tex] \longrightarrow \tt 44 m = 44h[/tex]
[tex]\longrightarrow \tt \dfrac{44}{44} m = h[/tex]
[tex]\longrightarrow \tt \red{ 1 m } = h[/tex]
Therefore, the height of cylinder = 1 m.
[tex]\begin{gathered} {\underline{\rule{290pt}{2pt}}} \end{gathered}[/tex]
What is the area of the polygon given below?
Answer:
340 i am pretty sure
Step-by-step explanation:
Finding the inverse of the function x^3+3x+1 is beyond the scope of this course. Nevertheless, you should be able to use your knowledge of functions and their inverses as well as your graphing calculator to find the following values of the inverse function.
a. f^-1(1)
b. f^-1(5)
c. f^-1(3)
Step-by-step explanation:
[tex] {x}^{3} + 3x + 1 = 1 = = = > \\ {x}^{3} + 3x = 0 = = = > \\ x({x}^{2} + 3) = 0 \\ x = 0 \: or \\ {x}^{2} + 3 = 0 = = = > \\ {x}^{2} = - 3 = = = > x 1= \sqrt{ - 3} \: or \: i \sqrt{3} \\ x2 = - \sqrt{ - 3} = = = > x2 = - i \sqrt{3} [/tex]
[tex] {x}^{3} + 3x + 1 = 5 = = = > \\ {x}^{3} + 3x - 4 = = = > \\ (x - 1)( {x}^{2} + x + 4) = 0 = = = > \\ x - 1 = 0 = = > x1 = 1 \\ {x}^{2} + x + 4 = 0 = = = > \\ x2 = - 1 + i \sqrt{3} \\ x3 = - 1 - i \sqrt{3} [/tex]
[tex] {x}^{3} + 3x + 1 = 3 = = = > \\{ x}^{3} + 3x - 2 = 0 = = = > x = 0.6[/tex]
The values of the inverse of the function, f(x) = x³ + 3·x + 1, obtained from graphing of the function are;
a. f⁻¹(1) = 0
b. f⁻¹(5) = 1
c. f⁻¹(3) ≈ 0.59607
What is an inverse function?An inverse function is a function that reverses the action of another function, such that the inverse function maps the output of the function to the corresponding input.
The inverse of the function can be found by graphing the function, f(x) = x³ + 3·x + 1, using technology and then using inverse or table function to find the values of the inverse functions at the specified points
a. The value of the inverse function, f⁻¹(1), is the x-value, on the graph that corresponds to the point with a y-coordinate of 1.
The graph of the function indicates that at a y-value of 1, x = 0, therefore;
f⁻¹(1) = 0
b. Similarly, the graph indicates that a y-value of 5, x = 1, therefore;
f⁻¹(5) = 1
c. When the y-value = 3, we get;
x³ + 3·x + 1 = 3
x³ + 3·x - 2 = 0
Solving the above equation with an online tool, we get; x ≈ 0.59607
Therefore; f⁻¹(3) ≈ 0.59607
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Which is the domain and range of the parabola with the equation y = 0.5(x2 – 8x – 6)?
D: (–∞, ∞); R: (–∞, –11]
D: (–∞, ∞); R: [–11, ∞)
D: (–∞, –11]; R: (–∞, ∞)
D: [–11, ∞); R: (–∞, ∞)
Answer:
D: (–∞, ∞); R: [–11, ∞)
Step-by-step explanation:
The domain of a quadratic function is all real numbers, so eliminate the third and fourth options.
Also, since the coefficient of [tex]x^2[/tex] is positive, we know the graph opens up and thus has a minimum.
This means that the first option must be wrong since the range has a maximum, not a minimum.
Therefore, the correct answer is Option 2.
Answer:
D: (–∞, ∞); R: [–11, ∞)
Step-by-step explanation:
I honestly don't know the answer but the other person said this so I'm putting it as my answer ill update this answer when i find out if its right or not.
update I GOT A 100% woop woop
Finding the Domain and Range of a Graph
Determine the domain and range for the graph below. Write your answer in interval notation.
Answer:
Domain: [tex][-3, 1)[/tex]Range: [tex][-5, 4][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
#40 is it true or false
Answer:
True
Step-by-step explanation:
-77 is less than -76. Since the symbol refers to less than or equal to, this statement will be true.
Helppp needed plx as fast as u can
Answer:
The answer is either 30 degrees or 36 degrees.
You need a protractor to measure it.
Most probably, the answer is 30 degrees.
BUT PLEASE MEASURE THE ANGLE WITH A PROTRACTOR!
Answer:
d. 60°
Step-by-step explanation:
Since the clock is a full circle, it has a degree span of 360°.
∴ every 5-min interval on the clock
= 360° ÷ 12 five min intervals
= 30°
∴ acute angle formed by clock in figure
= two 5-min intervals
= 60°
