Answer:
Step-by-step explanation:
Simplifying square roots
Example
Let's simplify \sqrt{75}
75
square root of, 75, end square root by removing all perfect squares from inside the square root.
We start by factoring 757575, looking for a perfect square:
75=5\times5\times3=\blueD{5^2}\times375=5×5×3=5
2
×375, equals, 5, times, 5, times, 3, equals, start color #11accd, 5, squared, end color #11accd, times, 3.
We found one! This allows us to simplify the radical:
\begin{aligned} \sqrt{75}&=\sqrt{\blueD{5^2}\cdot3} \\\\ &=\sqrt{\blueD{5^2}} \cdot \sqrt{{3}} \\\\ &=5\cdot \sqrt{3} \end{aligned}
75
=
5
2
⋅3
=
5
2
⋅
3
=5⋅
3
So \sqrt{75}=5\sqrt{3}
75
=5
3
square root of, 75, end square root, equals, 5, square root of, 3, end square root.
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Practice
PROBLEM 1.1
Simplify.
Remove all perfect squares from inside the square root.
{\sqrt[]{12}}=
12
=root, start index, end index, equals
Explain
Want to try more problems like these? Check out this exercise.
Simplifying square roots with variables
Example
Let's simplify \sqrt{54x^7}
54x
7
square root of, 54, x, start superscript, 7, end superscript, end square root by removing all perfect squares from inside the square root.
First, we factor 545454:
54=3\cdot 3\cdot 3\cdot 2=3^2\cdot 654=3⋅3⋅3⋅2=3
2
⋅654, equals, 3, dot, 3, dot, 3, dot, 2, equals, 3, squared, dot, 6
Then, we find the greatest perfect square in x^7x
7
x, start superscript, 7, end superscript:
x^7=\left(x^3\right)^2\cdot xx
7
=(x
3
)
2
⋅xx, start superscript, 7, end superscript, equals, left parenthesis, x, cubed, right parenthesis, squared, dot, x
And now we can simplify:
\begin{aligned} \sqrt{54x^7}&=\sqrt{3^2\cdot 6\cdot\left(x^3\right)^2\cdot x} \\\\ &=\sqrt{3^2}\cdot \sqrt6 \cdot\sqrt{\left(x^3\right)^2}\cdot \sqrt x \\\\ &=3\cdot\sqrt6\cdot x^3\cdot\sqrt x \\\\ &=3x^3\sqrt{6x} \end{aligned}
54x
7
=
3
2
⋅6⋅(x
3
)
2
⋅x
=
3
2
⋅
6
⋅
(x
3
)
2
⋅
x
=3⋅
6
⋅x
3
⋅
x
=3x
3
6x
Practice
PROBLEM 2.1
Simplify.
Remove all perfect squares from inside the square root.
\sqrt{20x^8}=
20x
8
=square root of, 20, x, start superscript, 8, end superscript, end square root, equals
Explain
Want to try more problems like these? Check out this exercise.
More challenging square root expressions
PROBLEM 3.1
Simplify.
Combine like terms and remove all perfect squares from inside the square roots.
2\sqrt{7x}\cdot 3\sqrt{14x^2}=2
7x
⋅3
14x
2
=2, square root of, 7, x, end square root, dot, 3, square root of, 14, x, squared, end square root, equals
Explain
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Solve: StartFraction 20 Over x EndFraction = 2 a. x = 40 c. x = 20 b. x = 10 d. x = 15
The value of 'x' in the expression 20/x = 2 is 10.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, A numerical expression in the form of fraction 20/x = 2.
Now, To make 'x' in the numerator we'll move it to the other side which is,
2x = 20.
x = 20/2.
x = 10
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Question 17
Suppose that the given statement is true.
If Stacie likes pizza, then Amir likes soda.
Which statement must also be true?
O If Amir likes soda, then Stacie likes pizza.
O If Stacie likes pizza, then Amir does not like soda.
If Stacie does not like pizza, then Amir does not like soda.
O If Amir does not like soda, then Stacie does not like pizza.
The conditional statement that must also be true is given as follows:
If Stacie does not like pizza, then Amir does not like soda.
What is a conditional statement?A conditional statement has the format defined as follows:
p -> q.
It is read as follows:
If p then q.
In which:
p is the hypothesis.q is the conclusion.The statement in this problem is given as follows:
If Stacie likes pizza, then Amir likes soda.
Then the parameters are given as follows:
p: Stacie likes pizza.q: Amir likes soda.When the conditional statement is true, the inverse statement must also be true, that is:
~p -> ~q.
The symbol ~ represents negation.
Thus the inverse statement is given as follows:
If Stacie does not like pizza, then Amir does not like soda.
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Graph the solution to this inequality on the number line. −18≤−3p
100 points pls help me
Answer:
Look at the image
Step-by-step explanation:
You can solve the problem like in the image
Angle 0 is in standard position and (5, -6) is a point on the terminal
side of 0. If 0° 0 < 360°, what is the measure of 0, to the nearest
tenth of a degree (if necessary)?
The corresponding trigonometric ratios are -6/√61, 5/√61, -6/5, -5/6, √61/5, -√61/6
What are trigonometric ratios?Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec) are the six trigonometric ratios. A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.
First of all we need to find the distance between the point (5,-6) and origin (0,0)
Distance (r) = √(5-0)²+(-6-0)²
= √25+36
= √61
Now, P(5,-6) is compared with (x,y)
Now, sin Ф = y/r = -6/√61
cos Ф = x/r = 5/√61
tan Ф = y/x = -6/5
cot Ф = 1/tan Ф = -5/6
sec Ф = 1/cos Ф = √61/5
cosec Ф = 1/sin Ф = -√61/6
The corresponding trigonometric ratios are -6/√61, 5/√61, -6/5, -5/6, √61/5, -√61/6
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Decide which of the two given prices is the better deal. You can buy laundry product in a 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08 .
A) not enough information
B) 24-ounce bottle for $4.08
C) equal value
D) 30-ounce bottle for $6.00
30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.
The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of the logical grammar, such as the operation order.
We are given that there are two conditions for bottles. A 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08. The unit price for each bottle will be: The bottle having the lower price will be:-
30-ounce bottle = $6.00
One ounce bottle = 30 / 6.00 = $5.00
and
24-ounce bottle = $4.08
One ounce bottle = $24/ 4.08 = $5.88
30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.
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Use a proof by contraposition to prove that if m and n are integers and mn is even, then m is even or n is even.
In order for mn to be even, m must be even or n must be an even number.
What is Contraposition ?The relationship between two propositions when the subject and predicate of one are respectively the negation of the predicate and the negation of the subject of the other.
Suppose that the statement “m is even or n is even” is not true. Then both m and n are supposed to be odd. Let’s see if the product of two odd numbers is an even or an odd number:
Let n and m be equal to 2a +1 and 2b + 1 respectively, then their product is:
(2a +1) (2b + 1) = 4ab + 2a + 2b + 1
= 2(2ab +a + b) + 1
This shows that the expression 2(2ab +a + b) + 1 is of the form 2n +1, thus the product is odd. If the product of odd numbers is odd, then mn is not true to be even. Therefore, in order for mn to be even, m must be even or n must be an even number.
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A rectangular floor tile is shown.
Its dimensions are given to the nearest 0.1 metres.
1.6m
The tile is only able to sustain a maximum pressure
of 200 Newtons per square metre (N/mf),
correct to the nearest 5 N/mf.
2.3m
Given that Pressure =
Force
Area
work out the maximum force, in Newtons, that can safely be applied to the tile.
The maximum force on the rectangular floor tile is 32 N.
What is force?Force is the product of mass and acceleration.
To calculate the maximum force, we use the formula below
Formual:
F = Plw..................... Equation 1Where:
F = ForceP = Pressurel = Length of the tilew = Width of the tileFrom the question,
Given:
P = 200 N/m²l = 1.6 mw = 0.1 mSubstitute these values into equation 1
F = 200×1.6×0.1F = 32 NHence, the maximum force is 32 N.
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k x 20 = 1.07 what is k
consider the value of t such that 0.05 of the area under the curve is to the right of t. step 2 of 2: assuming the degrees of freedom equals 18, select the t value from the t table.
Thus after assuming the degrees of freedom equals 18 so the t-critical value will be =2.306
Degree of freedom {df}=18
We have to calculate the t-value such that 0.05 of the area under the curve is to the right of t
It means that, [tex]$\mathrm{P}(\mathrm{T} > \mathrm{t})=0.05$[/tex]
As we know, t distribution provides the cumulative probability
As the value of the total area under the t distribution will 1
So, we can write it as:
[tex]$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-\mathrm{P}(\mathrm{T} > \mathrm{t})$$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-0.05$$=0.95$[/tex]
Now, using excel, we can easily calculate the t-critical value as follows
=T. INV ( Probability, DF)
Where Probability is the area and DF is the degree of freedom,
Now we will enter these values in excel:
=T. INV (0.95,18)
t-critical value can also be found using t table
Look up for df = 18, in very first column
Now look up for 0.05 in one tail row
Now intersect both of them to get the t-critical value
We will get it as: 2.306
So t-critical value will be =2.306
[tex]$\mathrm{P}(\mathrm{T} > 2.306)=0.05$[/tex]
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DUE IN AN HOUR HELP!!!!
Answer:
D. x=4
Step-by-step explanation:
32. m<1=m<2 ==> angle bisectors divide an angle into two equal angles
m<2=m<RQP
m<1=m<SQP
m<RQP+m<SQP=m<SQR
m<2+m<1=m<SQR
m<2+m<2=m<SQR
(2+7x)+(2+7x)=16x-4
2+7x+2+7x=16x-4
2+2+7x+7x=16x-4
4+14x=16x-4
4-4+14x=16x-4+4
4+4+14x=16x-4+4
14x+8=16x
14x-14x+8=16x-14x
8=2x
x=8/2
x=4 ==> D
In the current year, Bonnie, who is single, sells stock valued at $60,000 to Linda for $15,000. Later that year, Bonnie gives Linda $25,000 in cash. Bonnie's taxable gifts from these transfers totalO $55,000.
O $70,000.
O $59,000.
O $25,000.
In the current year, Bonnie sells stock valued at $60,000 to Linda for $15,000. Later that year, Bonnie gives Linda $25,000 in cash. Bonnie's taxable gifts from these transfers total a) $55,000.
Shares, also known as stocks, are securities that represent partial ownership of the issuing company. A unit of stock is called a "share" and allows the holder to receive a portion of the company's assets and profits equal to the number of shares held.
shares are traded primarily on stock exchanges and form the basis of many individual investor portfolios. Stock trading must comply with government regulations designed to protect investors from fraud.
Taxable Gifts:
Gifts valued at $75 or more are taxable.
Non-cash gifts of small value (less than $75 annually) to employees. Holiday turkeys are tax exempt.
tax-free value is capped at $1,600 for all her awards for one year.
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Solve x²-3x + 7 = 0.
OA. 3+√-37
2
OB. 3+√-19
2
and 3-√-37
2
and ³-v-19
3-√-19
2
O C. 3+√19 and 3-√/19
2
2
O D. 3+√37 and 3-√37
2
2
Solutions of x²-3x + 7 = 0 is 3 + √19/2 and 3 - √19/2.
Define quadratic formula.The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. The phrase "quadratic" in mathematics refers to something that has to do with squares, the squaring operation, terms of the second degree, or equations or formulas that contain such terms. Latin's word for square is quadratus.
Given
Equation
x²-3x + 7 = 0
Using quadratic formula,
x = -b±√b² - 4ac/2a
x = -(-3) ± √((-3)² - 4×1×7/2×1
x = 3/2± √19 1/2i
x = 3 + √19/2 and 3 - √19/2
Solutions of x²-3x + 7 = 0 is 3 + √19/2 and 3 - √19/2.
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plified and labeled.
4) Mindy bought a new painting. It was
8 feet wide. The wall she wants to
place it on is 12 1/4feet wide. About how
far from each side will she have to place
the painting for it to be centered?
Mindy needs to place the painting at 2.125 feet away from each side of the wall.
what do we mean by wall dimension?The horizontal distance of two side of a wall is defined as width and the vertical distance is called length of wall.
How do we place a paint at the center of a wall?We need to place the paint at an equal distance from each side of wall (horizontal distance).
suppose Mindy will place the paint at x feet away from each side of wall.
for both side she counts 2x feet
width of wall =12.25 feet
width of painting= 8 feet
now, 8+ 2x = 12.25
2x= 4.25
x=2.125 feet
hence, Mindy will place the paint at 2.125 feet away from each side horizontally.
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If the radio program plays 40 minutes of music, how many minutes will be used for commercials?
The number of minutes that will be used for commercials will be 20 minutes.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
If the radio program plays 40 minutes of music.
Suppose the radio program is of one hour which is 60 minutes. Then the number of minutes will be used for commercials will be given as,
⇒ 60 - 40
⇒ 20 minutes
The number of minutes that will be utilized for plugs will be 20 minutes.
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Janelle works at Heedle's Computer
Outlet. She receives a weekly salary of
$200 plus 3% commission on her sales.
Last week, she sold $29,700 of
computer equipment. How much did
Janelle earn last week?
Using the concept of percentage, she earned a total of $1091 last week
PercentageA percentage is a number or ratio that can be expressed as a fraction of 100. Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
To determine the amount she earned last week, we need to calculate the amount in commission and add it with her weekly salary.
She received 3% commission on her sales and she made a sale of $29700.
Let's find 3% of 29700
3 / 100 = x / 29700
0.03 = x / 29700
x = 29700 * 0.03
x = 891
The amount she earns will be 891 + 200 = 1091
Janelle earned $1091 last week
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Erin has a balance of $1,123.72 in her check register. On her statement, the balance of her account is $879.87.
Not reported on the bank statement are deposits of $62.42, $21, and $61.14. There are outstanding checks in the
amount of $60.24 and $50.24 and an ATM withdrawal of $40. After Erin reconciles her check register with her
statement, what entry does she need to make in her register?
Answer: After reconciling her check register with her statement, Erin needs to make the following entry in her register: $1123.72 - $879.87 + $62.42 + $21 + $61.14 - $60.24 - $50.24 - $40 = $226.23. This is the updated balance in Erin's account after accounting for all the transactions that were not reflected on her bank statement.
Express tan P as a fraction in simplest terms.
Q
15
R
29
P
Tan P expressed as a fraction in simplest terms is 15/29
What are trigonometric identities?Trigonometric Identities are defined as equalities involving trigonometry functions and also holds true for all the values of variables given in the equation.
There are five types of trigonometric identities;
sinecosinetangentcosecantsecantFrom the information given, we have that;
Opposite side = 15
Adjacent side = 29
But the tangent trigonometric identity is;
Tan P = opposite/adjacent
Substitute the value
Tan P = 15/29
Hence, the value is 15/29
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1. Which of the following inequalities is equivalent to
1
3
-
O A
x ≥ 2?
x 22
x 21
B
x ≤ 2
x ≤ 1
1 point
Answer: A
Step-by-step explanation:
To solve this type of problem we must move some things around
3-(1/2)x>= 2
Isolate the variable: 3-3-(1/2)x>= 2-3
Simplify: -(1/2)x>= -1
Isolate the variable(continued): (-(1/2)*x)/(-1/2) >= -1/(-1/2)
Simplify: x>=2
Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students. You may use your calculator to solve.
Confidence interval for the mean score of all students is (91.679, 98.321)
Given:
Sample mean = 95
Standard deviation = 6.6
The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.
We have to construct a 99% confidence interval for the mean score of all the students.
Sample Standard Error =
[tex]\frac{Standard Deviation}{\sqrt{n} } \\= \frac{6.6}{\sqrt{30} }[/tex]
= 1.205
t-value for the 99% confidence interval = 2.756
(use the t-tables for this)
Margin of error = 2.756 x 1.205 = 3.321
If you are asked to report the confidence interval, you should include the upper and lower bounds of the confidence interval.
So, for the 99% confidence interval:
(95 - 3.321, 95 + 3.321) = (91.679, 98.321)
This is the final confidence interval.
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Convert the hexadecimal expansion of each of these integers to a binary expansion.a) (80E)_{16} b) (135AB)_{16} c) (ABBA)_{16} d) (DEFACED)_{16}
The binary representation of each of these hexadecimal numbers is given as follows:
a) 80E = 100000001110
b) 135AB = 00010011010110101011
c) ABBA = 1010101110111010
d) DEFACED = 1101111011111010110011101101
How to convert from hexadecimal to binary?To convert a number from hexadecimal to binary, each hexadecimal character is converted to it's respective four bit binary code, given as follows:
0 = 00001 = 00012 = 00103 = 00114 = 00105 = 01016 = 01107 = 01118 = 10009 = 1001A = 1010B = 1011C = 1010D = 1101E = 1110F = F111Then, for example:
80E hexadecimal = 100000001110.
As:
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What is the root of the polynomial equation x(x-2)(x+3)= 18? Use a graphing calculator and a system of equations.
-3
0
2
3
Answer:
3
Step-by-step explanation:
on edge
Answer:
x = 3
Step-by-step explanation:
You want the root of the polynomial equation x(x -2)(x +3) = 18.
GraphA graph of the equation in the form x(x -2)(x +3) -18 = 0 is attached. The solution is the x-intercept. It shows the only real root is x = 3.
System of equationsThere are many ways the polynomial can give rise to a system of equations. The basic idea is to write two expressions that are supposed to be equal to each other. The graphing calculator can show the value(s) of x that make them equal.
Dividing both sides of the given polynomial by (x -2)(x +3) gives the equation ...
x = 18/((x -2)(x +3))
This can be graphed as two equations:
y = x
y = 18/((x -2)(x +3))
This is shown in the second attachment. It tells us the root is x=3. (Both sides of the "x=" equation have the value 3 at x=3.)
__
Additional comment
Here, you are asked to use a system of equations. A graphing calculator can usually find the solution more easily when the equation is written in the form f(x) = 0. Often x-intercepts are easier to identify than points where graphs cross each other.
Does anyone know how to do this? i tried it and got it wrong so i’m not sure anymore, lol.
The simplified form of the expression 12c + 8k - 8 - 6c + 6, combining the like term is 6c + 8k - 2.
How to simplify an expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations like subtraction and addition.
To simplify an expression means rewriting the same algebraic expression with no like terms or to write an equivalent expression which contains no similar terms.
Therefore, let's simplify the expression with no like terms.
12c + 8k - 8 - 6c + 6
combine the like terms
12c - 6c + 8k - 8 + 6
Therefore, the simplified expression is 6c + 8k - 2
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Determine the solution/s to the following quadratic equation. Type "NONE" in any unused blank.
y = x² + 14x + 49
Answer:
Step-by-step explanation:i'm pretty sure that y=x^2+14x+49=625.
A square name tag has sides that are 10 centimeters long. What is the name tag's area?
The area of square is 100 square centimeter.
What is square?
A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can also be explained as a rectangle with two adjacent sides that are of equal length.
Given:
A square has sides 10 centimeters long.
We have to find the area of square.
Since,
Area of square = (side)^2
Here side of square is 10cm
So,
Area of square = (10 cm)^2
Area of square = 100 cm^2
Hence, the area of square is 100 square centimeter.
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If a boat travels on course of bearing S 34 degrees W for 15 miles, how far south and how far west will the boat travel? Round each number to the nearest tenth of a mile and include a sketch.
It is to be noted that the boat traveled a distance of 8.39 miles South, and 12.44 miles west. This is solved using trigonometric ratios principles.
What is the rationale for the above answer?Using the trigonometric ratio involving the right triangle, we can answer how far the boat moved northward and westward, or the vertical and horizontal components of the displacement vector.
Solving for the horizontal component Vₓ, we'll be using the ratio of the sine function with regard to angle 34°
Thus,
Sin 34° = Vₓ/ 15
Vₓ = 15 * (Sin 34°)
= 15 * 0.55919290
Vₓ = 8.39 miles.
Solving for the vertical component of, V[tex]_{y}[/tex] we'll be using the ratio of Cosine Function with respect to the angle 34°
Cos 34° = V[tex]_{y}[/tex] / 15
V[tex]_{y}[/tex] = 15 * Cos 34°
V[tex]_{y}[/tex]= 15 * 0.82903757255
V[tex]_{y}[/tex] = 12.44 miles.
Thus, the boat traveled a distance of 8.39 miles South, and 12.44 miles west.
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we would like to understand how psa level is related to the other predictors in the dataset. note that vesinv is a qualitative variable. you can treat gleason as a quantitative variable.
We can examine the relationship between PSA level and the other predictors by running a regression analysis. The regression analysis will allow us to determine the strength of the relationship and the direction of the relationship (positive or negative) between PSA level and the other predictors. For example, if we find that PSA level is positively correlated with age, then it indicates that PSA level increases with age. For the qualitative variable, vesinv, we can use dummy variables to represent the different categories. For example, if there are three categories of vesinv, we can create three dummy variables, each representing one category. After constructing the dummy variables, we can then add them to the regression model to examine the relationship between PSA level and vesinv.
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Type your answers into the boxes.
What are the next two numbers in this sequence?
45.7
46.2
46.7
47.2
Answer:
Step-by-step explanation:
Well, it seems like you're adding 5 each time so
45.7
46.2
46.7
47.7
48.2
48.7
A manufacturer cuts a piece of metal for a microscope. The resulting piece of metal can be
represented in a coordinate plane by a triangle with vertices A(0, 0), B(3, 8), and C(6,0).
One unit in the coordinate plane represents one millimeter.
Prove that AABC is isosceles.
The triangle ABC is an isosceles triangle because AB = BC = √73
How to prove that the triangle is an isosceles triangle?From the question, we have the following parameters that can be used in our computation:
A(0, 0), B(3, 8), and C(6,0).
An isosceles triangle is any triangle that has two of its sides to be equal
So, we start by calculating the lengths of the sides using the distance equation represented as follows
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substitute the known values in the above equation, so, we have the following representation
AB = √[(0 - 3)² + (0 - 8)²]
AB = √73
AC = √[(0 - 6)² + (0 - 0)²]
AC = 6
BC = √[(3 - 6)² + (8 - 0)²]
BC = √73
Because AB = BC = √73, then the triangle is an isosceles triangle
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9. In the diagram below, a Il b. Use the following information to find the missin
measures.
m21 =
m22 =
m23 =
d
(8.x-8)
2
1
m24=
m25 =
m26=
CT
(4y+44)
(3x + 17)
9
3
7
a
8
6
4
5
m27 =
m28 =
m29=
b
10
11 12
(6y+46)
m210=
m211=
m212=
The measurement of all the angles in the given geometrical image are mentioned below.
What are angles? What is a mathematical function, equation and expression?angle : In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the anglefunction : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is a figure as shown in the image.
We can write the following equations -
∠1 + ∠2 + (8x - 8)° + (3x + 17)° = 360°
and
(8x - 8)° = (3x + 17)° {Vertically opposite angles}
8x - 3x = 17 + 8
5x = 25
x = 5
So -
8x - 8 = 8 x 5 - 8 = 32°
3x + 17 = 3 x 5 + 17 = 32°
So -
∠1 + ∠2 + (2 x 32) = 360°
2∠1 + 64 = 360
2∠1 = 296
∠1 = 148° = ∠2 {Vertically opposite angles}
∠6 = ∠1 = 148°
∠3 = 32°
∠5 = (180 - 148) = 32°
∠4 = 148°
∠6 = 148°
∠5 = 32°
Now -
(4y + 44) + (6y + 46) = 180°
10y + 90 = 180
10y = 90
y = 9
So -
(4y + 44) = 4 x 9 + 44 = 36 + 44 = 80
∠8 = 80°
Now -
6y + 46 = 6 x 9 + 46 = 100°
∠10 = 100°
∠11 = 80°
∠7 = ∠10 = 100°
∠7 = 100°
∠11 = ∠12 = 80°
∠12 = 80°
Therefore, the measurement of all the angles in the given geometrical image are mentioned above.
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Choose ALL solutions of the following system of linear inequalities listed below.
A (0, -1)
B (6, 2)
C (9, 9)
D (8, 2)
E (-2, 4)
F (2, 6)
All solutions of the following system of linear inequalities are given-
B (6, 2), C (9, 9), D (8, 2)
Explain the term linear inequalities?Mathematical expressions known as linear inequalities compare two expressions using the inequality sign. The expression may be either a numerical or an algebraic expression, or it may be both.The linear inequality x - 5 > 3x - 10 is an illustration. Due to the greater than symbol being utilized in this inequality, the LHS is clearly greater than the RHS.For the stated question,
The solution for the blue line given in graph will be the region under the line including the values on the line.Similarly, the solution for the red line given in graph will be the region above the line excluding the values on the line.Thus, the total solution becomes, the common shaded region of containing both lines.Therefore, the solutions of the following system of linear inequalities are-
B (6, 2), C (9, 9), D (8, 2).
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