Answers
Related Questions
Vector u has initial point P at (0, 0) and terminal point Q at (5, -8). What are the component form and magnitude of u?
• u = (5, -8): ||u|| = -√89
• u = (5, 8): ||u|| = -√89
• u = (5, -8): ||u|| = √89
• u = (5, 8): ||u|| = √89
Answers
The correct option for the given vector is the third one:
u = (5, -8): ||u|| = √89What are the component form and magnitude of u?If the initial point is (0, 0), then the component form of the vector is just equal to the terminal point of the vector.
Then we have:
u = (5, -8)
For a vector w = (x, y) the magnitude is:
[tex]||w|| = \sqrt{x^2 + y^2}[/tex]
In this case, the magnitude will be:
[tex]||u|| = \sqrt{5^2 + (-8)^2} = \sqrt{89}[/tex]
Then the correct option is the third one.
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Simplify the following expression 7a + 5b - 2a + b
Answers
Answer:
5a + 6bStep-by-step explanation:
Simplify the following expression:
Simplify the following expression:
7a + 5b - 2a + b =
5a + 6b
Determine the relationship between the two triangles and whether or not they
can be
proven to be congruent.
Answers
Answer: These ARE congruent to each other.
Step-by-step explanation: Do you see the ''tick marks?'' They both have 1 set of 2, and 1 set of 1. If that makes sense. They also have a "angle" in one of their acute angles.
please help
PLEASE
Answers
Answer:
Step-by-step explanation:
4567890987654345678
Round 969.991 to the nearest whole number
Answers
Answer:
Round of 969.991
970
Rules of round off
1) If the digit is odd no. the no. will increase to 1
2) if it is even the no. will be same.
Which polynomial is factored completely? 4 (4 x superscript 4 baseline minus 1) 2 x (y cubed minus 4 y squared 5y) 3 x (9 x squared 1) 5 x squared minus 17 x 14
Answers
The answer choice which represents a polynomial which is factored completely is; (y³ - 4y² +5)
Which polynomial is factored completely?The polynomials as given in the task content are;
4(4x⁴ -1) + 2x
(y³ - 4y² +5)
3x (9x² -1)
5x² -17x +14
Hence it follows that the polynomial which cannot be further factorised is; (y³ - 4y² +5).
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Answer:3 x (9 x squared + 1)
it is c because i did the test and put b but got it wrong
Step-by-step explanation:
Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Select three options.
1 ≥ 2x
6x ≥ 3 + 8x – 4
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at negative 0.5 and a bold line starts at negative 0.5 and is pointing to the right.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the right.
Answers
1≥2x and 6x≥3+8x-4 are correct representations of the inequality 6x ≥ 3 + 4(2x – 1).Option A,B and C are correct.
What is the definition of inequality?Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.
The solution to the given inequality is;
6x≥3+4(2x-1)
6x≥3+8x-4
2x≤1
x≤(1/2)
The correct options are;
A)1 ≥ 2x
B)6x ≥ 3 + 8x – 4
C)A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.
1≥2x and 6x≥3+8x-4 are correct representations of the inequality 6x ≥ 3 + 4(2x – 1).
Hence, options A, B, and C are correct.
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Answer:
A, B, C
Step-by-step explanation:
Solve for x in the equation x/5 -2=11
Answers
Answer:
x = 65Step-by-step explanation:
Solve for x in the equation
x/5 - 2 = 11
x/5 = 11 + 2
x/5 = 13
x = 5 * 13
x = 65
-----------------
check
65/5 - 2 = 11
13 - 2 = 11
11 = 11
the answer is good
The triangle inequality theorem states the sum of the lengths of any two sides of a triangle is _____ the length of the third side.
Answers
Answer:
see explanation
Step-by-step explanation:
the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
if the sides are a, b, c , then the following must be true
a + b > c
a + c < b
b + c > a
for the 3 sides to form a triangle
Using Newton-Raphson method to find the approximate root of the equation x log_{10}x=1.2
( Carry out three iterations ). [tex] \\ \\ [/tex]
Thank uh!
Answers
Answer:
[tex]x \approx 2.740646096[/tex]
Step-by-step explanation:
Given:
[tex]x\log_{10}x=1.2[/tex]
Rewrite so that it's equal to zero:
[tex]\implies x\log_{10}x-1.2=0[/tex]
Therefore:
[tex]\implies f(x)=x\log_{10}(x)-1.2[/tex]
Differentiate the function:
Use the product rule to differentiate [tex]x\log_{10}(x)[/tex]:
[tex]\textsf{Let }u=x \implies \dfrac{du}{dx}=1[/tex]
[tex]\textsf{Let }v=\log_{10}(x) \implies \dfrac{dv}{dx}=\dfrac{1}{x \ln 10}[/tex]
[tex]\begin{aligned}\implies \dfrac{dy}{dx} & = u\dfrac{dv}{dx}+v \dfrac{du}{dx}\\& = \dfrac{x}{x \ln 10}+\log_{10}(x)\\& = \dfrac{1}{\ln 10}+\log_{10}(x)\end{aligned}[/tex]
[tex]\implies f'(x)=\dfrac{1}{\ln 10}+\log_{10}(x)[/tex]
[tex]\implies f'(x)=\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}[/tex]
Newton-Rhapson iteration formula
[tex]x_{n+1}=x_n-\dfrac{f(x_n)}{f'(x_n)}[/tex]
Substitute the function and its derivative into the formula, replacing x with [tex]x_n[/tex]:
[tex]\implies x_{n+1}=x_n-\dfrac{x_n\log_{10}(x_n)-1.2}{\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}}[/tex]
[tex]\implies x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]
Therefore, the iteration formula is:
[tex]x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]
Let [tex]x_0=3[/tex]
Substitute this into the formula and carry out 3 iterations:
[tex]\implies x_{1}=3-\dfrac{3\ln 10\log_{10}(3)-1.2\ln 10}{1+\ln 10 \log_{10}(3)}=2.746149035[/tex]
[tex]\implies x_2=2.740648841[/tex]
[tex]\implies x_3= 2.740646096[/tex]
which choice is equivalent to the the expression
square root of -64
Answers
The equivalent expression of square root of -64 is 8i
How to determine the equivalent expression?We have:
square root of -64
Rewrite as:
√-64
Expand
√64 * √-1
Take the square root of 64
8√-1
In complex numbers
√-1 = i
So, we have:
8i
Hence, the equivalent expression of square root of -64 is 8i
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Jill has c comic books. Tonya has 4 more than twice Jill's comic books. What variable expressions represents the total number of comic books Jill & Tony have all together?
Answers
Answer:
3c + 4
Step-by-step explanation:
Forming an expression
Number of books with Jill = c
To find the number of books with Tonya, multiply 'c' by 2 and then add 4 to it.
Number of books with Tonya = 2*c + 4
= 2c + 4
Total books all together = c + 2c + 4 {Combine like terms}
= 3c + 4
Which value must be added to the expression x2 16x to make it a perfect-square trinomial?
Answers
Answer:
16
Step-by-step explanation:
x^2+16x+16
(x+4)(x+4)
x^2+ 4x+4x+16
Answer:
The answer is C.) 64 on edge.
Could use help asap please
Answers
Observe the diagram below with indexes on the shapes.
The transformations are:
Shape I is given a 90° clockwise rotation about the origin and then a reflection across the x-axis.In doing this transformation we first get the shape b by rotating shape I 90° clockwise about the origin and then when we reflect shape b about the x-axis we get shape a.
Ultimately, we get shape a after doing the above transformation on Shape I.
Shape I is given a 90° counterclockwise rotation about the origin and then reflection across the x-axis.
In doing this transformation we first get the shape e by rotating shape I 90° counterclockwise about the origin. And then after reflecting this shape e about x-axis we get shape d.
Ultimately, we get shape d after doing the above transformations on Shape I.
Shape I is given a 180° rotation about the origin and then translation right 4 uints.
In doing this transformation we first get the shape c by rotating shape I 180° about the origin. After that when it is translated 4 units right we get shape c at 4 uints right to shape c's original position.
That means congruent to shape c.
Ultimately, we get shape c after doing the above transformations on Shape I.
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write equation of the log base of 3
Answers
Answer:
see below
Step-by-step explanation:
The graph is shifted to the RIGHT so it will be a ' x-1'
and it is shifted UP 3 units so:
Looks like log3 (x-1) + 3
at x = 4 the value of the graph is 4
log3 (4-1) + 3 = 4 CHECK !
simplify the mathematical expression to determine the appropriate india product or quotient in a scientific notation round round do the 1st fractor goes to the 10th place 3.3x10^3 7.8 3.7 2.1x10^-3
Answers
From the power rules, the matching of each expression with its result is:
[tex](8.6*10^7)(9.1*10^{-8})=7.8[/tex]
[tex](6.9*10^5)(4.8*10^{-3})=3.3*10^3[/tex]
[tex]\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})} =2.1*10^{-3}[/tex]
[tex]\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}=3.7[/tex]
Power RulesThere are different power rules, see some them:
1. Multiplication with the same base: you should repeat the base and add the exponents.
2. Division with the same base: you should repeat the base and subctract the exponents.
3.Power. For this rule, you should repeat the base and multiply the exponents.
4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.
From this for your question, you have:
[tex](8.6*10^7)(9.1*10^{-8})[/tex] - From the distributive property of multiplication and power rules you can do:[tex](8.6*10^7)(9.1*10^{-8})=(8.6*9.1)*(10^7*10^{-8})=78.26*10^{-1}=7.8[/tex][tex](6.9*10^5)(4.8*10^{-3})[/tex] - From the distributive property of multiplication and power rules you can do:[tex](6.9*10^5)(4.8*10^{-3})=(6.9*4.8)*(10^5*10{-3})=33.12*10^2=3.3*10^3[/tex][tex]\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})}[/tex] - From the distributive property of multiplication and power rules you can do:[tex]\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})} =\frac{(3.7*4.6)*(10^2*10^{-3})}{(1.4*5.7)*(10^{-6}*10^{8})} =\frac{17.02*10^{-1}}{7.98*10^2} =2.13*10^{-3}=2.1*10^{-3}[/tex]
[tex]\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}[/tex] - From the distributive property of multiplication and power rules you can do:[tex]\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}=\frac{(3.1*5.3)*(10^{5}*10^{-9})}{(7.3*6.1)*(10^{2}*10^{-7})} =\frac{16.43*10^{-4}}{44.53*10^{-5}}=0.36896*10^1=3.7[/tex]
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Now write 40,630 in scientific notation
Answers
Answer:
40630=4.063× 10 power 4The coordinates of the vertices of △ABC are A(−2,2), B(5,−3), and C(−4,−1). Identify the perimeter of △ABC. Round each side length to the nearest tenth before adding.
Answers
The perimeter of the triangle is 21.4 units
How to determine the perimeter?The points are given as:
A(−2,2), B(5,−3), and C(−4,−1)
Calculate the side lengths using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]AB = \sqrt{(-2 -5)^2 + (2 + 3)^2} = 8.6[/tex]
[tex]AC = \sqrt{(-2 +4)^2 + (2 + 1)^2} = 3.6[/tex]
[tex]BC = \sqrt{(5+4)^2 + (-3 + 1)^2} = 9.2[/tex]
The perimeter is then calculated as:
P = AB + AC + BC
This gives
P = 8.6 + 3.6 + 9.2
Evaluate
P = 21.4
Hence, the perimeter of the triangle is 21.4 units
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please help me with my math
Answers
[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve for y and z ~
[tex]\qquad \sf \dashrightarrow \: z + 61 = 180[/tex]
[ Co- interior angle pair ]
[tex]\qquad \sf \dashrightarrow \: z = 180 - 61[/tex]
[tex]\qquad \sf \dashrightarrow \: z = 119 \degree[/tex]
now,
[tex]\qquad \sf \dashrightarrow \: 5y + 14 = 119[/tex]
[ by Alternate interior angle pair ]
[tex]\qquad \sf \dashrightarrow \: 5y = 119 - 14[/tex]
[tex]\qquad \sf \dashrightarrow \: 5y = 105[/tex]
[tex]\qquad \sf \dashrightarrow \: y = 21 °[/tex]
a) Copy a segment using the construction tool. Insert a screenshot of the construction here.
Alternatively, construct a segment and copy it by hand using a compass and straightedge. Leave
all circle and arc markings.
Answers
We need to understand circles and colinear points in order to use the building tool to create a circle.
What exactly is a circle?It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.
Draw arcs such that they all bisect one another at a point, which will be the center of the circle, starting with three non-colinear points (points A, B, and C).
Additionally, the radius will match the distance between the arcs' centers and their correspondingly drawn arcs.
Hence we need to understand circles and colinear points in order to use the building tool to create a circle.
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Select the correct answer.
Which expression is equivalent to √48x5, if x > 0?
OA. 12x³√3x
OB. 4x³√3
OC. 4x²√3x
OD. 12x²√
Answers
Answer:
C
Step-by-step explanation:
Comment
The square root of 48 is nowhere near 12. That means that A and D are wrong. On a test that's an important consideration because if you have to guess, you've just cut the possibilities down to 2.
So the answer must be B or C. Furthermore, you don't have to go to the trouble of factoring 48 to show that it is 4 sqrt(3). There's no other choice.
So what about x^5. 5 is an odd number. That means that one of the xs is left underneath the square root sign. That makes B incorrect. Without doing a calculation, I know that C is the answer.
Note
x^5 = x * x * x * x * x
The rule is for ever 2 factors that are the same, 1 factor is put in front of the square root sign and the other 1 is thrown out.
√x^5 = √x * x * x * x * x = x * x √x
Therefore the answer to the problem is 4 x * x√3 x = 4x^2√3x
How many solutions are there for the system of equations of shown on the graph?
O No solution
O One solution
O Two solutions
O Infinitely many solutions
Answers
Answer:
1
Step-by-step explanation:
the number of solutions corelatea with number of cross-points in the graphs, in our exame, 1 point, hence 1 solution
Question 29 of 40
Find f(-2) for f(x) = 5.3*.
Answers
Answer:
A. [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
To find f(-2) in f(x)=5*3^x, plug in -2 into all the x values.
f(-2)=5*3^-2, you can use calculator to calculate 3^-2 which equals 0.1, forever 1's.
f(-2)=5*0.1=0.5 Forever 5's.
f(-2)=0.5 or [tex]\frac{5}{9}[/tex]
Hope this helps!
If not, I am sorry.
A set of equations is given below.
Equation C: y = 7x + 12
Equation D: y = 7x + 2
How many solutions are there to the given set of equations?
O One solution
OTwo solutions
O Infinitely many solutions
O No solution
Answers
Answer:
2
Step-by-step explanation:
lucky guess from my boi tony
The slope of the line containing the points (-5, 3) and (-2, 1) is
O-2/3
02/3
0-3/2
Answers
Answer:
Step-by-step explanation:
slope=(1-3)/(-2-(-5))
=-2/(-2+5)
=-2/3
help with both please :)
Answers
Answer: I know two methods of solving both of the sums. One is the method of elimination, the other is method of substitution. You can do any of the given methods which is easier for you. Both methods will be shown below:
Method of Elimination1) 5x + y = 9 - - - - (i)
10x - 7y = - 18 - - - - (ii)
eq. (i) multiplied by 2
10x + 2y = 18 - - - - (i)
10x - 7y = - 18 - - - - (ii) {subtraction of eq. (ii) from eq. (i)}
0 + 9y = 36
y = 36/9
y = 4
From eq. (i),
5x + y = 9
-> 5x + 4 = 9
-> 5x = 9 - 4
-> x = 5/5
-> x = 1
So, x = 1 and y = 4
2) - 4x + 9y = 9 - - - - (i)
x - 3y = - 6 - - - - (ii)
eq. (ii) multiplied by 3
- 4x + 9y = 9 - - - - (i)
3x - 9y = - 18 - - (ii) {addition of eq. (ii) and eq. (i)}
- x + 0 = - 9
x = 9
From eq. (ii),
x - 3y = - 6
-> 9 - 3y = - 6
-> - 3y = -6-9
-> y = -15/-3
-> y = 5
So, x = 9 and y = 5
Method of Substitution1) 5x + y = 9 - - - - (i)
10x - 7y = - 18 - - - - (ii)
eq. (i)
5x + y = 9
-> y = 9 - 5x
Value of eq. (i) in eq. (ii)
10x - 7y = - 18
-> 10x - 7(9 - 5x) = - 18
-> 10x - 63 + 35x = - 18
-> 45x = - 18 + 63
-> x = 45/45
-> x = 1
From eq. (i),
5x + y = 9
-> 5 + y = 9
-> y = 9 - 5
-> y = 4
So, x = 1 and y = 4
2) - 4x + 9y = 9 - - - - (i)
x - 3y = - 6 - - - - (ii)
eq. (i)
- 4x + 9y = 9
-> - 4x = 9 - 9y
-> x = (9 - 9y) / -4
Value of eq. (i) in eq. (ii)
x - 3y = - 6
-> (9 - 9y) / -4 -3y = - 6
-> (9 - 9y + 12y) = - 6 * - 4
-> 3y = 24 - 9
-> y = 15/3
-> y = 5
From eq. (ii)
x - 3y = - 6
-> x - 3(5) = - 6
-> x - 15 = - 6
-> x = - 6 + 15
-> x = 9
So, x = 9 and y = 5
∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
hope it helped
┗━━━━━━━┛
Solve for r in the following equation:
5r - r - 9 = 15
what is the first step?
A. Use the subtraction property of equality
B. Use the addition property of equality
C. Combine like terms
What does the equation look like now?
(type your answer)
Use your answer and finish solving the equation for r.
R=____
Answers
An equation is formed of two equal expressions. The value of r in the given equation is 6.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution for the value of r in the given equation will be,
5r - r - 9 = 15
5r - r - 9 + 9 = 15 + 9
4r = 24
r = 6
A.) The first step is to Use the addition property of equality. Thus, the correct option is B.
B.) The value of r in the given equation is 6.
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11. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. n=12, x = 5, p = 0,25
A) 0.082
B) 0.091
C) 0.027
D) 0.103
Answers
Answer
D
Step-by-step explanation:
The probability of 5 successes given n = 12, x = 5, and p = 0.25 is approximately 0.082 by solving binomial probability.
The correct answer is A) 0.082.
The probability of x successes given the probability p of success on a single trial, with n trials, can be calculated using the binomial probability formula:
[tex]P(x) = (n_C_x) * p^x * (1-p)^{(n-x)[/tex]
In this case, n = 12, x = 5, and p = 0.25. Let's substitute these values into the formula:
[tex]P(5) = (12C5) * (0.25)^5 * (1-0.25)^{(12-5)[/tex]
Using the combination formula ([tex]n_C_r[/tex]) to calculate ([tex]{12}_C_5[/tex]):
[tex]P(5) = (12!)/(5!(12-5)!) * (0.25)^5 * (0.75)^7[/tex]
Simplifying the combination:
[tex]P(5) = (12!)/(5!7!) * (0.25)^5 * (0.75)^7[/tex]
Calculating the factorial terms:
[tex]P(5) = (12111098)/(54321) * (0.25)^5 * (0.75)^7[/tex]
[tex]P(5) = 792 * 0.0009765625 * 0.1334838867[/tex]
P(5) ≈ 0.082
Therefore, the probability of 5 successes given n = 12, x = 5, and p = 0.25 is approximately 0.082 by solving binomial probability.
The correct answer is A) 0.082.
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The graph shows the growth rate of a certain bacteria in a lab, where the number of bacteria depends on the number of hours since the start of the experiment.Based on the graph, what is the approximate number of bacteria after 16 hours? 6 bacteria 8 bacteria 60 bacteria 80 bacteria
Answers
The approximate number of bacteria after 16 hours is 60 bacteria ,Option C is the right answer.
What is a Function ?A function is a Mathematical statement which connects a dependent variable and an independent variable.
The graph shows the the growth rate of a certain bacteria in a lab
the number of bacteria is on the y axis and
the number of hours is on the x axis
The function is continuous ,
From the graph the approximate number of bacteria after 16 hours is
60 bacteria
Therefore Option C is the right answer.
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Please help me answer question 6/11
Answers
The value of a₄₁ mean the expression in 4th row and 1st column will be 2. Then the correct option is B.
The complete question is attached below.
What is the matrix?A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The [tex]\rm a_{ij}[/tex] element in a matrix, such as M, refers to the i-th row and j-th column element.
The matrix is given below.
[tex]\begin{bmatrix} 1&3&8&5&\\ 5&4&6&2\\6&7&1&8\\2&9&3&7&\\\end{bmatrix}[/tex]
Then the value of a₄₁ mean the expression in 4th row and 1st column will be 2.
Then the correct option is B.
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