The unit vector has a magnitude = 1
So, for the given vectors, we will find the magnitude of every vector
[tex]\begin{gathered} u=<\frac{\sqrt[]{3}}{2},-\frac{1}{2}> \\ |u|=\sqrt[]{(\frac{\sqrt[]{3}}{2})^2+(-\frac{1}{2})^2}=\sqrt[]{\frac{3}{4}+\frac{1}{4}}=\sqrt[]{\frac{4}{4}}=\sqrt[]{1}=1 \end{gathered}[/tex]So, it is a unit vector
[tex]\begin{gathered} u=<-\frac{2}{\sqrt[]{5}},\frac{1}{\sqrt[]{5}}> \\ |u|=\sqrt[]{(-\frac{2}{\sqrt[]{5}})^2+(\frac{1}{\sqrt[]{5}})^2}=\sqrt[]{\frac{4}{5}+\frac{1}{5}}=\sqrt[]{\frac{5}{5}}=1 \end{gathered}[/tex]So, it is a unit vector
[tex]\begin{gathered} u=<1,1> \\ |u|=\sqrt[]{1^2+1^2}=\sqrt[]{1+1}=\sqrt[]{2}=1.414 \end{gathered}[/tex]So, it is not a unit vector
[tex]\begin{gathered} u=<-\frac{5}{\sqrt[]{6}},\frac{1}{\sqrt[]{6}}> \\ |u|=\sqrt[]{(-\frac{5}{\sqrt[]{6}})^2+(\frac{1}{\sqrt[]{6}})^2}=\sqrt[]{\frac{25}{6}+\frac{1}{6}}=\sqrt[]{\frac{26}{6}}=2.08 \end{gathered}[/tex]So, it is not a unit vector
So, the correct options are: 1 and 2
pls answer!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: -49
Step-by-step explanation: 7 x 7 = 49, but since it has the (-) symbol it will be -49.
Question 1-4
Rectangle ABCD is dilated into rectangle AB'C'D', as shown.
B'
B
A
3
6
C
2
D
C'
D'
What is the scale factor of dilation? Enter the answer as a whole number or a simplified fraction in the box. Use "/" for the fraction bar.
Estimate by rounding each number to the nearest ten. Then find the difference.32.76 - 22.168An estimation of the difference isThe exact difference is
ANSWER
EXPLANATION
First let us find the actual difference:
32.76 -
if one face of a cubr has a area of 6.75 square inches, what is the surface of the entire cube.
The surface area of the entire cube is 40.5 square inches
Here, we want to get the surface area of a cube given the measure of the area of one of the faces
Looking at the net of a cube, we can identify six identical and equal-dimension faces
So to get the total surface area of the cube, we have to multiply the surface area of one of the faces by 6
Mathematically, that would be;
[tex]6.75\text{ }\times\text{ 6 = 40.5}[/tex]Identify all pairs of congruent corresponding parts. Then write another congruence statement for the triangles.
..
SOLUTION
[tex]\begin{gathered} \Delta FED\cong\Delta CBA \\ \angle F\cong\angle C \end{gathered}[/tex][tex]\begin{gathered} \Delta EFD\cong BCA \\ \angle E\cong\angle B \\ \bar{DE}\cong\bar{AB} \end{gathered}[/tex][tex]\begin{gathered} \bar{EF}=\bar{BC} \\ \angle D=\angle A \\ \bar{DF}=\bar{AC} \end{gathered}[/tex]box with a square base and open top must have a volume of 171500c * m ^ 3 . We wish to find the imensions of the box that minimize the amount of material used.
step 1
Find out the equation of the volume of the box
[tex]\begin{gathered} V=x^2h \\ V=171,500\text{ cm}^3 \\ 171,500=x^2h \\ h=\frac{171,500}{x^2} \end{gathered}[/tex]step 2
Find out the expression for the surface area
The surface area is given by the expression
[tex]A=x^2+4xh[/tex]substitute the value of h
[tex]\begin{gathered} A=x^2+4x\frac{171,500}{x^2} \\ simplify \\ A(x)=x^2+\frac{686,000}{x} \\ \\ A(x)=\frac{x^3+686,000}{x} \end{gathered}[/tex]step 3
Find out the derivative A'(x)
[tex]A^{\prime}(x)=2x-\frac{686,000}{x^2}[/tex]step 4
Equate the derivative to zero
[tex]\begin{gathered} 2x-\frac{686,000}{x^2}=0 \\ 2x=\frac{686,000}{x^2} \\ \\ 2x^3=686,000 \\ x^3=343,000 \\ x=70 \end{gathered}[/tex]A'(x)=0 when x=70step 5
Find out the second derivative A''(x)
[tex]A^{\prime}^{\prime}(x)=2+\frac{1,372,000}{x^3}[/tex]Evaluate the second derivative for x=70
[tex]\begin{gathered} A^{\prime}^{\prime}(x)=2+\frac{1,372,000}{(70)^3} \\ A^{\prime}^{\prime}(x)\text{ is positive} \\ that\text{ means} \\ The\text{ value of A\lparen x\rparen i}s\text{ a maximum for x=70 cm} \end{gathered}[/tex]There is one number that is neither crossed out nor circled. Why is it treated differently?
r is the character which is not treated
Marbel surveyed 55 people to find out their favorite types of music the results shown in the bar graph
To find the correct option, we need to find, first, the rate of the population that chose each type of music. Then, when we sum the rates of the types in the correct answer, it should result in 40%.
The rate of population for each type of music is given by the number of peaple that chose this type, divided by the total amount of people (55):
Country: 15/55
Jazz: 12/55
Opera: 10/55
Roch: 18/55
In the first option, we have:
Country and Opera
4. (02.05 MC)
Which statement is true if the quantity demanded of a good decreases by 10% while consumer incomes increase by 2 %? (5 points)
O The income elasticity of demand is -20, and the good is inferior.
The income elasticity of demand is -5, and the good is inferior.
The income elasticity of demand is 0.2, and the good is normal.
The income elasticity of demand is 5, and the good is inferior.
The income elasticity of demand is 20, and the good is normal.
Based on the decrease in the quantity demanded and the increase in income, the true statement is The income elasticity of demand is -5, and the good is inferior.
How to find the income elasticity?The income elasticity of a good can be found by the formula:
= Change in quantity demanded / Change in income
= -10% / 2%
= - 5
When the income elasticity of demand for a good is negative, it means that it is an inferior good. This is because people only buy them because its what they can afford but if income rises, people stop buying them.
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Please help me with this problem Let f(x)=25x2−2. The function g(x) is a vertical stretch of f(x) by a factor of 2. What is the equation of g(x)? Enter your answer in the box. g(x) =
Solution
Given the function below
[tex]f(x)=\frac{2}{5}x^2-2[/tex]The function g(x) is a vertical stretch of f(x) by a factor of 2, i.e
[tex]\begin{gathered} g(x)=2(\frac{2}{5}x^2-2) \\ g(x)=\frac{4}{5}x^2-4 \end{gathered}[/tex]Hence, the equation of g(x) is
[tex]g(x)=\frac{4}{5}x^2-4[/tex]Draw a model to show a 26-pack of candy bars divided equally among 7 people. Howmany candy bars will each person have?
The diagram would be:
To find how many candy bars each person will get we divide 26 by 7:
[tex]\frac{26}{7}=3\frac{5}{7}[/tex]Therefore each person will get 3 5/7 of candy bar (appoximately 3.71 candy bars)
Which of the following equations below is a linear inequality?
Inequality occurs when a non-equal comparison is made between two mathematical expressions or two numbers.
Linear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another algebraic expression of degree less than or equal to 1.
Of the options, the only one that represents a linear inequality is:
[tex]yThe FIRST OPTION is correct.the first answer is correct
Find the missing value. X 5 3 3 6 equal
Similar triangles
The image provided with the question shows 3 similar triangles. The lines of length a, m, and 5 are parallel, so the lengths are proportional
The proportionality can be written as:
[tex]\frac{3}{2}=\frac{3+6}{2+4}=\frac{3+6+3}{x+4+2}[/tex]Operating:
[tex]\frac{3}{2}=\frac{9}{6}=\frac{12}{x+6}[/tex]The first two parts of the equalities are the same fraction (when simplified). We can use the last and the first one to find x:
[tex]\frac{3}{2}=\frac{12}{x+6}[/tex]Cross-multiplying:
3(x + 6) = 2*12
Dividing by 3:
x + 6 = 8
Subtracting 6:
x = 2
A C, С B, AC = 10 BC = 15 What is the length of AB? Round your answer to the nearest tenth, if necessary. Figure is not drawn to scale
You have a right triangle and the length of the legs, use Pythaorean theorem to find the length of the hypotenuse (AB)
[tex]\begin{gathered} AB^2=AC^2+BC^2 \\ \\ AB=\sqrt[]{AC^2+BC^2} \\ AB=\sqrt[]{10^2+15^2} \\ AB=\sqrt[]{100+225} \\ AB=\sqrt[]{325} \\ AB=18 \end{gathered}[/tex]Then, the length of AB is 18This is a two part question just need help figuring out what exactly it is I need to mark up for the first section up on top and also on the second part of it I need help figuring out if both triangles are congruent and if they are need help stating the congruency
Given the triangles CDE and JLM
For the triangles we have the following:
1) CD = JL
2) CE = JM
3) DE = LM
So, there 3 pairs of congruent sides
So, the triangles are congrurent by S.S.S ( Side-Side-Side) postulate
C is corresponding to J
D is corresponding to L
E is corresponding to M
So,
[tex]\triangle\text{CDE}\cong\triangle\text{JLM}[/tex]For marking the triangles, see the following figure:
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x
Answer:
Step-by-step explanation:
The statements below represent some possible deposits and withdrawals from Rachel's bank account Match each statement with the total amount that Rachel's account would change. -47.50 -22.50 22.50 She deposits $35 to her account. Then spends $12.50 from her account on lunch. She withdraws $35 from her account. Then spends $12.50 from her account on lunch. She spends $35 from her account on clothes. Then she deposits $12.50 to her account 17 Pause Previous
ok, If she did not initially have anything on the account, this is the process
[tex]\begin{gathered} +35 \\ -12.5 \\ -35 \\ -12.50 \\ -35 \\ +12.50 \\ -------- \\ -47.50 \end{gathered}[/tex]his bank account is at -47.50 dollars
A student argued that a pizza cut into 12 pieces was more than a pizza cut into 6 pieces. How would you respond?
Answer:
i say a pizza with six has more for less people but twelve is for more people so equally they are both a lot.
Step-by-step explanation:
In a bag of Jolly Ranchers, the ratio of blue to red is 3 to 4. If I have a TOTAL of 56 Jolly Ranchers, how many of them are blue?
Answer:
24
Step-by-step explanation:
If ratio of blue to red is 3:4 or in fraction terms 3/4 then the ratio of blue to all Jolly ranchers = 3/(3+4) = 3/7
Since there are a total of 56, the number of blue ones = 56 x 3/7 = 24
Answer:
24
Step-by-step explanation:
Based on the given conditions, formulate: 56 x 3 divided by (3 + 4)
Calculate the product or quotient: 168/3+4
Calculate the sum or difference:168/7
Cross out the common factor:24
get the result:24
Answer: 24
I need help with something
Answer:
S'(-2, 6)
Explanation:
Translating a point to the right, meaning adding to the x-coordinate
For f(x) = -6x-2, find the rate of change on the interval [-2, 4].
The most appropriate choice for rate of change will be given by -
Rate of change of f(x) = -6x -2 on the interval [-2, 4] = -6
What is rate of change of a function?
Rate of change of a function represents the rate at which the value of one quantity changes with change in the value of other quantity.
Here,
f(x) = -6x - 2
[tex]f^{'} (x) = \frac{d}{dx}(-6x - 2)\\[/tex]
[tex]= -6[/tex]
[tex]f^{'} (x)[/tex] represents rate of change
Rate of change of f(x) = -6x -2 on the interval [-2, 4] = -6
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Pls help with this problem
Answer:
[tex] \frac{5}{24} [/tex]
Step-by-step explanation:
5/24 * 3 = 15/24 that can be reduced to 5/8
Answer: 5/24
Step-by-step explanation:
5/8 devided by 3
3 turns into 1/3
5/8 X 1/3 =5/24
Consider functions f and g.
The correct option regarding the multiplication of the functions f(x) and g(x) is given by:
C. [tex](f \times g)(x) = \frac{x^2 + 6x + 8}{x^2 + 2x - 15}, x \neq -5, x \neq 3[/tex]
Multiplication of functionsTo multiply two rational functions, we multiply the numerators of each function and the denominator of each function to generate the rational functions.
In the context of this problem, before multiplying the functions, we can simplify them.
Function f(x) is given by:
[tex]f(x) = \frac{x^2 - 16}{x^2 + 3x - 10}[/tex]
The numerator and the denominator can be simplified as follows:
Numerator: (x + 4)(x - 4): applying subtraction of perfect squares.Denominator: (x + 5)(x - 2): due to it's roots.Function g(x) is given by:
[tex]g(x) = \frac{x^2 - 4}{x^2 - 7x + 12}[/tex]
The numerator and the denominator can be simplified as follows:
Numerator: (x + 2)(x - 2): applying subtraction of perfect squares.Denominator: (x - 3)(x - 4): due to it's roots.Then the multiplication function is:
[tex](f \times g)(x) = \frac{(x + 4)(x - 4)}{(x + 5)(x - 2)} \times \frac{(x + 2)(x - 2)}{(x - 3)(x - 4)}[/tex]
The common terms (x - 4) and (x - 2) are simplified, hence the function is given by:
[tex](f \times g)(x) = \frac{x + 4}{x + 5} \times \frac{x + 2}{x - 3} = \frac{x^2 + 6x + 8}{x^2 + 2x - 15}[/tex]
Hence option C is correct, with x = -5 and x = 3 being removed from the function due to the fact that they are the zeros of the denominator.
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is this relation a function ? yes or noif no , identify two ordered pairs as proof.
A relation is said to be a function when each input value is related to only one output.
It can also be said that a function is a relation that has only output for any unique input.
In a function, each x-value is related to only one output.
From the relation given here, we have a straight-line graph. Here, each x-value is related to only one y-value.
Since each x-value is related to only one y-value, this relation is a function.
ANSWER:
Yes, this relation is function.
Hi guys.I was sick today and I’m still not feeling good.I missed out on class and I’ll be giving 25 points to whoever helps me.Thank you
Answer:
x = 11
Step-by-step explanation:
(9x - 5) + (6x + 20) = 180
15x + 15 = 180
15x + 15 -15 = 180 -15
15x = 165
15x/15 = 165/15
x = 11
76 cm57 cmWhat is the length of the hypotenuse?C=centimeters
Using pythagoras Theory which is:
(Hypotenuse)^2 = (opposite)^2 + (Adjacent)^2
C^2 = 76^2 + 57^2
C^2 = 7776 + 3249
C^2 = 11025
C = SQUAREROOT(11025)
C = 105cm
g(x)=3x^2-4 if the graph of g is translated vertically upward by 7 units it becomes the graph of a function f. Find the expression for f(x).
The expression for f(x) when moving the graph vertically up by 7 units is f(x)=3x²- 6/2.3.
What are expressions?An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) You can think of expressions as being similar to phrases. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.So, the expression for f(x):
We have, g(x)=3x²-4Moving the graph upwards by 7 units vertically, we get the expression for f(x) as:
f(x)=3x²- 6/2.3(Refer to the graph attached below)
Therefore, the expression for f(x) when moving the graph vertically up by 7 units is f(x)=3x²- 6/2.3.
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Enter the equation of the circle with the given center and radlus. Center: (0,5); radius: 8 The equation of the circle is
The equation of the circle with the given data is given as,
where,
[tex]centeris(x_1,y_1\text{) and radius is r}[/tex][tex]\begin{gathered} (x-x_1)^2+(y-y_1)^2=r^2 \\ (x-0)^2+(y-5)^2=8^2 \\ x^2+(y-5)^2=64 \end{gathered}[/tex]On Tuesday d dollars worth of merchandise was sold. On Wednesday the amount of merchandise sold was $150 less than twice the amount of merchandise sold on Tuesday
Answer:
2d-150
Explanation:
The worth of Merchandise sold on Tuesday = d dollars.
On Wednesday the amount of merchandise sold was $150 less than twice the amount of merchandise sold on Tuesday .
• Twice the amount of merchandise sold on Tuesday = 2d
,• 150 less than 2d = 2d-150.
An expression for the amount of merchandise sold on Wednesday is:
[tex]2d-150[/tex]The third option is correct.
What is the sum of the polynomials?(8x2-9y2-4x)+(x2-3y2–7x)7x2 - 6y2 + 3x9x2 - 6y2+3x9x2 - 12y2 + 3x9x2 - 12/2 - 11x
Let's simplify the following expression:
[tex]\text{ (8x}^2-9y^2-4x)+(x^2-3y^2-7x)[/tex]We get,
[tex]\text{ (8x}^2-9y^2-4x)+(x^2-3y^2-7x)[/tex][tex]\text{ 8x}^2-9y^2-4x+x^2-3y^2-7x[/tex]Let's put like terms beside each other and proceed with the operation:
[tex]\text{ 8x}^2-9y^2-4x+x^2-3y^2-7x[/tex][tex]\text{ 8x}^2+x^2-9y^2-3y^2-7x-4x[/tex][tex]\text{ (8x}^2+x^2)+(-9y^2-3y^2)+(-7x-4x)[/tex][tex]\text{ (9x}^2^{})+(-12y^2)+(-11x)[/tex][tex]\text{ 9x}^2-12y^2-11x[/tex]Therefore, the sum of the given polynomials (8x^2-9y^2-4x)+(x^2-3y^2–7x) is 9x^2 - 12y^2 - 11x.
The answer is letter D.
