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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Find the length of x. Assume the triangles are similar.
Triangles are similar and only differ in size meaning they are dilated
So first we have to find the scale factor of dilation (by how much the smaller triangle got bigger)
Find scale factor:
2.4a=4.8
z=2
Find x:
we multiply the original side of the small side with the scale factor of 2
2.8(2)=x
5.6=x
So, x=5.6
work out the equation of the line
Step-by-step explanation:
Hi there!
According to the question;
The gradient of line is 1/2 and passes through the point (4,-2).
Since, It has one point and gradient we use one point formula to find the equation of the line.
Note:
One point formula: (y-y1) = m (x-x1)
(4,-2) = (x1,y1)
So, using this formula we get;
(y+2) = 1/2(x-4)
Multiply both sides by 2.
2(y+2) = (1/2)*2(x-4)
2y+4 = x-4
Take 2y+4 in right side
0 = x-4 - (2y+4)
Therefore, x-2y-8 = 0 is the required equation.
Hope it helps!
Hi there!
We're given the following information:
Slope (gradient) = ¹/₂Point = (4,2)With this information, we can go ahead and plug the data into the point slope equation: y - y₁ = m(x - x₁).
Plug in 1/2 for m, and (4,2) for x1 and y1:
[tex]\sf{y-y_1=m(x-x_1)}[/tex]
[tex]\sf{y-(-2)=\dfrac{1}{2}(x-4)}[/tex]
[tex]\sf{y+2=\dfrac{1}{2}(x-4)}[/tex]
[tex]\sf{y+2=\dfrac{1}{2}x-2}\\\sf{y=\dfrac{1}{2}x-2-2}\\\\\sf{y=\dfrac{1}{2}x-4}[/tex]
Hence, y = 1/2x - 4.
I hope that helps! :)
f (x) = √x + 9 what is the domain?
Answer:
Step-by-step explanation:
Given: ABC with AD | CB Prove: m/1 + m/3 + m/2 = 180, by putting the reasons in the correct order. A 3 Z C 5 8 Given : AABC with AD | CB Prove : m / 1 + m / 3 + m / 2 = 180 , by putting the reasons in the correct order .
Answer:
98798765
Step-by-step explanation:
67654678765
Which graph shows the solution to the system of linear inequalities? Edge.
x + 3y > 6
y ≥ 2x + 4
A system of inequalities can be solved graphically.
See attachment for the required graph
The inequalities are given as
[tex]x + 3y > 6\\y \geq 2x + 4[/tex]
The options are not given.
So, I have attached the graph that illustrates the solution to the system of inequalities.
What is the inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
From the graph, we have the solutions as
[tex]x > -0.857[/tex]
[tex]y\geq 2.276[/tex]
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F(x)=-x^2+3 find(-2)
Answer:
F(-2) = 7
Step-by-step explanation:
Finding a specific point on a function given the x position can be done by substituting x in the function for the given number, then solving said function. The value on the right side of the function is the y position.
For this specific function [F(x) = x² + 3], substitute x for -2.
F(-2) = (2)² + 3
Next, solve the equation.
F(-2) = 4 + 3
F(-2) = 7
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Required answer: f(2) = -1
Detailed explanation:
To find f(-2), we will substitute -2 for x in the function:
[tex]\bf{f(x)=-x^2+3}[/tex]
[tex]\bf{f(-2)=-(-2)^2+3}[/tex]
[tex]\bf{f(-2)=-4+3}[/tex]
[tex]\bf{f(-2)=-1}[/tex]
[tex]\hrulefill[/tex]
Have a wonderful day!
the sum of a certain number and -3
Answer:
[tex]\huge\boxed{\sf x - 3 }[/tex]
Step-by-step explanation:
Let the certain number be x
So,
Given condition:Sum is to add so we'll use the sign +
= x + (-3)
We know that + and - makes - because - sign will flip the + sign and make it negative, So:
= x - 3
[tex]\rule[225]{225}{2}[/tex]
Solution: c-3
[tex]\searrow[/tex]
Detailed explanation:
[tex]\searrow[/tex]
This problem tells us to convert the verbal phrase (in words) "the sum of a certain number and -3" into an algebraic expression, which is written in numbers.
Let's start by taking a look at our problem.
"the sum of a certain number and -3". We can first write this "certain number" as one letter (any letter you want). Let it be c.
Our expression already looks a little easier: "the sum of c and -3".
Now, the word "sum" tells us to add. So we should add c and -3.
[tex]--\mapsto\boldsymbol{c+-3}[/tex]
Which is the exact same thing as [tex]\boldsymbol{c-3}[/tex].
Voila! There's our answer.
Cheers!! ^-^______________________
Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
_______________________
Belfast Giants have played 5 matches and the mean number of goals scored is 3
When they play the 6th match, the mean increases to 4.
Answer:
2 goals
Step-by-step explanation:
After 5 games the team scored 1.8*5=91.8∗5=9 goals.
After 6 games the team scored 9+3=129+3=12 goals.
The mean after 6 games is \frac{12}{6}=2
6
12
=2 goals.
Find the value of x. Round to the
nearest tenth.
12
x=[?]
Answer:
17.1
Step-by-step explanation:
Given we have one side and one degree, we can use the trigonometric function "tangent" to solve this right triangle.
Remember that tangent is opposite side over adjacent side, so lets set up the equation:
[tex]tan(35)=\frac{12}{x}[/tex]
Now solve:
[tex]x(tan(35))=12\\x=\frac{12}{tan(35)}[/tex]
As a result, x is equal to approximately 17.1
Any questions feel free to ask :)
Consider this liner function: y=-2x-5
Where would you plot the ordered pairs for the values in the domain?
D: {-6, -5, -2, 0, 1}
The graph of the linear function, considering the points in the domain, is given at the end of the answer.
What is the linear function?
The linear function is defined by:
y = -2x - 5.
Considering the domain, the points are given as follows:
A: x = -6, y = -2(-6) - 5 = 7.B: x = -5, y = -2(-5) - 5 = 5.C: x = -2, y = -2(-2) - 5 = -1.D: x = 0, y = -2(0) - 5 = -5.E: x = 1, y = -2(1) - 5 = -7.More can be learned about linear functions at https://brainly.com/question/24808124
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W+15x-9y+2z
Terms:
Coefficients:
In the problem given:
W + 15x - 9y + 2z
The term are single mathematical expressions that separate values.
In the expression, there is a + and -; these concludes 2 terms.
There are 3 coefficients next to each variable.
The coefficients are 15x, -9y, and 2z.
That means there are 3 coefficients.
Cheers
- ROR
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex] \sf{W \rightarrow coefficient = 1} [/tex][tex] \sf{15x \rightarrow coefficient = 15} [/tex][tex] \sf{-9y\rightarrow coefficient = -9} [/tex][tex] \sf{2z\rightarrow coefficient = 2} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Term refers to each variable or constant separated by a mathematical operator.
Coefficient refers to the numberic part of variable or a constant number present in an expression.
[tex]\qquad \tt \rightarrow \: 12a - 10b + 6[/tex]
[tex] \large\textsf{Terms :} [/tex]
[tex] \texttt{W } [/tex][tex] \texttt{coefficient = 1} [/tex]
[tex] \texttt{15x} [/tex][tex] \texttt{coefficient = 15} [/tex]
[tex] \texttt{-9y} [/tex][tex] \texttt{coefficient = -9} [/tex]
[tex] \texttt{ 2z} [/tex][tex] \texttt{coefficient= 2} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Imagina that the cook is using a potato-chopping machine instead of a knife, allowing him to chop a maximum of 120 potatoes instead of 100. Which is the best estimate of the number of hamburgers he could cook if he chopped 100 potatoes with the machine
The number of hamburgers he could cook is 14 if he chopped 100 potatoes with the machine option (B) is correct.
What is the graph of the best estimate?A mathematical notion called the graph of the best estimate connects points spread throughout a graph.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have shown a graph in the picture that shows the number of hamburgers cooked versus the number of potatoes chopped.
As we can see in the graph,
Number of potatoes chopped = 80
number of hamburgers cooked = 30
Number of potatoes chopped = 90
number of hamburgers cooked = 20
Number of potatoes chopped = 95
number of hamburgers cooked = 10
Number of potatoes chopped = 100
number of hamburgers cooked = 14 (best estimate)
Thus, the number of hamburgers he could cook is 14 if he chopped 100 potatoes with the machine option (B) is correct.
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Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3
Help me please
Answer:
y-2=1/3(x-3)
Step-by-step explanation:
please mark me as brainlest
Answer: y-2=1/3(x-3), which is Choice [B]
Step-by-step explanation:
Hii, do you need to know the answer to your question? No problem! (:
First, do you remember what the "point-slope" formula is? It's
y-y1=m(x-x1)
Now it's just a matter of sticking in the known values.
y-2=1/3(x-3)
Voila! There's our solution, cheers! (:
--
Hope that this helped! Best wishes.
[tex]\bigstar\underbrace[/tex]
17/21 - (2/7 + 1/7)
Please solve!!
Answer:
8/21
Step-by-step explanation:
17/21 - (2/7 + 1/7)
= 17/21 - ( 3/7)
= 17/21 - (3×3/7×3)
= 17/21 - 9/21
= 8/21
Will a stand that hold up to 40 pounds support a 21-kilograms television? Explain used 2.2 Lb = kg
Answer: No, the stand will not support the TV. It is too heavy.
Work Shown:
1 kg = 2.2 lbs approximately
21*1 kg = 21*2.2 lbs
21 kg = 46.2 lbs
A 21 kilogram tv is roughly equivalent to 46.2 pounds.
This exceeds the 40 pound weight limit, so this stand will not support it.
Answer: No
Step-by-step explanation:
Weight limit = 40 Lb
Weight given = 21 kg
Conversion factor
2.2 Lb = 1 kg
2.2 x 21 = 46.2
46.2 Lb = 21 kg
46.2 > 40, the stand cannot support the TV
Give ur answer in standard form.
3 x 10^4 ÷6 x 10^-4
Answer:
5.0×10⁷
Step-by-step explanation:
(3÷6)×(10⁴÷10^-4)
(0.5)×(10⁸)
5.0×10^-1×10⁸
5.0×10⁷
[tex] \frac{3 \times {10}^{4} }{6 \times {10}^{ - 4} } \\ \\ \frac{1 \times {10}^{4 - ( - 4)} }{2 } \\ \\ \frac{ 1 \times {10}^{4 + 4} }{2} \\ \\ \frac{1 \times {10}^{8} }{2} \\ \\ 0.5 \times {10}^{8} .[/tex]
What is the line that has a slope of -2/3 and passes through point -3,-1?
Answer:
y = (- 2/3)x - 3
Step-by-step explanation:
y = mx + c
y = (- 2/3)x + c
Now let's substitute the values (-3,-1)- 1 = (- 2/3)(-3) + c
-1 = 2 + c
c = - 3
Therefore,
y = (-2/3)x - 3
Answer:
y = -2/3x - 3
Step-by-step explanation:
y = mx + b
y = y coordinate → given: - 1
m = slope → given: - 2/3
x = x coordinate → given: - 3
b = y intercept → need to find
y = -2/3x + b → -1 = -2/3(-3) + b
-1 = 2 + b
subtract 2 from both sides
-1 - 2 = 2 - 2 + b
-3 = b
y = -2/3x - 3
A survey found that 50% of teenagers prefer to watch a movie at a theater over other viewing options. You want to know the estimated probability that three out of four randomly chosen teenagers do not prefer watching a movie at a theater. How could you design a simulation for this situation?
Answer:
7m tall convert this into imperial measurement
There are 7 pieces of pie left over in the cafeteria. If 4 pieces are apple and 3
are cherry, what fraction of the remaining pieces are apple?
Which congruence theorem can be used to prove ?
Answer:
ASA
Step-by-step explanation:
by ASA congruence theorem
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 14°52'. When the boat stops, the angle of depression is 45°10'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.
The boat's travel from when it was first noticed until it stopped is 554.89 ft.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly.
From the given information we can draw a right-angle triangle.
14°52' = 14 + 0.86 = 14.86 degree
45°10' = 45 + 0.16 = 45.16 degree
In the right-angle triangle ACD
tan14.86 = 200/AC
AC = 753.772 ft
In the right-angle triangle DBC:
tan45.16 = 200/CB
CB = 198.886 ft
AB = AC - CB
AB = 753.772 ft - 198.886 ft
AB = 554.886 ≈ 554.89 ft
Thus, the boat's travel from when it was first noticed until it stopped is 554.89 ft.
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In a spelling bee $50\%$ of the students were eliminated after the first round. Only $\frac{1}{3}$ of the remaining students were still in the contest after the second round. If 24 students were still in the contest after the second round, how many students began the contest
There were 144 students when the contest began
What is Equation ?Equation is formed when an algebraic expression is equated by a constant or another algebraic expression.
On the basis of given data :
Let the total number of students are x
50% of the students are eliminated after the first round
the remaining students are 0.5x
After the second round = (1/3) * 0.5 x were remaining
and
(1/3) * 0.5 x = 24
then solving this equation will give the total number of students
0.5x = 24 * 3
x = 24*3 /0.5 = 144
Therefore there were 144 students when the contest began
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What is the image of (-9,3)(−9,3) after a reflection over the y-axis?
Answer:
(9, 3 )
Step-by-step explanation:
under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
(- 9, 3 ) → (9, 3 )
The table shows the probability of how a certain score will
compare to a listed score on a popular video game. Use the
probability distribution to find the variance, o².
The variance of the probability distribution is 400
The Variables of X and their Probability Distribution.
To find Variance, first we should find out Mean and then Variance
The expected value of a discrete random variable X, symbolized as E(X), is often referred to as the long-term average or mean (symbolized as μ)
The variance of a probability distribution is symbolized as σ2. To find the variance σ2 of a discrete probability distribution, find each deviation from its expected value, square it, multiply it by its probability, and add the products.
Step – 1: Calculation of Mean Step – 2: Calculation of Standard Deviation= σ2=∑(x−μ)²P(x)
Mean = X * P(X) Variance = Sum of (X – Mean)²*P(X)
X P(X) X*P(X)
-50 0.029 -1.45
-30 0.121 -3.63
-10 0.210 -2.1
10 0.485 4.85
30 0.145 4.35
50 0.010 0.5
Mean 2.52
X P(X) X - Mean (X – Mean)² (X – Mean)²*P(X)
-50 0.029 -52.52 2758.35 79.99216
-30 0.121 -32.52 1057.55 127.9636
-10 0.210 -12.52 156.7504 32.91758
10 0.485 7.48 55.950 27.13594
30 0.145 27.48 755.1504 109.4968
50 0.019 47.48 2254.35 22.5435
Variance=400.00
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Select the correct answer.
Which function is the inverse of ?
Answer:
B. [tex]f^{-1}(x) = \frac{x + 3}{9}[/tex]
Step-by-step explanation:
[tex]let \space\ y = f(x)\\\\y = 9x -3\\[/tex]
• Now make x the subject of the equation:
[tex]9x = y + 3\\\\x = \frac{y + 3}{9} \\[/tex]
• Replace x with f⁻¹(x) and y with x:
[tex]f^{-1}(x) = \frac{x + 3}{9}[/tex]
how can i soolve it?
Answer:
x = 4 y = 1
Step-by-step explanation:
Opposite sides are equal , so
2x-3y = 5
x+5y =9 <====== multiply this by -2 and add to first equation
-13y = -13
then y = 1 and x + 5y = 9 so x = 4
What is the GCF of the numbers in the expression (32 + 16)?
Answer:
the GCF of the number in the given expression (32+16) is 16.
Step-by-step explanation:
This is your answer
The mass of Jupiter is 1.898x10^27 kg, while the mass of Earth is 5.972x10^24 kg. How many times greater is the mass of Jupiter compared to the mass of the Earth? Round the answer in standard form to the nearest whole number.
Answer:
318
Step-by-step explanation:
(1.898×10^27)÷(5.972×10^24)=317.82=318
Absolute value of (-1, -3/7)
The absolute value of -1 is 1 and -3/7 is 3/7.
We have given that,
(-1, -3/7)
We have to determine the absolute value of (-1, -3/7)
What is the absolute value?The absolute value or modulus of a real number x denoted |x|, is the non-negative value of x without regard to its sign. Namely, [tex]{\displaystyle |x|=x}[/tex]if x is a positive number, and [tex]{\displaystyle |x|=-x}[/tex] if x is negative, and[tex]{\displaystyle |0|=0}[/tex].
Therefore the absolute value of -1 is 1 and -3/7 is 3/7.
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What is the value of k?
Answer:
The value of K in free space is 9 × 109
Step-by-step explanation:
