Answer:
θ = 53.1° (to the nearest tenth)
Step-by-step explanation:
FORMULA :
Let θ be the measure of the angle between U and V :
[tex]\cos \theta =\frac{\overrightarrow{U} .\overrightarrow{V} }{\left\Vert \overrightarrow{U} \right\Vert \times \left\Vert \overrightarrow{V} \right\Vert }[/tex]
========================
[tex]\overrightarrow{U} \times \overrightarrow{V} =6\times 2+\left( -3\right) \times 1=9[/tex]
[tex]\left\Vert \overrightarrow{U} \right\Vert =\sqrt{6^{2}+\left( -3\right)^{2} } =\sqrt{45} =3\sqrt{5}[/tex]
[tex]\left\Vert \overrightarrow{U} \right\Vert =\sqrt{2^{2}+\left( 1\right)^{2} } =\sqrt{5}[/tex]
[tex]\left\Vert \overrightarrow{U} \right\Vert \times \left\Vert \overrightarrow{V} \right\Vert =3\sqrt{5} \times \sqrt{5} = 15[/tex]
…………………………………………………
Then
[tex]\cos \theta =\frac{9}{15} =\frac{3}{5}[/tex]
[tex]\theta =\cos^{-1} \left( \frac{3}{5} \right) =53.130102354156[/tex]
3. Eden has completed 7⅝ laps of a 10 lap race How many more laps does she still need to run?
eden must run 2 3/8 laps to complete the race.
How to calculate the laps that Eden is missing?To calculate the laps that Eden is missing, we must perform the following operation:
We must take into account that he has already completed 7 laps and a segment of the eighth lap that is equivalent to 5/8, that is to say that he has 3/8 to complete the eighth lap.
On the other hand, once he completes the eighth lap, he will have 2 full laps left to finish the race. Due to the above, it can be stated that it is missing 2 3/8 laps.
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Tran is solving the quadratic equation 2x2 – 4x – 3 = 0 by completing the square. His first four steps are shown in the table.
A table listing the first few steps in deriving the quadratic formula
In which step did Tran first make an error?
The solution to the quadratic equation 2x² - 4x - 3 = 0 is x = 1 ± √2.5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Solving the polynomial using completing the square:
2x² - 4x - 3 = 0
First divide through by 2:
x² - 2x - 3/2 = 0
add 3/2 to both sides:
x² - 2x - 3/2 + 3/2 = 0 + 3/2
x² - 2x = 3/2
add the square of half the coefficient x to both sides:
x² - 2x + 1 = 3/2 + 1
(x - 1)² = 2.5
taking square root:
x - 1 = ±√2.5
x = 1 ± √2.5
The solution to the quadratic equation 2x² - 4x - 3 = 0 is x = 1 ± √2.5
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Answer: Step 3
Step-by-step explanation: this is the right answer on the edge, hope this helps!
A translation maps A(1,2) onto A'(-1,3). What are the coordinates of the image of the origin under the same translation?
Using translation concepts, it is found that the coordinates of the image of the origin under the same translation are given by:
3. (-2,1).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
A translation maps A(1,2) onto A'(-1,3), hence the rule is given by:
(x,y) -> (x - 2, y + 1).
Then the image of the origin (0,0) is given by:
(0,0) -> (0 - 2, 0 + 1) = (-2,1)
Which means that option 3 is correct.
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According to the line of best fit, about how many words would a person remember after being distracted by 7 text messages? 4 5 6 7
Using the line of best fit, it is found that a person would remember 5 words after being distracted by 7 text messages.
What does the line of best fit states?Researching the problem on the internet, it is found that it states that the number of words a person remembers after being distracted by x text messages is given by a linear function.
Looking at the line, it is found that when x = 7, N(x) = 5, hence a person would remember 5 words after being distracted by 7 text messages.
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Which of the following is most likely the next step in the series?
Answer:
A
Step-by-step explanation:
has more arrows coming out
the reason it's not D is because it is going in a red-blue pattern not red-red
hope that helps :)
Answer:
A
Step-by-step explanation:
red blue red ??? and 1 arrow, 3 arrows, 5 arrows so next is blue 7 arrows
Expand.
Your answer should be a polynomial in standard form. WILL GIVE BRAINLIEST AND BIG POINTS
Answer:
-q^2-q+72
Step-by-step explanation:
We can use the FOIL (First Outer Inner Last) method for this. First, multiply 9*8 (72). Then, multiply 9*-q(-9q). After that, multiply q*8 (8q). Finally, multiply q*-q(-q^2). Arrange the different terms:
-q^2-9q+8q+72
Finally, combine like terms:
-q^2-q+72
Hope this helps!
Suppose you and your friends form a band and you want to record a demo. Studio A rents for $75 plus $75 an hour and Studio B
rents for $150 and $50 an hour. Let t= the number of hours and c = cost.
Part A
Write a system of equations to represent the cost at each studio.
Part B
Solve the system of equations from Part A. Explain your method.
Part C
Explain what the solution to the system means in terms of where your band will rent a studio.
Answer:
Step-by-step explanation:
Studio A rents for $75 plus $75 an hour .
Studio B rents for $150 and $50 an hour.
Let t = the number of hours and c = cost.
Part A
Write a system of equations to represent the cost at each studio.
Studio A: c = 75 +75·t
Studio B: c = 150 +50·t
Part B
Solve the system of equations from Part A. Explain your method.
We solve the system of equation using substitution method, where we substitute c in the first equation with 150 +50t.
150 +50·t = 75 +75·t, subtract 75 and 50t from both sides
150 -75 = 75t -50t, combine likes terms
75 = 25t, divide both sides by 25
3 = t
Now we know that t = 3 so we find c by substituting t with 3 in the second equation.
c = 150 +50·t
c = 150 +50·3
c = 300
The solution of the system of equations is c = 300 and t = 3
Part C
Explain what the solution to the system means in terms of where your band will rent a studio.
The solution of the system of equation tells us that if we rent either studio A or B for 3 hours will pay the same price $300.
The price will be different if we rent studio A then studio B if we rent it for a different amount of time than 3 hours.
Determine the value of X
AB is the mid segment of triangle LMN. Determine the value of X
Answer:
B. 4Step-by-step explanation:
Since ,AB is the mid segment of triangle LMN
Then
[tex]\Longleftrightarrow AB=\frac{MN}{2}[/tex]
[tex]\Longleftrightarrow x+8=\frac{5x+4}{2}[/tex]
[tex]\Longleftrightarrow 2\times(x+8)=5x+4[/tex]
[tex]\Longleftrightarrow 2x+16=5x+4[/tex]
[tex]\Longleftrightarrow 16-4=5x-2x[/tex]
[tex]\Longleftrightarrow 3x=12[/tex]
[tex]\Longleftrightarrow x=\frac{12}{3}=4[/tex]
The tables show linear functions representing the cost for purchasing different amounts of broccoli and cauliflower. which function has the greater slope and what does it indicate? the broccoli function has the greater slope, which shows that the cost per pound of broccoli is less than the cost per pound of cauliflower. the broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower. the cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is less than the cost per pound of broccoli. the cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is greater than the cost per pound of broccoli.
The function that has a greater slope will be B. The broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower.
What is a linear function?It should be noted that a linear function simply means a function whose graph is a straight line.
From the information given, the slope will be:
= (y2 - y1(/(x2 - x1)
= (3.6 - 3)/(3 - 2.5)
= 1.2
The slope for broccoli is 1.2
The slope of the cauli flower will be:
= (3.20 - 2.75)/(3.20 - 2.75)
= 1
Therefore, the broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower.
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Answer:
B
Step-by-step explanation:
right on 2022 edg
Which points in a scatterplot or outliners select each correct answer PLEASE HELP!
Answer:
F and D
Step-by-step explanation:
there 2 out of the other lead
Which equation represents a line that passes through (5’1) and has a slope of 1/2?
Answer:
third one passes through the slope .
Answer:
Step-by-step explanation:
y - 1 = 1/2(x - 5)
y - 1 = 1/2x - 5/2
y - 2/2 = 1/2x - 5/2
y = 1/2x - 3/2
Option 3
Using a straightedge and compass the ancient Greeks were able to construct many geometric objects
Step-by-step explanation:
A department has five employees with five jobs to be performed. the time in hours each man will take to perform each jobs is given in the effectiveness matrix .
Find the volume of the pyramid
Step-by-step Explanation:
the volume of a pyramid is:
volume = (1/3) • base_area • height
(area = length • width)
(area) • (height) = (volume)³
Example:
area = 12cm² (12 cm squared)
height = 4cm
12 • 4 = 48cm³ (48 cm cubed)
Answer:
area: 6 • 8 = 48(1/2) = 24cm²
height: 12
volume: 24 • 12 = 288cm³(1/3) = 96cm³
Given the right triangle, evaluate: sin 0.
Answer: B. 5/13
This is the same as writing [tex]\frac{5}{13}[/tex]
==========================================================
Reason:
We have two given sides of this right triangle. Use the pythagorean theorem to find the missing side.
a = 5 and b = 12 are the two known legs; c is the unknown hypotenuse
[tex]a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{5^2+12^2}\\\\c = \sqrt{25+144}\\\\c = \sqrt{169}\\\\c = 13\\\\[/tex]
The hypotenuse is exactly 13 units long. This is a 5-12-13 right triangle.
Now we can compute sine of theta
[tex]\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{5}{13}\\\\[/tex]
This points us to choice B as the final answer.
----------------
Extra Info (optional)
5/12 is the value of tan(theta) since it's opposite/adjacent12/5 is the value of cot(theta), the reciprocal of tangent12/13 is the value of cos(theta), because cos = adjacent/hypotenuse9.) List three things vertical and horizontal lines have in common.
Answer:
Horizontal lines have a slope of zero, and run parallel to the x axis. Vertical lines have a undefined slope, and run parallel to the y axis. The equation for a horizontal line equals y=c, and the equation for a vertical line equals x=c. If a horizontal line crosses a vertical line the two lines would be perpendicular to one another.
Step-by-step explanation:
Use this:
What is a Horizontal Line?A Horizontal Line is a line that goes straight from left to right (or right to left) parallel to the x-axis of the coordinate plane. All of the points on the line will have the same y-coordinates.
What is a Vertical Line?A Vertical Line is a line that goes straight up and down Parallel to the y-axis of the coordinate plane. All of the points on the line will have the same x-coordinates.
Commonality:The length of a rectangle is four feet more than twice the width of the rectangle. The area of the rectangle is 240 square feet. What, in feet, are the length and width of the rectangle
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The width of the rectangle is 10ft , while the length of the rectangle is 24ft.
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
Let the width of the rectangle be represented by x.
The length of the rectangle is (2x+4), therefore, the area is,
Area = x(2x+4)
240 ft² = 2x² + 4x
2x² + 4x - 240 = 0
x² + 2x - 120 = 0
x = -12, 10
Since the width can not be negative, the width of the rectangle is 10, while the length of the rectangle is 24.
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Which statement below best describes whether or not the triangles are similar and
why?
A. ∆XXXXXX ~ ∆TTTTTT by AA similarity.
B. ∆XXXXXX ~ ∆TTTTTT by ASA similarity.
C. ∆XXXXXX ~ ∆TTTTTT by SSS similarity.
D. There is not enough information to determine similarity.
In the given figure if AOB = 132°, COD = 141°, if measure of BOD equals x°, then x is
Answer:
BOD = 189 °
Step-by-step explanation:
that is the answer above
Find the value of (8 × 10³)²
Answer:
64 × [tex]10^{6}[/tex]
Step-by-step explanation:
(8 × 10³)² = (8 × 10³)(8 × 10³)
= 8 × 10³ × 8 × 10³
= 64 × [tex]10^{6}[/tex]
Answer:
64000000Step-by-step explanation:
Find the value of (8 × 10³)²
(8 × 10³)² =
(8 × 1000)² =
8000² =
64000000
Help me please !!!!!!!!!
Answer:
A
Step-by-step explanation:
The solution matrices shown are the result of reducing the augmented coefficient matrix to "reduced row-echelon form". Many calculators and spreadsheets have functions specifically for that purpose.
The attachment shows the result of a TI-84 work-alike calculator's reduction of the coefficient matrix. It matches the first choice.
__
Additional comment
When the equations are written in the form shown here, with the variables in the same order, and the constant on the right side of the equal sign, the augmented matrix is simply the matrix of the numbers. It is shown as the argument of the RREF function in the attachment.
The left-right order of the variables on the left side of the equal sign matches the top-down order of the solution values in the rightmost column of the reduced matrix. That is, ...
a = 2, b = -2, c = 0.
Part E
Use the table showing Manuel's and Gretchen's data to determine the mean, median, standard deviation, and
interquartile range for each data set. Use this information to complete the second table. Use the graphing tool to
determine the value of standard deviation.
The mean, median, standard deviation, and interquartile range for each data set is given below.
What is the definition of Interquartile Range (IQR)?When arranged from lowest to highest, the IQR represents the central 50% of values.
Find the median (middle value) of the lower and higher half of the data to get the interquartile range (IQR).
These are the quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The difference between Q3 and Q1 is the IQR.
What are the measures of central tendency for Manuels Data?Using the statistical tool, the following were arrived at:
Standard Deviation = 3.13961Mean = 8Median = 8IQR = Q3-Q1 = 10 - 6 = 4What are the measures of central tendency for Grethcen's Data?Using the statistical tool, the following were arrived at:
Standard Deviation = 4.68737.Mean = 9.6Median = 9IQR = IQR = Q3-Q1 = 12 - 7 = 5.See the respective Histograms attached.
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Please help :)))))))))))))
Answer:
\frac{9}{20} (or 9/20, if this doesn't show up the right way in my answer.)
Step-by-step explanation:
Fist what we'll do here is divide 1000 by 450. 1000÷450=2\frac{2}{9} (2/9, if this doesn't show up the right way either).
Then, we'll apply the inverse formula. In case you've forgotten, the inverse of a number is what you have to multiply a number by to get 1. The inverse of 2/9 (too lazy to put it in that form anymore) is 0.45, or 9/20.
If that doesn't work, I might be interpreting this incorrectly.
Here.
Answer:
0.05, or 1/20
Step-by-step explanation:
So, we have the fraction. we can simplify it to 20/9, making the numerator 20. As previously stated, the inverse of a number is what you have to multiply a number by to get 1. So, 1÷20=0.05
Let me know which one works!
Warmest regards,
Sanjana
Professional 6th grader and quantum physics lover
Ax -c=bx+d solve for x
Answer:
[tex] x = \dfrac{c + d}{a - b} [/tex]
Step-by-step explanation:
ax - c = bx + d
ax - bx = c + d
x(a - b) = c + d
[tex] x = \dfrac{c + d}{a - b} [/tex]
Latoya created a factor tree and wrote the prime factorization of 90 shown below.
Answer:
it’s b
Step-by-step explanation:
the answer is 2x3x3x5, but it’s the same thing when you put an exponent of two on a 3.
Hope it helps
Sry if I’m wrong
The equation of a circle is given below:
x squared minus 4 x plus y squared minus 6 y minus 7 equals 0
Identify the center and radius of the circle.
Group of answer choices
Center: left parenthesis 2 comma 3 right parenthesis
Radius: 20
Center: left parenthesis 4 comma minus 6 right parenthesis
Radius: 2 square root of 5
Center: left parenthesis negative 4 comma 6 right parenthesis
Radius: 20
Center: left parenthesis 2 comma 3 right parenthesis
Radius: 2 square root of 5
Given:
The equation of the circle is
We need to determine the center and radius of the circle.
Center:
The general form of the equation of the circle is
where (h,k) is the center of the circle and r is the radius.
Let us compare the general form of the equation of the circle with the given equation to determine the center.
The given equation can be written as,
Comparing the two equations, we get;
(h,k) = (0,-4)
Therefore, the center of the circle is (0,-4)
Radius:
Let us compare the general form of the equation of the circle with the given equation to determine the radius.
Hence, the given equation can be written as,
Comparing the two equation, we get;
Thus, the radius of the circle is 8
Please help, its urgent. (Question Below)
The highest common factor of the numbers 210 and 308 is 4.
What is the highest common factor?The highest factor of the two numbers which divides both the numbers is called as greatest common factor or HCF.
The highest common factor will be calculated by finding the factors of the two numbers. The factors of the two numbers are as follows:-
308 = 2 x 2 x 7 x 11
210 = 2 x 2 x 3 x 17
We can see that the 2 x 2 = 4 is the highest factor which is common between the two numbers 210 and 308. So 4 is the HCF which can divide both the numbers 210 and 308.
Therefore the highest common factor of the numbers 210 and 308 is 4.
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Solve the following system of equations by substitution. Show all steps.
f (x) = -x^{2} + 2x +3
g (x) = -2x + 3
Answer:
Given system of equations:
[tex]\begin{cases}f(x)=-x^2+2x+3\\g(x)=-2x+3\end{cases}[/tex]
To solve by substitution, equate the equations and solve for x:
[tex]\begin{aligned}f(x) & = g(x)\\\implies -x^2+2x+3 & = -2x+3\\-x^2+4x & = 0\\x^2-4x & = 0\\x(x-4) & = 0\\\implies x & = 0\\\implies x-4 & = 0 \implies x=4\end{aligned}[/tex]
Therefore, the x-values of the solution are [tex]x = 0[/tex] and [tex]x = 4[/tex].
To find the y-values of the solution, substitute the found values of x into the functions:
[tex]f(0)=-(0)^2+2(0)+3=3[/tex]
[tex]g(0)=-2(0)+3=3[/tex]
[tex]f(4)=-(4)^2+2(4)+3=-5[/tex]
[tex]g(4)=-2(4)+3=-5[/tex]
Therefore, the solutions to the given system of equations are:
[tex](0, 3)[/tex] and [tex](4, -5)[/tex]
If 7 is added to the product of 7 and 3 what is the answer
Answer:
28
Step-by-step explanation:
[tex]7+7\times 3 = 7(1+3)= 7 \times 4 = 28[/tex]
Answer:
28
Step-by-step explanation:
When we find the product of 2 or more numbers, we multiply them.
so
product of 7 and 3 = 7 x 3 = 21
7 + 21 = 28
Hope this helps. I attempted to make it as simple as possible.
- profparis
part 3 to the please help question sorry im asking so many questions
Answer:
the answer would be 6,600ft
Step-by-step explanation:
I hope this helps!!
Factorise 2x^2 + x - 6
[tex] \rm \: {2x}^{2} + x - 6[/tex]
[tex] \rm \: {2x}^{2} + 4x - 3x - 6[/tex]
[tex] \rm \: {2x} \times (x + 2)- 3x \times (x + 2)[/tex]
[tex] \rm \: (x + 2) \times (2x - 3)[/tex]