50 F
32 F - - 18 = 32 F + 18= 50 F
Part A
given that P=(5,4), Q=(7,3), R=(8,6), and S=(4,1), find the component form of the vector PQ+4RS.
a.(18,19)
b.(-2,-6)
c.(-14,-21)
d.(-18,-19)
Part B
Use the information from part A to find the magnitude of the vector PQ+4RS.
a. 2sqrt10
b. 7sqrt13
c. sqrt35
d. 637
Answer:
[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:-14,-21\:>\:[/tex]
[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=7\sqrt{13}[/tex]
Step-by-step explanation:
The given points have coordinates; P=(5,4), Q=(7,3), R=(8,6), and S=(4,1).
[tex]^{\to}_{PQ}=^{\to}_{OQ}-^{\to}_{OP}[/tex]
[tex]^{\to}_{PQ}=<\:7,3\:>\:-\:<\:5,4\:>[/tex]
[tex]^{\to}_{PQ}=<\:7-5,3-4\:>\:[/tex]
[tex]^{\to}_{PQ}=<\:2,-1\:>\:[/tex]
[tex]^{\to}_{RS}=^{\to}_{OS}-^{\to}_{OR}[/tex]
[tex]^{\to}_{RS}=<\:4,1\:>\:-\:<\:8,6\:>[/tex]
[tex]^{\to}_{RS}=<\:4-8,1-6\:>\:[/tex]
[tex]^{\to}_{RS}=<\:-4,-5\:>\:[/tex]
[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:2,-1\:>\:+4\:<\:-4,-5\:>\:[/tex]
[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:2,-1\:>\:+\:<\:-16,-20\:>\:[/tex]
[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:2-16,-1-20\:>\:[/tex]
[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:-14,-21\:>\:[/tex]
The correct answer is C
The magnitude is given by:
[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{x^2+y^2}[/tex]
[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{(-14)^2+(-21)^2}[/tex]
[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{196+441}[/tex]
[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{637}[/tex]
[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=7\sqrt{13}[/tex]
The correct answer is B
the width of a rectangular flower bed is 7ft less than the length. The area is 18ftsq. Find the length and the width
Answer:
width = 2ft and length = 9ft
Step-by-step explanation:
width W = x
length L = x +7
area of a rectangle A = L * W
18 = (x + 7) * x
18 = x² + 7x
x² + 7x -18 =0
solve the equation by factorisation
x² -2x + 9x - 18 =0
x(x - 2) + 9(x - 2) =0
(x - 2)(x + 9) = 0
x = 2 and -9
therefore the width is 2ft because it is positive and the negative value is ignored
the length = 2 + 7 = 9ft
Answer:
width = 2ft and length = 9ft
Step-by-step explanation:
The height of a cylinder is 4 yards. The volume of the cylinder is 452.16 cubic yards. What is the radius of the cylinder?
Answer:
r = 5.9984789350480924657633167413961 yards
Step-by-step explanation:
h = 4 yards
V = 452.16 yards Cubed (cubic yards)
V = π[tex]r^{2}[/tex]h
452.16 = π[tex]r^{2}[/tex]*4
divide by pi and 4 and you get approx 35.98
35.981 = [tex]r^{2}[/tex]
the square root of 35.98 is approx 5.9984789350480924657633167413961
which is equal to r, or the radius
r = 5.9984789350480924657633167413961 yards
How many x-intercepts does the graph of the given equation have use the discriminant y=-4x^2+4x-1
[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-4}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{-1} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} \boxed{0}&\textit{one solution}~~\checkmark\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 4^2-4(-4)(-1)\implies 16-16\implies \boxed{0}[/tex]
What is the answer to 1/4c+2/3=1/3
Simplify 1/4c to c/4
c/4 + 2/3 = 1/3
Subtract 2/3 from both sides
c/4 = 1/3 - 2/3
Simplify 1/3 - 2/3 to -1/3
c/4 = -1/3
Multiply both sides by 4
c = -1/3 × 4
Simplify 1/3 × 4 to 4/3
c = -4/3
Let f(x) = -2x - 7 and g(x) = -4x + 3. Find (fog)(-5)
ANSWER
[tex]( f \circ \: g)( - 5)= -53[/tex]
EXPLANATION
The given functions are:
f(x) = -2x - 7 and g(x) = -4x + 3
[tex]( f \circ \: g)(x) = f(g(x))[/tex]
[tex]( f \circ \: g)(x) = f( - 4x + 3)[/tex]
[tex]( f \circ \: g)(x) = - 2( - 4x + 3) - 7[/tex]
Expand:
[tex]( f \circ \: g)(x) = 8x - 6 - 7[/tex]
[tex]( f \circ \: g)(x) = 8x - 13[/tex]
We substitute x=-5
[tex]( f \circ \: g)( - 5) = 8( - 5) - 13 = -53[/tex]
Which graph represents the function f(x) = |x|? Image for option 1 Image for option 2 Image for option 3 Image for option 4
Answer:
The correct option is 4.
Step-by-step explanation:
The given function is,
It is a modulus function and its parent function is,
In a function,
If k>1, then the graph of g(x) stretch vertically and if k<1 then the graph of g(x) compressed vertically.
Since k is , therefore the shoes the vertical compression.
put x=0 in the given function.
Put x=3.
Therefore the graph passing through (0,0) and (3,1).
So the fourth option is correct.
Hope this helps :)
The graph represents the function f(x) = |x| correct option is fourth image 4.
The given function is,
It is a modulus function and its parent function is,
In a function,
If k>1, then the graph of g(x) stretches vertically, and if k<1 then the graph of g(x) is compressed vertically.
Since k is, therefore the shoes the vertical compression.
What is vertical compression?Vertical compression means making the y-value smaller for any given value of x, and you can do it by multiplying the entire function by something less than 1. Horizontal stretching means making the x-value bigger for any given value of y, and you can do it by multiplying x by a fraction before any other operations.
put x=0 in the given function.
Put x=3.
Therefore the graph passes through (0,0) and (3,1).
So the fourth option is correct.
To learn more about the graph of function visit:
https://brainly.com/question/4025726
#SPJ2
Tiffani works in a baby shop in which she prints personalized bibs. She uses a probability model to predict that the next customer ordering a white bib would be 30%. For one day, Tiffani gathers data by tallying the the number of customers who order each color in this table.
Color Tally
white 21
grey 9
blue 15
pink 26
Based on her experiment, which statement is true?
Tiffani's prediction is valid. The probability of the next customer ordering a white bib is about 30%.
Tiffani's prediction is not valid. The probability of the next customer ordering a white bib should be about 21% because 21 people ordered white in her data.
Tiffani's prediction is not valid. The next customer ordering a white bib would be the same as any color, so the probability should be about 25%.
There is not enough information to determine the validity of her prediction.
Answer:
Tiffani's prediction is valid. The probability of the next customer ordering a white bib is about 30%.
Step-by-step explanation:
First you add all of your amounts together
21 + 9 + 15 + 26 = 71
Then to find the probability of the next customer buying a white bib you divide 21 by 71
21/71 = 0.295
Which is approximately 30%
I hope this helped!
please help me this is kinda hard
All sides of a square/cube are the same. Since this is a cube, you'll find the volume by "cubing" (get it?) 4.4m.
4.4³ or 4.4 * 4.4 * 4.4 = 85.184m³ but you can round that to 85m³
I hope that helps!
WILL GIVE BRAINEST IF CORRECT!!!!!
The area of a triangle is 24 square inches. What is the height of the triangle if the base length is 8 inches?
Answer:
6
Step-by-step explanation:
Which statement describes the graph of g(x) with respect to the graph f(x)?
a. let f(x)=(x+3)^2+2
let g(x)=(x+3)^2-3
* it is translated right 5 units
* stretched horizontally by a
factor of -3
* compressed vertically by a
factor of -3
* it is translated down 5 units
b. let f(x)=x^2 +5
let g(x)=(x+1)^2+5
* it is translated right 1 unit
* it is translated left 1 unit
*it is translated up 1 unit
* compressed vertically by a
factor of 5
c. Let f(x)=(x+6)^2
let g(x)=2(x+6)^2
* it is compressed horizontally by a factor of 2
* it is translated up 2 units
* it is translated right 2 units
* it is stretched vertically by a factor of 2
show work and answer please
Answer:
a. Translated down 5 units.
b. Translated 1 to the left.
c. Stretched vertically by a factor 2.
Step-by-step explanation:
a. It is translated down by 2 - (-3) = 5 units.
b. The x in f(x) is replaced by (x + 1) to gives g(x).
It is translated left by 1 unit.
c. The 2 stretches it vertically by a factor of 2.
Using translation concepts, it is found that the correct options are given by:
a) it is translated down 5 units.
b) it is translated left 1 unit.
c) it is stretched vertically by a factor of 2.
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.
In this problem:
In item a, 5 was subtracted from the function, hence it was shifted down 5 units.In item b, we have that x -> x + 1, hence it was shifted left 1 unit.In item c, the function was multiplied by 2, hence it was vertically stretched 2 units.More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ2
write an equation that is the slope-intercept form of the equation of the line that passes through (1,2) and is parallel to 4x-2y=6
Answer:
y=2x
Step-by-step explanation:
If the line is parallel to 4x-2y=6, it means that it has the same slope. So let's first find the slope.
Rearranging, we get
-2y=-4x+6
2y=4x-6
y=2x-3.
So, the slope is 2.
Next, we can use the point slope formula
y-y_1=m(x-x_1)
Substituting, we get
y-2=2(x-1)
y-2=2x-2
y=2x
What is the difference and what is their value?
g+g+g+g = g^4 or 4g
g•g•g•g= g^4 or 4g
Step-by-step explanation:
We know that g^4 is g multiplied by itself 4 times, so it has to be g·g·g·g.
We know that 4g is g 4 times, which means it is g+g+g+g.
It's important to focus on the fact that g^4 is g multiplied by itself 4 times, while 4g is g multiplied by 4.
Answer:
Step-by-step explanation:
We know that g^4 is g multiplied by itself 4 times, so it has to be g·g·g·g.
We know that 4g is g 4 times, which means it is g+g+g+g.
It's important to focus on the fact that g^4 is g multiplied by itself 4 times, while 4g is g multiplied by 4.
Step-by-step explanation:
Find the inverse of the given function f(x) =2^x+6
Answer:
[tex]f^{-1}(x) = log_2(x-6)[/tex]
Step-by-step explanation:
To find the inverse [tex]f^{-1}(x)[/tex] of a function follow the following steps.
1) Do y = f (x)
[tex]f(x) =y= 2 ^ x + 6[/tex]
[tex]y= 2 ^ x + 6[/tex]
2) Solve the equation for the variable x.
[tex]y= 2 ^ x + 6\\\\y-6 = 2^x\\\\log_2(y-6) = x\\\\x=log_2(y-6)[/tex]
3) exchange the variable y with the variable x
[tex]x=log_2(y-6)\\\\y=log_2(x-6)[/tex]
Finally the inverse is:
[tex]f^{-1}(x) = log_2(x-6)[/tex]
How to convert 186 into radians?
Answer:
see explanation
Step-by-step explanation:
To convert from degree to radian measure
radian measure = degree measure × [tex]\frac{\pi }{180}[/tex], thus
radian measure = 186 × [tex]\frac{\pi }{180}[/tex] = [tex]\frac{31\pi }{30}[/tex]
Mike 55 pieces of gum playing hoops at the County Fair. At school he gave 4 to every student in his math class he only has 3 remaining. How many students are in his class?
13 classmates because 55/4 = 13.75 and the .75 is the extra three pieces
I did 55-3=52 and then divided 52 by 4 to get 13 !!
calculate the angle between the longest side and the diagonal of a 577mm by 1000mm rectangle
Final answer:
The angle between the longest side and the diagonal of a 577mm by 1000mm rectangle can be found by first calculating the diagonal using the Pythagorean theorem and then using the arccosine function to find the angle with the longest side.
Explanation:
To calculate the angle between the longest side of a 577mm by 1000mm rectangle and the diagonal, we first need to determine the length of the diagonal using the Pythagorean theorem. The diagonal (d) can be found using the formula d = [tex]\sqrt{(width^2 + height^2)}[/tex]. After calculating the diagonal, we can find the angle using trigonometric ratios, specifically the arccosine function or cos-1.
Step 1: Calculate the diagonal
d = [tex]\sqrt{(577mm^2 + 1000mm^2) }[/tex]= [tex]\sqrt{(333929 + 1000000) }[/tex] = [tex]\sqrt{1333929}[/tex] ≈ 1155mm
Step 2: Calculate the angle
The angle (θ) between the longest side (adjacent side) and the diagonal (hypotenuse) is given by:
θ = cos-1(adjacent side / hypotenuse) = cos-1(1000mm / 1155mm)
To find the angle, use a calculator to compute the arccosine of 1000/1155.
what is a nonlinear function
Answer: A set of dots that arent in a line-esc shape.
(Think of a scatter plot)
I'm bad at explaining, sorry.
The best way to define this is *any highest degree term greater than 1⃣*.
Help me with this problem
Answer:
XY = 74
Step-by-step explanation:
Using the information given, plug it into the perimeter formula [P=2(l)+2(w)]
90 = 2 (5y - 1) + 2 (4y + 1)
Distribute
90 = 10y - 2 + 8y + 2
Combine like-terms
90 = 18y
Isolate the variable
y = 15
Then, plug it into XY
5 (15) - 1
Multiply
75 - 1
Combine
74
Answer:
XY = 24
Step-by-step explanation:
The perimeter of the rectangle is
2(5y - 1) + 2(4y + 1) = 90 ← distribute parenthesis on left side
10y - 2 + 8y + 2 = 90
18y = 90 ( divide both sides by 18 )
y = 5
XY = 5y - 1 = (5 × 5) - 1 = 25 - 1 = 24
What’s is the next number?
2,3,5,7,11,13,17
Answer:
19
Step-by-step explanation:
It is all prime numbers. The next prime number after 17 is 19.
PLEASE HELP!! WILL MARK BRAINLEST!!!! 2/n=2/3
2/n=2/3 ok to start you cross multiply so you would end up with 2*3=2n then you simplify and you get 6=2n now you divide both sides by 2 and end up with 3 so you answer is C. n=3
Answer:
The correct answer option is C. n = 3.
Step-by-step explanation:
We are given the following expression and we are to solve for [tex] n [/tex]:
[tex] \frac { 2 } { n } = \frac { 2 } { 3 } [/tex]
To solve this, we will use the method called cross multiplication where the numerator of left side is multiplied with the denominator of right side and vice versa.
[tex]3 \times 2 = 2 \times n[/tex]
[tex]2n = 6[/tex]
[tex]n=\frac{6}{2}[/tex]
[tex]n=3[/tex]
Therefore, the correct answer option is C. n = 3.
How much paper will it take to make each tree including the bottom??
The bottom is a square with a side length of 2 ft.
The area of a square is Area = S^2 = 2^2 = 4 square ft. Bottom)
The area of one side ( triangle) = 1/2 x base x height = 1/2 x 2 x 4 = 4 square ft.
There are 4 triangles: 4 x 4 sq. ft. = 16 sq.ft. ( four sides)
Total area = four sides + bottom = 16 + 4 = 20 feet^2
find the solution to the equation by completing the square x^2-6x=7. what is the smallest and largest value of x
Answer:
smallest value of x = -1
Largest value of x = 7
Step-by-step explanation:
[tex]x^2-6x=7[/tex]
coefficient of x = -6
Half of the coefficient of x = -6/2 = -3
Square of the half value [tex]=(-3)^2=9[/tex]
Add the square value on both sides of equation
[tex]x^2-6x+9=7+9[/tex]
[tex](x-3)^2=16[/tex]
Take square root
[tex]x-3= \pm \sqrt{16}[/tex]
[tex]x-3= \pm 4[/tex]
[tex]x-3=+4[/tex] or [tex]x-3=-4[/tex]
[tex]x=+4+3[/tex] or [tex]x=-4+3[/tex]
[tex]x=7[/tex] or [tex]x=-1[/tex]
Hence smallest value of x = -1
Largest value of x = 7
Six times the sum of a number and twelve is forty.
Which equation represents this?
O 6N + 12N = 40
O 6N + 12 = 40
6(N + 12) = 40
Answer:
6(N + 12) = 40
Step-by-step explanation:
Number = N
Sum of a number and twelve:
N + 12
Six times the sum of a number and twelve:
6(N + 12)
Six times the sum of a number and twelve is forty:
6(N + 12) = 40
Answer:
6(N+12) = 40
Step-by-step explanation:
The statement says six times the sum . . .
From this we can tell that the answer will be 6 times two numbers added together. Those two numbers are "a number" (some variable) and 12.
We can tell that the variable is N, so it answer must be 6(N + 12) = 40
Factor the polynomial. 3x^3 - 12x^2 + 27x
Answer:
3x(x^2-4x+9)
Step-by-step explanation:
The polynomial 3x^3 - 12x^2 + 27x is factored by first taking out the greatest common factor of 3x, resulting in the final form of 3x(x^2 - 4x + 9), which cannot be factored further over the real numbers due to a negative discriminant.
To factor the polynomial 3x^3 - 12x^2 + 27x, we look for common factors in each term.
We can see that each term of the polynomial has a factor of 3x. So, we factor out 3x from the polynomial:
3x(x^2 - 4x + 9)
Now, we try to factor the quadratic expression x^2 - 4x + 9. However, this quadratic does not have real roots since the discriminant (b^2 - 4ac) is negative (-4^2 - 4 ×1 ×9 = -20). Therefore, it cannot be factored over the real numbers. Our final factored form of the polynomial is 3x(x^2 - 4x + 9), as we factored out the greatest common factor (GCF).
Find the area of a circle with a circumference of 31.42 centimeters.
Answer:
A≈78.56cm²
Hope this helps you out!
c = 2(pi)r = 31.42cm
2(3.14)r = 31.42cm
6.28r = 31.42cm
r = 31.42cm / 6.28
r = 5cm
A = (pi)r^2
= (3.14) (5)^2
5x5 = 25cm
25x3.14= 78.5cm
the area equals 78.5cm
Please put in order to least to greatest.
Answer:
1/3, 1/2, and 4/5.
Step-by-step explanation:
This is the correct answer to this question.
Hope this helps!!!
Kyle.
The question is in the picture
Answer:
45 degrees
Step-by-step explanation:
Inscribed angles are always half of the value of the central angle, therefore half of 90 degrees would be 45 degrees.
Which is the graph of f(x) = (x + 3)(x – 2)? Image for option 1 Image for option 2 Image for option 3 Image for option 4
Answer:
image 1
Step-by-step explanation:
Given data:
f(x) = (x+3)(x-2)
= x^2 + x-6
As the given expression is a quadratic expression so the graph will be parabola.
Also coefficient of x^2 is 1, 1>0 hence we'll the parabola opens upwards
that reduces our options to image 1 and 2 only
now to find the x-axis points of parabola
let (x+3)(x-2)=0
(x+3)=0 and (x-2)=0
x= -3 and x= 2
when at y=0, x= -3 and x=2
hence the image 1 !
5÷7=35÷(y+1)
Added some points :)
Answer:
y=48
Step-by-step explanation:
5/7=35/y+1
Step 1: Cross-multiply.
5 /7=35/y+1
5*(y+1)=(35)*(7)
5y+5=245
Step 2: Subtract 5 from both sides.
5y+5−5=245−5
5y=240
Step 3: Divide both sides by 5.
5y /5=240/5
y=48
HOPE THIS HELPS!!