Mathematics College

Find the specified vector or scalar.

u = -4i + 1j and v = 4i + 1j; Find ||u+v||

a. sqrt32

b. 2

c. 5

d. 8

Answers

Answer 1
[tex]\bf \begin{cases} u=-4i+1j\implies & \ \textless \ -4,1\ \textgreater \ \\ v=4i+1j\implies &\ \textless \ 4,1\ \textgreater \ \end{cases}\qquad u+v\implies \ \textless \ -4,1\ \textgreater \ +\ \textless \ 4,1\ \textgreater \ \\\\\\ \ \textless \ -4+4~,~1+1\ \textgreater \ \implies \ \textless \ 0,2\ \textgreater \ \\\\ -------------------------------\\\\ \stackrel{magnitude}{||u+v||}\implies \sqrt{0^2+2^2}\implies 2[/tex]

Related Questions

toby needs 2 4/5 poundscof clay to make one sculpture how many sculptures can he make from 14 pounds of clay show your work

Answers

He can make 5 sculptures.

We divide the amount of clay, 14 pounds, by the amount it takes to make one sculpture, 2 4/5 pounds:

14 ÷ 2/45 = 14 ÷ 14/5 = 14/1 ÷14/5 = 14/1 × 5/14 = 70/14 = 5

You mix the letters S, E, M, I, T, R, O, P, I, C, A, and L thoroughly. Without looking, you draw one letter. Find the probability that you select a vowel. Write your answer as a fraction in simplest form.

Answers

5/12 would be your simplest form
 5
__  is the answer hope that i helped
12

a triangular prism and two nets are shown which is the correct net of the prism and what is the surface area of the prism???
A)net A with 420 square inches
B) net A with 480 square inches
C) net B with 510 square inches
D) net B with 534 square inches

Answers

B: net A with 480 in^(2)

-21 is located to the right or left of -20

Answers

Its located to the left. 

If y varies directly as x and y=3 when x=12, what is the value of when x=18

Answers

[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=3\\ x=12 \end{cases}\implies 3=k12\implies \cfrac{3}{12}=k \\\\\\ \cfrac{1}{4}=k\qquad therefore\qquad \boxed{y=\cfrac{1}{4}x} \\\\\\ \textit{when x = 18, what is \underline{y}?}\qquad y=\cfrac{1}{4}(18)[/tex]

Answer:

1/4(18)

Step-by-step explanation:

Solve for x in the inequality below. 5 > -3x - 1 A. -2 > x B. 2 > x C. 2 < x D. -2 < x

Answers

D because you first add 1+5=6 then divide 6 by -3 which is -2, and the inequality sign flips since you divide by a negative.

If the central angle is 60 degrees, what is its arc measure?

Answers

The arc measure is defined by its corresponding central angle. The arc measure is 60°.

Samantha had 300 beads 30% were black 25% were red 15% were white.the remaining beads are blue. how many were blue?

Answers

Hello!

For this you have to find the amount of every color of beads.

300 * 0.30 which is 90 black beads

300 * 0.25 is 75 red beads

300 * 0.15 is 45 white beads

Then you add them.

90+75+45 = 210

Then subtract them from the total

300 - 210 = 90

The answer is 90 blue beads or 30%

Hope this helps!

If the constant c is chosen so that the curve given parametrically by ct, c 2 16 t 2 , 0 ≤ t ≤ 3 , is the arc of the parabola 16y = x 2 from (0, 0) to (8, 4), find the coordinates of the point p on this arc corresponding to t = 2.

Answers

Final answer:

The coordinates of point p corresponding to t = 2 on the specified parametric curve, when matching the arc of the parabola 16y = x^2, are (8, 2).

Explanation:

The student is asking to find the coordinates of the point p corresponding to t = 2 on the curve defined parametrically by ct, [tex]c^2/16[/tex] × [tex]t^2[/tex] where c is chosen such that the curve becomes the arc of the parabola 16y = x² from (0, 0) to (8, 4).

To find c, we match the parametric equations to the standard form 16y = x², which implies c = 4 because for any point (x, y) on the parabola, y must equal [tex]x^2/16[/tex].

Substituting t = 2 into the corrected parametric equations x = 4t and y = 4 · [tex](t^2/16)[/tex], we obtain the coordinates of point p as (8, 2).

3x³+25x²+42x-40=0
How to solve this equation in detail

Answers

Solve equation step by step!

3x^3 + 25x^2 + 42x - 40 = 0

Step 1 Factor left side of equation
(3x - 2)(x + 4x)(x + 5) = 0


Step 2  Set Factors  equal to Zero(0)
3x - 2 = 0, or x + 4 = 0, or  x + 5 = 0


X = 2/3 or x = - 4, or x = - 5

Answer 
X = 2/3 or x = - 4, or x = - 5



Hope this helps!!!!

Solve for x and y.


y=x^2-5x+1
x+y=-2

Answers

y = x² - 5x + 1
x + y = -2

substitute the first equation into the second one....

x + x² - 5x + 1 = -2
x² - 4x + 1 = -2
add 2 on both sides to make the equation equal to 0.

x² - 4x + 3 = 0
factor this.

(x - 1)(x - 3) = 0
x = 1 , x = 3

to find the y values, you would have to substitute x = 1 and x = 3.
1 + y = -2       3 + y = -2
y = -3                   y = -5


So your answers are
x = 1 , x = 3
y = -3, y = -5

Hope this helped!

A plasma TV is on sale at a 22% discount. The sale price is $776.10. What was the orginal price?

Answers

To find the original price, we must use the equation below...

Original Price = Discounted Price / (1 - Discount %)

Original Price = 776.1 / (1 - 0.22) = $881.93

Which expression is equivalent to 3*5*5*5*5*5*5

Answers

3*5*5*5*5*5*5 = 3 * 5^6 = 46,875

Answer:

Step-by-step explanation:

3(5)6

at an airport it costs $7 to park for up to one hour and $5 per hour for each additional hour. let x represent the number of hours parked. write the function that modles the cost, C(x), of the parking x hours, where x is an integer greater then 1.

Answers

Answer:

C(X) = 7 + 5(X-1)

Step-by-step explanation:

So, the cost for parking from 0 to 1 hour is $7. Then, for one extra hour, from 1 to 2, you have to pay an additional $5. For another hour, from 2 to 3, an extra $5, and so on. So, lets make a quick table:

Hours       Cost

[0-1]               $7

(1-2]               $7+$5

(2-3]              $7+$5+$5

(3-4]             $7+$5+$5+$5

So, for 1 hour the cost is $7, for 2 hours $12, 3 hours $17, 4 hours $22, and so on. We can see a pattern here: the cost for X hours is $7 plus $5 for each hour greater than 1. So we can write the cost function as:

C(X) = 7 + 5(X-1)

If X=2, 2 hours, the cost is:

C(2) = 7 + 5(2-1) = 7 + 5 = 12, so the function fits.

Notice that here I used the parenthesis in a (--] form, however, it could also be used in a [--) form. If the last is chosen, 2 hours would cost $17 instead of $12. The function would be C(X) = 7 + 5X.

As the statement does not specifies, any of this ways can be used.

PLEASE HELP WITH THIS QUESTION! WILL MARK BRAINLIEST

Riley made a scale drawing of a triangular clock face. Riley used a scale factor of 3 when making her drawing. If the base and the height of Riley's drawing are 10 centimeters and 15 centimeters respectively, what is the area of the triangular clock face?
A. 75 square centimeters
B. 225 square centimeters
C. 675 square centimeters
D. 2,700 square centimeters

Answers

we know that
[scale factor ]=[real]/[drawing]
[real]=[drawing]*[scale factor ]

step 1
find the real values

if the base of Riley's drawing is 10 centimeters
 [real]=[drawing]*[scale factor ]--------> 10*3-------> 30 cm
the base of the triangular clock face is 30 cm

the  height of Riley's drawing is 15 centimeters 
[real]=[drawing]*[scale factor ]--------> 15*3-------> 45 cm
the  height of the triangular clock face is 30 cm

the  area of the triangular clock face is-----> 45*30/2-------> 675 cm²

the answer is the option C. 675 square centimeters

Answer:

we know that[scale factor ]=[real]/[drawing][real]=[drawing]*[scale factor ]step 1find the real valuesif the base of Riley's drawing is 10 centimeters [real]=[drawing]*[scale factor ]--------> 10*3-------> 30 cmthe base of the triangular clock face is 30 cmthe height of Riley's drawing is 15 centimeters [real]=[drawing]*[scale factor ]--------> 15*3-------> 45 cmthe height of the triangular clock face is 30 cmthe area of the triangular clock face is-----> 45*30/2-------> 675 cm²the answer is the option C. 675 square centimeters

Step-by-step explanation:

How far does a ball, hit from a height of 3 feet at a speed of 120 feet per second and an angle of 30 degrees, go before it hits the ground? Round your answer to the nearest integer.

Answers

The time of flight ends once the height of the ball hits the ground. First we look at the ball's upward trajectory. Its initial vertical velocity is (120 ft/s)(sin 30) = 60 ft/s. Since gravity is -32 ft/s^2, this means that the ball will fly upward for 60/32 = 1.875 s. By then, it will be at a height of:
h = h0 + vi*t - 0.5gt^2 = 3 ft + (60 ft/s)(1.875 s) - 0.5(32 ft/s^2)(1.875)^2 = 59.25 ft
So the time of its downward flight is solved by:
59.25 = 0.5(32)t^2
t = 1.924 s
Total time of flight = 1.875 + 1.924 = 3.799 s
The ball's horizontal velocity is constant at (120 ft/s)(cos 30) = 103.923 ft/s.
Multiplying this by the time of flight of 3.799 s gives a total distance of 395 ft.
Hello,
Please, see the attached files.
Thanks.

Michael sold 23 of his CDs and purchased 16 more. If Michael has 25 CDs now, how many CDs did he have to begin with?

Answers

the correct question is
Michael sold 2/3 of his CDs and purchased 16 more. If Michael has 25 CDs now, how many CDs did he have to begin with?

Let
x--------------> numbers of CDs Michael have to begin

if Michael sold (2/3)x-----------> are pending to sell (1/3)x

we know that
(1/3)x+16=25--------> (1/3)x=25-16-------> (1/3)x=9---------> x=27

the answer is 27 CDs

What is the area of triangle with base 5m and height 12m

Answers

The area of a triangle can be found using the formula 1/2bh, where the variable b represents the value of the base and the variable h represents the value of the height.

If we plug in the given values into this formula, we get:

(1/2)(5m)(12m)

When we simplify this expression, we get:

30 m^2

Therefore, your answer is 30 m^2.

Hope this helps!

1+3x/4=5/2 Solve the proportion for x. A.7/5 B.3 C.5 D.6

Answers

[tex] \frac{1+3x}{4}= \frac{5}{2} [/tex]

To solve the proportion, we first need to do cross mutiplication.

[tex](1+3x)(2)=(5)(4)[/tex]
[tex]2+6x=20[/tex]

After that, we simply just need to simplify and perform the necessary algebra to solve for the value of x.

[tex]6x=18[/tex]
[tex]x=3[/tex]

ANSWER: B. The value of x is equal to 3.

Plz help i want to learn how to do this math


Jenny's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Jenny 5.25
per pound, and type B coffee costs 4.15
per pound. This month, Jenny made 150
pounds of the blend, for a total cost of
642.60. How many pounds of type B coffee did she use?

Answers

In order to know the answer, you would have to set up a system of equations:

Given that type A coffee costs $4.15 per pound
(4.15x)
Given that type B coffee costs $5.25 per pound
(5.25y)
And that the total cost of it all was $642.60

[tex]4.15x + 5.25y = 642.60[/tex]
Also, the amount of pounds, represented by x and y add up to 150 pounds total:

[tex]x + y = 150[/tex]
A+B=167lbs
A=167lbs-B
$4.35A+$5.70B=$846.60 Substitute for A
$4.35(167lbs-B)+$5.70B=$846.60
$726.45-$4.35B+$5.70B=$846.60 Subtract $726.45 from each side.
$1.35B=$120.15 Divide each side by $1.35.
B=89 lbs
ANSWER: The mix contained 89 pounds of Type B coffee.
CHECK:
167lbs-89lbs=78 lbs She used 78 pounds of Type A coffee.
$4.35A+$5.70B=$846.60
$4.35(78)+$5.70(89)=$846.60
$339.30+$507.30=$846.60
$846.60=$846.60 

the area of a rectangle is text square and the length of the rectangle is 3 ft more than twice the width. find the dimensions of the rectangle length and width

Answers

Area of rectangle = 35 feet square
Let the Width of rectangle is x feet.
Length of rectangle is 3 feet more than twice the width.
Thus,Length can be written as: 2x + 3

Area of rectangle is product of its length and width.
So,

Area = Length x Width

[tex]35 = x (2x + 3) \\ \\ 35 = 2 x^{2} +3x \\ \\ 2 x^{2} + 3x - 35 = 0 \\ \\ 2 x^{2} + 10x - 7x - 35 =0 \\ \\ 2x (x + 5) - 7 (x+5) = 0 \\ \\ (2x-7)(x+5)=0[/tex]

Thus
x = -5
or
x =7/2 = 3.5

Since the measure of width cannot be negative, we neglect x = -5. and keep the value x = 3.5

Therefore,
Width = 3.5 feet
Length = 2x + 3 = 2(3.5) + 3 = 10 feet  

Convert y-3=(1/3)(x+1) to slope intercept form

Answers

Slope-intercept form is [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.

Here, we first need to distribute the 1/3.

[tex]y-3= \frac{1}{3} x+\frac{1}{3}[/tex]

Next, we add 3 to both sides of the equation.

[tex]y= \frac{1}{3} x+\frac{10}{3}[/tex]

Experts/ace/geniuses helpp

Answers

the irrational number would be square root 15

Write a polynomial expression for the perimeter of a rectangle whose sides have the following lengths. Length: x2+3x-5 Width: 3x2-2x+6 A. 8x2+8x+2 B.8x2+2x+2 C.4x2+x+1 D. 4x2-5x+1

Answers

Final answer:

The perimeter of the rectangle with given dimensions is represented by the polynomial 8x^2 + 2x + 2, which corresponds to option A.

Explanation:

To determine the perimeter of a rectangle, we need to add up all sides of the rectangle. The formula for the perimeter (P) of a rectangle is P = 2(length) + 2(width). Given the length is x2 + 3x - 5 and the width is 3x2 - 2x + 6, we would calculate the perimeter as follows:

P = 2(x2 + 3x - 5) + 2(3x2 - 2x + 6)

Expanding this expression:

P = 2x2 + 6x - 10 + 6x2 - 4x + 12

Combining like terms gives us:

P = (2x2 + 6x2) + (6x - 4x) + (-10 + 12)

P = 8x2 + 2x + 2

So the correct polynomial expression for the perimeter of the rectangle is option A: 8x2 + 2x + 2.

Final answer:

The polynomial expression for the perimeter of the rectangle with given side lengths is 8x^2 + 2x + 2.

Explanation:

The perimeter of a rectangle is given by the formula P = 2l + 2w, where l represents the length and w represents the width. For the lengths provided, the length (l) is x2 + 3x - 5 and the width (w) is 3x2 - 2x + 6. To find the polynomial expression for the perimeter, we will multiply both the length and the width by 2 and then sum them:

Perimeter (P) = 2(x2 + 3x - 5) + 2(3x2 - 2x + 6)

On simplifying:

P = 2x2 + 6x - 10 + 6x2 - 4x + 12

P = (2 + 6)x2 + (6 - 4)x - (10 - 12)

P = 8x2 + 2x + 2

Therefore, the correct polynomial expression for the perimeter is 8x2 + 2x + 2, which corresponds to option B.

the function f(x) varies inversely with x and f(x) = 0.2 when x = 0.4.


what is f(x) when x = 1.6

Answers

Varies inversely :

f(x) = k/x

There is always a constant of variation , k to solve for using the given information. when x = 0.4 ; f(x) = 0.2

0.2 = k/0.4
0.2(0.4) = k
0.08 = k

final equation : f(x) = 0.08/x

when x = 1.6

f(x) = 0.08/1.6
f(x) = 0.05

if 12 newborn babies are randomly selected, how many different gender sequences are possible?

Answers

Final answer:

The question concerns the different combinations or sequences possible in a group of 12 newborn babies, each of whom could be either male or female. Using the formula 2ⁿ, where n represents the number of babies, we find there are 4096 different gender sequences possible.

Explanation:

This question pertains to combinations, specifically the different combinations of male and female sequences possible with a random selection of 12 newborn babies. When considering gender sequences, we have two possibilities for each newborn, male (M) or female (F).

With 12 newborns, each having two possible genders, we calculate the total gender sequences as 2 raised to the power of 12, based on the rule of the product in probability theory. Therefore, we use the formula 2n, where 'n' is the number of babies. Here, 'n' is 12, so 212 gives us 4096.

So, there are 4096 different gender sequences possible when 12 newborn babies are randomly selected.

Learn more about Combinations here:

https://brainly.com/question/39347572

#SPJ12

nee help with y this question

Answers

He would make $108 in 9 hours.

This can be found by dividing $216 by 2, to equal the division of hours by 2.

a straight line through points p and q is drawn perpendicular to a line through points p(x,y) and r(x,(y+10)) . the possible coordinates of the point q are_?

Answers

On the X-Y plane, the points p and r are on the vertical line X=x. Then the perpendicular (horizontal) line through p will have the equation Y=y. Points q on that line will have coordinates

... q(<anything>, y)

A customer tells you that they will call at 3PM Eastern Standard Time. If you are located in the Pacific Standard Time Zone (which is 3 hours earlier), when should you expect the call?

Answers

You should expect the call at 12:00pm

Answer:

At midday. In a 24 hours clock, 12:00, in a midday format 12 PM.

Step-by-step explanation:

In order to calculate this you just have to withdraw the hour difference between both the Eastern Standar Time and the Pacific Standar Time, which normally are 3 hours of difference, since he is in the Eastern Standar Time, that means he is 3 hours ahead of you, so in order to calculate the hour at which you should expect the call, you have to withdraw 3 hours frmo 3 P.M which would make it midday or 12 P.M

what is the probability of picking a red card from a standard deck of 52 cards?

Answers

well, the suits of ♦  ,  ♥ are both red, and each suit has 13 cards, there are 52 cards in the deck,

[tex]\bf P(\diamondsuit~or~\heartsuit)\implies \cfrac{13}{52}+\cfrac{13}{52}\implies \cfrac{26}{52}\implies \cfrac{1}{2}[/tex]

Answer: 50

Step-by-step explanation:

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