Answer:
The vector that describes their hike from their starting position to their final destination is [tex]\vec r = 7\,\hat{i}+1\,\hat{j}\,\,\,[mi][/tex].
Step-by-step explanation:
In this problem we assume that orthogonal axes coincide with the north and east. We proceed to translate each sentence from statement into vectorial equations:
(i) A group of hikers walks 3 miles east and then 1 mile north:
[tex]\vec r_{A} = 3\,\hat{i}+1\,\hat{j}\,\,\,[mi][/tex]
(ii) After taking a break, they then hike 4 miles east to their final destination:
[tex]\vec r_{B} = 4\,\hat{i}\,\,\,[mi][/tex]
The vector that describes their hike from their starting position to their final destination is the sum of the vectors deducted above. That is:
[tex]\vec r = \vec r_{A}+\vec r_{B}[/tex] (1)
[tex]\vec r = (3\,\hat{i}+1\,\hat{j})+4\,\hat{i}\,\,\,[mi][/tex]
[tex]\vec r = 7\,\hat{i}+1\,\hat{j}\,\,\,[mi][/tex]
The vector that describes their hike from their starting position to their final destination is [tex]\vec r = 7\,\hat{i}+1\,\hat{j}\,\,\,[mi][/tex].
Hai has 24 video games. Six of his games are sports related and the rest are role-playing games. Which ratio represents the number of his role-playing games to the total number of games? One-fourth One-third Two-thirds Three-fourths
Answer:
3/4
Step-by-step explanation:
24-6=18--> role playing games
18/24=3/4
Answer: 3/4
Step-by-step explanation:
Choose the answer below that makes the following expression true:
108 ÷ ‒12
A.
9
B.
96
C.
‒9
D.
‒96
Answer:
-9.
Step-by-step explanation:
Claire wants to build a patio outside her café. The rectangular space outside of Claire's café is three times as long as it is wide. The area of the space is 48 m2. Claire
would like to build a patio with dimensions 3.5 m by 12.5 m in this space. Will it fit? Explain.
pls help
Answer:
Step-by-step explanation:
It will fit in the space but it won't cover the entire space. the area is 48m2, but the patio in question will cover 43.75 of the 48m2. Also, it stated that the rectangular space is 3 times as long, and the patio is 3.57x as long as the width. So yes, it will fit, but it will not be a picture perfect fit, there will be some obscenities.
Step-by-step explanation:
Let length of space be lm and width be wm.
l = 3w --(1)
lw = 48 --(2)
sub (1) into (2):
3w(w) = 48
3w^2 = 48
w^2 = 16
w = ± 4 (rej -4 since w > 0)
when w = 4, l = 3(4) = 12
Since dimensions of the patio is 3.5m by 12.5m, and the dimensions of the space is 4m by 12m it does not fit
This is a topic known as simultaneous equations. If you would like to find out more / know when and how to use it, you can check out my Instagram page (learntionary)
what is 4y³ - 3z⁴ when y=3 and z=2 =
Answer:
60Step-by-step explanation:
4(y)3 - 3(z)4
Sub:- 4(3)raise to three - 3(2)raise to four
4(27)-3(16)
4*27-3*16
108-48
=60.
Plssss helpppp ASAPP
will mark BRAINLIEST!!!
Answer:
I would say the last one
Step-by-step explanation:
The third works the same way but 46/17 is hard to calculate without a calculator
What is the quotient and the remainder of 2,461 ÷ 18
Answer:
Step-by-step explanation:
722222
Answer:
136 r 13
Step-by-step explanation:
divide the numbers using long division:
1 3 6
__________
18 | 2 4 6 1
- 1 8
___
6 6
- 54
_____
1 2 1
- 1 0 8
_____
1 3
So 2461 / 18 is 136, remainder 13
The vertices of a triangle are P(–2, –3), Q(–4, –2), and R(4, 8). What are the vertices of the image reflected across the y-axis?
P(–2, 3), Q(–4, 2), and R(4, -8)
P(2, –3), Q(4, –2), and R(-4, 8)
P(–2, –3), Q(–4, –2), and R(4, 8)
P(-3, -2), Q(-2, -4), and R(8, 4)
Answer:
[tex]\huge\boxed{P(2;\ -3);\ Q(4;\ -2)\ \text{and}\ R(-4;\ 8)}[/tex]
Step-by-step explanation:
[tex]A(x;\ y)\xrightarrow{S_{OY}}A'(-x;\ y)\\\\\text{The abscissa changes to the opposite:}\ x\to -x\\\\\text{Therefore}\\\\P(-2;\ -3)\xrightarrow{S_{OY}}P'(2;\ -3)\\\\Q(-4;\ -2)\xrightarrow{S_{OY}}Q'(4;\ -2)\\\\R(4;\ 8)\xrightarrow{S_{OY}}R'(-4;\ 8)[/tex]
EASY POINTS
Kite LMNO is shown below.
Kite L M N O. Angle L is 130 degrees and angle N is 74 degrees. Angle L and N are opposite to each other.
What is the measure of Angle M?
A. 56Degrees
B. 78Degrees
C. 156Degrees
D. 204Degrees
Step-by-step explanation:
What is the solution to the system of equations below?
y=-6x-10
and
y=-3x-21
(2, -22)
(2,48)
(-2, 2)
(-2, -20)
Answer:
Please check the explanation.
Step-by-step explanation:
Given the equations
[tex]y=-6x-10[/tex]
[tex]y=-3x-21[/tex]
solving the system of the equations
Arrange the equation variables for elimination
[tex]\begin{bmatrix}y+6x=-10\\ y+3x=-21\end{bmatrix}[/tex]
[tex]y+3x=-21[/tex]
[tex]-[/tex]
[tex]\underline{y+6x=-10}[/tex]
[tex]-3x=-11[/tex]
[tex]\begin{bmatrix}y+6x=-10\\ -3x=-11\end{bmatrix}[/tex]
solve
[tex]-3x=-11[/tex]
Divide both sides by -3
[tex]\frac{-3x}{-3}=\frac{-11}{-3}[/tex]
[tex]x=\frac{11}{3}[/tex]
[tex]\mathrm{For\:}y+6x=-10\mathrm{\:plug\:in\:}x=\frac{11}{3}[/tex]
[tex]y+6\cdot \frac{11}{3}=-10[/tex]
[tex]y+6\cdot \frac{11}{3}=-10[/tex]
[tex]y=-32[/tex]
Therefore, the solutions to the system of the equations are:
[tex]y=-32,\:x=\frac{11}{3}[/tex]
But, it seems none of the options is true.
Answer:
A. (2, -22)
Step-by-step explanation:
I just took the test and i got a one hundred! I really hope it helped!!!!
Find the circumference of the circle, round to the nearest tenth. Answer: H
Answer:
H
Step-by-step explanation:
Searches related to jay read 6 during the summer break he plans to read 5 books each month during the school year. Write the inequality he could use to find x the number of months after summer he will have read more than 50 books
Answer:
10
Step-by-step explanation:
One number is 2 less than a second number.twice the second number is 37 more than 5 times the first. Find more the two number
Answer:
The numbers are -11 and -9.
Step-by-step explanation:
The two numbers are x and y.
x = y - 2
2y = 5x + 37
2y = 5(y - 2) + 37
2y = 5y - 10 + 37
3y = - 27
y = -9
x = - 11
A glass is 1/3 full. Then 40cm3 of orange juice is poured in.
The glass is now 5/7 full. What is the total volume of the glass?
Answer:
105cm3
Step-by-step explanation:
subtract 5/7- 1/3
8/21=40cm3
21/21=105cm3=total volume
Answer:
5
Step-by-step explanation:
There is a relationship between the expected number of tickets sold for a raffle and the dollar value of the prize for the raffle. The equation T - 6P = 100 describes this relationship, where T is the expected number of tickets sold, and P is the dollar value of the raffle prize. Suppose the expected ticket sales for a certain raffle are 1900. Determine the dollar value of the raffle prize.
Answer: The dollar value of the raffle prize = 300
Step-by-step explanation:
Given: The equation T - 6P = 100 describes this relationship, where T is the expected number of tickets sold, and P is the dollar value of the raffle prize.
If T =1900
Then,
[tex]1900-6P=100[/tex] [Put T=1900 in given equation]
[tex]\Rightarrow\ 6P=1900-100\\\\\Rightarrow\ 6P= 1800\\\\\Rightarrow P=\dfrac{1800}{6}\\\\\Rightarrow\ P=300[/tex]
Hence, the dollar value of the raffle prize = 300
PLEASE HELP ILL GIVE BRAINLIEST!!!!
Answer:
The first one is x=45
The second one is w=14
The third one is x=6
Step-by-step explanation:
which is the line of best fit and why?
Responder:
Opción de respuesta c
Explicación paso a paso:
Es una pendiente positiva como los datos, también coincide con muchos de los puntos.
Espero que te aya ayudado
Answer:
Answer choice c
Step-by-step explanation:
It is a positive slope like the data, it also matches up with many of the points.
help i’ll give brainliest if it’s right
Answer:
C
Step-by-step explanation:
how to write decimal numbers 4.980
Answer:
The decimal is 4.980
Step-by-step explanation:
BRAINLIEST PLS
a line passes through the point (-6,4) and has a slope of 5/2
Solve the system of equations:
3x-3y = -15
and
-x+y = 5
Answer:
x=0 y=5
trust me I think its right
Helps me solve this problem please
Answer:
the slope is negative....
What is the x-intercept of the line described by the equation? 14x - 8y = 56
Answer:
The x intercept is (4,0) and the y intercept is (0,-7)
Step-by-step explanation:
Answer:
Step-by-step explanation:
The x-intercept of a line is when the y-coordinate is 0. To find that point on this line, we first want to rearrange the equation into the form
[tex]y = mx + b[/tex]
we are given
[tex]14x - 8y = 56\\so, \\14x - 56 = 8y\\\frac{14x}{8} - \frac{56}{8} = \frac{8y}{8} \\y = \frac{7}{4}(x) - 7[/tex]
now, we can set y to 0 and solve
[tex]\frac{7}{4}(x) = 7\\7x = 28\\x = 4[/tex]
The x-intercept is (4, 0)
Which of the following terminating decimals is equivalent to Negative 1 and three-fourths?
Answer:
-1.75
Step-by-step explanation:
This should be it, but you didn't provide options although you put "Which of the following.."
Answer:
-1.75 thatis the answer thank you HAHAHAHAHAHA
Solve the triangle, find m∠A and m∠C. Round angles to the nearest degree.
m∠A= __∘
m∠C= __∘
Answer:
[tex]m\angle A=63^\circ\\m\angle C=26^\circ[/tex]
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of the triangle is called the hypotenuse and the other two sides are called the legs.
Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.
The cosine ratio is defined as:
[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]
Note the angle A of the figure has 17 as the adjacent leg and 38 as the hypotenuse, so we can directly apply the formula:
[tex]\displaystyle \cos A=\frac{17}{38}[/tex]
[tex]\cos A=0.4474[/tex]
Using a scientific calculator, we get the inverse cosine:
[tex]A=\arccos(0.4474)[/tex]
[tex]A\approx 63^\circ[/tex]
Since A+B+C=180°, we can solve for C:
C = 180° - A - B
C = 180° - 63° - 90°
C = 26°
Thus:
[tex]m\angle A=63^\circ\\m\angle C=26^\circ[/tex]
In the given right triangle ABC, m∠A ≈ 26.44° and m∠C ≈ 63.56°.
To solve the right triangle ABC, we can use trigonometric ratios. In a right triangle, the three main trigonometric ratios are:
1. Sine (sin): [tex]\(\sin(\theta) = \frac{{\text{opposite side}}}{{\text{hypotenuse}}}\)[/tex]
2. Cosine (cos): [tex]\(\cos(\theta) = \frac{{\text{adjacent side}}}{{\text{hypotenuse}}}\)[/tex]
3. Tangent (tan): [tex]\(\tan(\theta) = \frac{{\text{opposite side}}}{{\text{adjacent side}}}\)[/tex]
Given:
AC = 38
AB = 17
To find the angles m∠A and m∠C, we can use the sine and cosine ratios, respectively.
1. For m∠A:
[tex]\(\sin(m\angle A) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle A= \sin^{-1}\left(\frac{{17}}{{38}}\right)\)[/tex]
2. For m∠C:
[tex]\(\cos(m\angle C) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle C = \cos^{-1}\left(\frac{{17}}{{38}}\right)\)[/tex]
Let's calculate the angles:
[tex]1. \(m\angle A \approx \sin^{-1}\left(\frac{{17}}{{38}}\right) \approx 26.44^\circ\)\\\\2. \(m\angle C \approx \cos^{-1}\left(\frac{{17}}{{38}}\right) \approx 63.56^\circ\)[/tex]
Therefore, m∠A ≈ 26.44° and m∠C ≈ 63.56° (rounded to the nearest degree).
To know more about right triangle, refer here:
https://brainly.com/question/31613708
#SPJ2
A television was marked down by 1/5 of the original price. a. If it was originally $150.00, how much is the sale price? The salesperson receives 1/10"commission on the sale price of the TV. How much does he make on the sale?
I need help please.
What are the answers at least for the first one. Please help.
Answer:
1. 0 weeks
2.$50 in savings
3.8 weeks
4. $90 in savings
Step-by-step explanation:
4 units right
hat are the
age?
11. Translate the figure 2 units left
and 4 units down. What are the
coordinates of the image?
22 REAS
trans
3 un
If so
A
y
23.
B
3
2
1
С
-4-3-2
3
4 x
D
2
-3
f
4
Can you guys plz help me
Answer:
[tex]\frac{20}{12}[/tex]
Step-by-step explanation:
Answer:
20/12 since 3*4 is 12 u do 5*4
Step-by-step explanation:
Please mark brainliest and hope this helps ya!!
In basketball, some baskets are worth two points. Others are worth three points. In one game, the ratio of three-point baskets to three-point tries for one team was . If the team scored 27 points from three-point baskets, how many three-point tries did the team have?
Answer:
36 attempts
Step-by-step explanation:
12х – 5y = — 20
y = x+4
can someone help me find the x and y
Answer:
0 I think because when you plug y in and combine like terms, you get 7x=0
Answer:
(I'm not sure what you're asking but I believe you're asking for the coordinate where they intersect!)
The lines intersect at (0, 4)
Step-by-step explanation:
Question:
12x-5y=-20
y=x+4
1) Simplify the first equation!
12x-5y=-20
Move 12x to the other side (remember when you move numbers to the opposite side of the equation, it makes them negative) to isolate y!
-5y=-20-12x
Divide all numbers by -5 to just get the variable y
y=4+12/5x
2) Solve
I'm going to be solving by substitution since I like this method the best!
y=4+12/5x
y=x+4
1) Set the equations equal to another (you'll be replacing the variable of y for an equation)
x+4 will be replacing y of the other equation
x+4 = 4+12/5x
2) Simplify
Subtract x on both sides
x-x + 4 = 4+ 12/5x-x
4=4+7/5x
Subtract 4 on both sides
0=7/5x
x is equal to 0!
3) Find y
1) Set x equal to 0 in an equation (I'm doing y=x+4 because it's easier!)
y=x+4
y=0+4
2) Simplify
y=4
Answer:
(0, 4)