[tex]\bold{\huge{\green{\underline{Solution}}}}[/tex]
A car travels 10 km southeast and then 15 km in a direction 60° north of east[tex]\bold{\underline{ To\: Find }}[/tex]
We have to find the magnitude of the car of resultant vector[tex]\bold{\underline{ Let's \: Begin }}[/tex]
Here,
In South east, car travels = 10kmIn North of east, it travels = 15kmAngle between south east and north east is 60°Therefore,
According to parallelogram law of resultant vector
If two vectors are represented by two adjacent sides of a parallelogram drawn from a point , the their resultant is equal to the diagonal of the parallelogram.
That is,
[tex]\sf{ R = AC^{2}= A^{2}+ B^{2}}[/tex]
But, we have to calculate the magnitude of the resultant vector
[tex]\sf{ | R |= √A^{2}+ B^{2}+ 2ABCos{\theta} }[/tex]
Subsitute the required values,
[tex]\sf{ | R |=\sqrt{ (10)^{2} + (15)^{2} + 2× 10 × 15 × cos 60{\degree}}}[/tex]
[tex]\sf{ | R | =\sqrt{ 100 + 225 + 20 × 15 × 1/2}}[/tex]
[tex]\sf{ | R | = \sqrt{100 + 225 + 10 × 15 }}[/tex]
[tex]\sf{ | R | = \sqrt{335 + 150 }}[/tex]
[tex]\sf{ | R | = \sqrt{485 }}[/tex]
[tex]\sf{\red{ | R | = 22.02 \: km}}[/tex]
Hence, The magnitude of the car resultant vector is 22.02 km.
A random sample of 24 corporate-owned stores finds an average number of customers of 313 with a standard deviation of 34.9. What is the upper bound of a 95% confidence interval for the average number of customers in corporate-owned stores
Answer:
95% is 1700 customers
Step-by-step explanation:
JK i actually dont know but thnks for the points BTW
i will mark brainliest
Answer:
2 1/2 (2.5)
Step-by-step explanation:
Multiply all the numbers then divide by 1/2
Your freezer produces 8 ice cubes every two hours. Your friends freezer produces 24 ice cubes every 5 hours what is the ratios?
Problem Situation: Eric is adding water to a 60-gallons pool. a The pool already has 12 gallons of water, and he wants to fill it to at least 27 gallons. The water flows at a rate of 6 gallons per minute. How many minutes, x, will it take for Eric to fill the pool with at least 27 gallons of water? Inequality that represents this situation: 27 < 12 +63 To solve the inequality, you can begin by solving the equation as shown. Drag a diagram to each row of the table to show which number line represents all of the solutions for the inequality and which number line represents all of the solutions for the problem situation
Answer:
16
Step-by-step explanation:
The number after 15 s 16.
Is the square root of 2times 10 the same as 2 square root 10
Answer:
no
Step-by-step explanation:
√(2*10= √20= 4.47
2*√10= 6.32
Answer:
No.
Step-by-step explanation:
[tex]=\sqrt{2*10}\\\\=2\sqrt{5}[/tex]
[tex]=2\sqrt{10} \\\\=2\sqrt{10}[/tex]
2√5≠2√10
i need answer please
Solve for g:
4g
--- =3j+7
h
Answer:
g= h(3j+7)
---------
4
Step-by-step explanation:
4g = h(3j + 7)
4g = h*3j+h*7
Napoleon's route through the alps involved a climb of 6km and a descent of 4km. His army travelled twice as fast downhill as it did uphill, the whole journey took 8 hours. How long did it take to reach the top?
Answer:
6 hours.
Step-by-step explanation:
since that is true we can use trial and error. if every km took an hour it would take six hours up and 4 hours down but they said they were twice as fast going down so that means it would take 2 hours going down. 6 add 2 is 8 which is our total meaning that 6 hours is the right answer
im having trouble solving this. y=5(x-3)
Hi there!!
If you need X to be solved then the answer is X=Y over 5+3 and if your looking for the answer for Y then the answer is Y=5x−15
When you are solving for X you will need to use the distributive property so you can multiply 5 by X-3.
Y=5x-15. Once you've done that then you need to swap sides so all of the variables are on the same side as each other (they need to be on the left side) 5x-15=Y.
Then you need to add 15 to both of the sides to make it look like this ->5x=Y+15
When that's done you then need to divide both sides by 5 so it then looks like this when done.
5x over 5= Y+15 over 5
When you divide this by 5, it then undoes the multiplication by 5.
X= Y+15 over 5
Finally, you need to divide Y+15 by 5
X=Y over 5 plus 3
When solving for Y, all you will need to do is use the distributive property to multiply 5 by X-3.
I REALLY HOPE THIS HELPED YOU OUT AND THAT I DIDN'T WASTE YOUR TIME WITH A WRONG ANSWER . BUT IF THIS WAS CORRECT THEN YOU ARE VERY WELCOME
M is the midpoint of segment CD. Given M(-2,2) and C(2,8), find the coordinates of D.
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{2}~,~\stackrel{y_1}{8})\qquad D(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x + 2}{2}~~~ ,~~~ \cfrac{ y + 8}{2} \right)~~ = ~~\stackrel{\stackrel{M}{\downarrow }}{(-2~~,~~2)}\implies \begin{cases} \cfrac{x+2}{2}=-2\\[1em] x+2=-4\\ \boxed{x=-6}\\[-0.5em] \hrulefill\\ \cfrac{y+8}{2}=2\\[1em] y+8=4\\ \boxed{y=-4} \end{cases}[/tex]
What is the surface area of this triangular prism rounded to the nearest tenth?
The surface area of the triangular prism, rounded to the nearest tenth is: 85.7 cm²
What is the Surface Area of a Triangular Prism?Surface area (SA) = bh + (s1 + s2 + s3)H
Given:
s1 = 6.8 cm
s2 = 5.1 cm
s3 = 8.5 cm
H = 2.5 cm
b = 6.8 cm
h = 5.1 cm
Plug in the values
Surface area of the triangular prism = 6.8 × 5.1 + (6.8 + 5.1 + 8.5)2.5
Surface area of the triangular prism = 85.7 cm²
Learn more about the surface area of a triangular prism on:
https://brainly.com/question/16147227
Amy is trying to determine how many different outfits she can make. She has 4 bottoms 7 tops, 2 belts, and 5 pairs of shoes. Assuming she wears one of each item, how many different outfits can
she make?
Answer:
Amy puede hacer 4 conjuntos.
Step-by-step explanation:
La solución sería
Se sabe que un conjunto de vestir se compone de camisa o blusa, pantalones, zapatos y cinturones, aunque este ultimo es opcional.
Lo que haremos es esto, empezamos a coger una pieza de cada prenda para armar un conjunto.
Primer conjunto:
1 blusa, 1 pantalón, 1 cinturón, y 1 par de zapatos.
Y esto quedaría así: 3 pantalones, 6 blusas, 1 cinturón y 4 pares de zapatos.
Segundo conjunto:
1 blusa, 1 pantalón, 1 cinturón y 1 par de zapatos.
Esto quedaría así: 2 pantalones, 5 blusas, 0 cinturones, 3 pares de zapatos. Sabemos que el cinturón es opcional, así que podemos continuar.
Tercer conjunto:
1 blusa, 1 pantalón y un par de zapatos.
Esto quedaría así: 1 pantalón, 4 blusas, 0 cinturones y 3 pares de zapatos.
Cuarto conjunto:
1 blusa, 1 pantalón y un par de zapatos.
Esto quedaría así: 0 pantalones, 3 blusas, 0 cinturones y 2 pares de zapatos. Como en un conjunto el pantalón es prioridad, al no tener más pantalones los conjuntos quedarían hasta aquí.
¡Recuerda!
No es lo mismo organizar tu ropa en conjuntos, a que hagas variaciones con ella.
True
Consider the equation q = 4 +0.8p.
=
What value of p would make the equation to
12?
Answer:
p=10
Step-by-step explanation:
q = 4 +0.8p
Let q = 12
12 = 4 +0.8p
Subtract 4 from each side
12-4 = 4+.8p -4
8 = .8p
Divide each side by .8
8/.8 = .8p/.8
10 =p
please help!! Tysm <33
Answer:
[tex] \frac{p}{3} = 5[/tex]
p = 15
[tex] \frac{15}{3} = 5[/tex]
this is not Math its SCIENCE if you can answer all u get to be brailiest
Answer:
1a) A chemical compound is a chemical substance composed of many identical molecules composed of atoms from more than one element held together by chemical bonds. A molecule consisting of atoms of only one element is therefore not a compound.
1b)An ionic compound formed by acid-base reactions and without those ions is called a salt. Water is definitely one of the most important inorganic compounds to all living things. It is a compound comprised of two hydrogen atoms and one oxygen atom.
The four major classes of biological macromolecules are carbohydrates, lipids, proteins, and nucleic acids.
2a)Regulates body temperature. Moistens tissues in the eyes, nose and mouth. Protects body organs and tissues. Carries nutrients and oxygen to cells.
2b)If a cell is seriously deprived of water,
this lack of water would most likely affect
the cell's enzymes because:
• The cytoplasm and plasma
membrane would not function
properly
Both the plant and animal cell needs
water in order to perform their basic
functions which include transport of
materials, waste distribution, production
of genetic information, and many more.
As a result of this, we can see that there
would be a serious problem if any
of these cells are deprived of water
which would lead to the cytoplasm and
plasma membrane to partially shut
down because they would not be able to
engage in protein synthesis and other
important functions.
3a)Carbohydrates provides energy rich for organic compounds made of elements carbon, hydrogen and oxygen. The lipids contain the element nitrogen. The carbohydrates contain the only elements carbon, hydrogen, and oxygen.
3b)Organic nitrogen occurs in many forms, including amino acids, proteins, nucleic acids, nucleotides, and urea.
3c)A carbohydrate has only Carbon, Hydrogen and Oxygen, with the hydrogen and oxygen in the ratio 2:1. A protein is made of amino acids. ... So without nitrogen atoms the compound can not be a protein.
please can someone explain to me how this is done the answer is 85 but how to figure it out I am giving away 10 points the question is one the image and the answer is 85 but just explain how it is done
Answer:
Step-by-step explanation:
A = [tex]\frac{hb}{2}[/tex]
h = 10 cm , b = 17 cm
A = 10 × 17 ÷ 2 = 85 cm²
what is the 10% of 1,500 show all the necessary steps
[tex] \rightarrow \: \sf \dfrac{10}{100} \times 1500[/tex]
[tex] \\ \\ [/tex]
[tex] \rightarrow \: \sf 10 \times 15[/tex]
[tex] \\ \\ [/tex]
[tex] \rightarrow \: \sf 150[/tex]
If the image of (x,-3) is (-3,4) under the reflection in y=x , find the value of x.
Step-by-step explanation:
4
........................
A triangle has angle measurements of 66°, 66°, and 48°. Is this triangle isosceles?
Answer:
yes
Step-by-step explanation:
The 2 base angles of an isosceles triangle are congruent.
66° + 66° + 48° = 180° ( sum of angles in a triangle )
Thus the triangle is isosceles with base angles = 66° and vertex = 48°
The product of 20 any y (Pls i need help in this)
Answer:
Step-by-step explanation:
20y
Meaning 20xy
Y=1
So 20 is 20
An angle bisector of a triangle divides the opposite side of the triangle into segments2 cm and 5cm long. The second side of the triangle is 7.5 cm long. Find all possible lengths for the third side of the triangle.
Answer:
3 cm or 18.75 cmStep-by-step explanation:
Let the third side is x.
According to Triangle-angle-bisector theorem, we have the possible ratios:
x/7.5 = 2/5or
x / 7.5 = 5/2Solve for x in each case:
1)
x = 7.5*2/5 = 3 cm2)
x = 7.5*5/2 = 18.75 cmthere are six red marbles and 11 orange marbles in a bag. You randomly choose one of the marbles. What is the probability of choosing a red marble?
Answer:
The probability of choosing a red marble is 35%.
Step-by-step explanation:
Total marbles: 17
Red marbles: 6Orange marbles: 11[tex]\frac{6}{17} = 0.35[/tex]
what is -5/2dividedby5/7
[tex]\frac{ - 5}{2} \: by \: \frac{5}{7} [/tex]
[tex] - 3.5[/tex]
Answer : [tex] - 3.5[/tex]
Finding the measure of each angle indicated
Answer:
50
Step-by-step explanation:
Because if the tringles are equal they'll be the same amount (110) 50+60= 110
WHAT IS THE VOLUME OF THE PRISM????
Answer:
78 3/4
Step-by-step explanation:
Convert all the mixed numbers to fraction : 4 1/2 = 9/2 ; 3 1/2 = 7/2
V = 9/2 x 5 x 7/2 = 315 / 4 = 78 3/4
Hope it helps
!!!HURRY PLS!!!
My BraIns nOt wOrkIng-
Answer:
x=5
Step-by-step explanation:
x+3=2x-2
1. take the square root's out
2. subtract -3 from both sides of the equation.
x+3-3=2x-2-3
3. subtract.
x=2x-5
4. subtract 2x from both sides of the equation.
x=-2x=2x-5-2x
5. solve
x=5
I need helppppp plssssssssss
Answer:
(x, y) = (9, 17)
Step-by-step explanation:
Any two pairs of equations can be used to form a system of equations that will give appropriate values of x and y. Let's set the upper and lower left expressions equal to the middle one.
2x +3y -20 = 4x +5y -72 . . . . upper left = middle
52 = 2x +2y . . . . . . . . add 72-2x-3y
x + y = 26 . . . . . . . . . . divide by 2
and ...
5x -2y +38 = 4x +5y -72 . . . . lower left = middle
110 = -x +7y . . . . . . . . . . . . . add 72-5x+2y
Now we have two equations in two unknowns that will give us the common values of x and y. Adding these equations eliminates x and gives the value of y:
(x +y) +(-x +7y) = (26) +(110)
8y = 136 . . . . . . . . simplify
y = 17 . . . . . . . . . divide by 8
x = 26 -y = 26 -17 = 9
The values of x and y that make all of these expressions equal are ...
(x, y) = (9, 17)
The value they are equal to is ...
2x +3y -20 = 2(9) +3(17) -20 = 18 +51 -20 = 49
__
Check
upper right = 9 -4(17) +108 = 9 -68 +108 = 49
lower right = 3(9) -17 +39 = 27 -17 +39 = 49
The cost of 3 scarves is $80.25. What is the unit price?
Answer:
$26.75 per scarf
Step-by-step explanation:
3 scarves = $80.25 (quite expensive)
1 scarf = $80.25/3
1 scarf = $26.75
Answer:
$8.75 because 26.25 divided by 3 equals 8.75.
Step-by-step explanation:
Which value of x makes the equation 0.1x – 2.5 = 1.0 true?
a. 10
b. 15
c. 20
d. 35
Answer:
d) 35
Step-by-step explanation:
0,1 *35 - 2,5 = 1,0
Please help rn
Compare -4 and 1. Which statement is not true?
A. 1 is farther from zero on a number line.
B. 1-4] > [1]
O c. 1 is farther to the right on a number line.
D. 1 has a lower absolute value.
Answer:
D. 1 has a lower absolute value
Step-by-step explanation:
D is the answer because -4 is negative and can never be more than a positive number like 1.
Answer:
D
Step-by-step explanation:
because 1 have 1 absolute value and -4 have 4 absolute value
since 4 is greater than 1
so 1 have lower absolute value