The net force on the cart is 62N
and the vertical component =36.64 N
the horizontal component= 50N
What is revolution of vector?
The process of splitting a vector into its components is called resolution of the vector. We resolve a vector into two components which are. component along the x-axis called horizontal component. component along the y-axis called vertical component
30N tension on the cart is westward which mean the vertical component will be 0 and the horizontal component will be 30N.
40N tension isN 30° E which means
the vertical component= 40 sin60=36.64N
Horizontal component= 40 cos 60= 20N
sum of vertical = 36.64N +0= 36.64N
sum of horizontal= 30N+20N= 50N
60° was used for tension 40N because the angle of vector must always lie on the horizontal axis
therefore the net force F is obtained by using Pythagoras theorem
F= √(50^2+36.64^2)
= 62N to the nearest whole number.
learn more about resolution of vectors from
https://brainly.com/question/17369412
#SPJ1
Solve the inequality for x.21 > x+2Simplify as much as posible.
The given inequality is 21>x+2.
The inequality can be solved as,
[tex]\begin{gathered} 21>x+2 \\ 21-2>x \\ 19>x \\ x\in(-\infty,19). \end{gathered}[/tex]Thus, the above expression gives the required solution for the inequality.
Given: GC bisects FGH. Determine the missing measure.a. m
Given that line segment, GC bisects ∠FGH
I made a sketch of the angles, they are not at scale.
That segment GC is an angle bisector indicates that it divides ∠FGH into halves. To determine the measure of the ∠FGC and ∠CGH you have to divide the measure of FGH by 2.
[tex]\angle\text{FGC}=\angle\text{CGH}=\frac{\angle\text{FGH}}{2}[/tex]a) ∠FGH=86º
[tex]\begin{gathered} \angle\text{FGC}=\frac{\angle FGH}{2} \\ \angle\text{FGC}=\frac{86º}{2} \\ \angle\text{FGC}=43º \end{gathered}[/tex]So, in this case, the measure of ∠FGC is 43º.
b) For this item you have to determine the measure of ∠FGH given that the measure of one of the angles determined by the bisector is ∠CGH. To determine the measure of ∠FGH you have to multiply ∠CGH by 2
[tex]\begin{gathered} \angle\text{FGH}=2\cdot\angle\text{CGH} \\ \angle\text{FGH}=2\cdot28º \\ \angle\text{FGH}=56º \end{gathered}[/tex]How many points of intersection are there between the graphs of the two hyperbolas?
The graphs of the hyperbola have zero point of intersection.
What is the point of intersection?The point of intersection is the point where two or more functions meet.
The given parameters;
3x² – 4y² + 4x – 8y +4= 0
3x² + y² + 4x – 3y +4= 0
To find the points of intersection, we simply equate both equations.
So;
3x² – 4y² + 4x – 8y +4= 3x² + y² + 4x – 3y +4
Now Cancel out the common terms
y² - 3y = - 4y² - 8y
Collect like terms;
y² + 4y²= 3y - 8y
5y² = - 5y
Divide through by 5
y² = -y
Divide through by y
y = -1
Hence, the graphs of the hyperbola have zero point of intersection.
Read more about points of intersection at:
brainly.com/question/13373561
#SPJ1
In a city in Ohio, the sales tax rate is 7.5%. If you buy a blanket for $22.00 and a pillow for $8.00, what is your total bill of the blanket and pillow including tax?
i need help with this question
Answer:
58.29 cm^2
Step-by-step explanation:
The area of a trapezium is calculated with the following formula:
[tex] \frac{a + b}{2} \times h[/tex]
(a: base, b: base, h: height)
[tex] \frac{ 7 + (10.4)}{2} \times (6.7) \\ \\ \frac{17.4}{2} \times (6.7)[/tex]
get rid of fraction by dividing (17.4) with 2
(17.4)÷2 = 8.7 multiply this with height
(8.7) × (6.7) = 58.29
The area of the given trapezium is 58.29 cm².
What is a trapezium?In American and Canadian English, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid. A trapezium is a term used for a trapezoid in British and other varieties of English. These two terms were transposed due to a typo in Charles Hutton's mathematical dictionary.So, the area of the trapezium:
Formula: (a+b)/2 × hWhere, a = 7, b = 10.4 and h = 6.7.Solve as follows:
(a+b)/2 × h(7 + 10.4)/2 × 6.717.4/2 × 6.78.7 × 6.758.29 cm²Therefore, the area of the given trapezium is 58.29 cm².
Know more about trapeziums here:
https://brainly.com/question/1410008
#SPJ13
Selena was comparing the flying seeds of different birds in science class. which of the three words why faster why?select the correct response 1. the blue jay Five Spices because it's rate is 20 m/s2. the Cardinal flies fast is because it's right is 10 m/s3.the robin Place passes because it's rate is 15 m/s4.they all fly at a rate of 10 m/s
Selena was comparing the flying seeds of different birds in science class.
Which of the three words why faster why?
Select the correct response
1. the blue jay Five Spices because it's rate is 20 m/s
2. the Cardinal flies fast is because it's right is 10 m/s
3. The robin Place passes because it's rate is 15 m/s
4.they all fly at a rate of 10 m/s
____________________________
The slope, in this case, expresses the variation of the distance with respect to time (that is, the speed).
Comparing the slopes
Blue Jay's Flight
slope 10 m/s
__________________
Robin's Flight
slope = (y1-y2)/ (x1-x2)
Selecting the points (x, y)
Point 1 (2, 30)
Point 2 (6, 90)
slope = (90- 30) m / (6-2 )s
=(60)/ 4
= 15 m/s
_______________________________
Answer
3. The robin Place passes because it's rate is 15 m/s
_______________________________
Can you see the updates?
Do you have any questions regarding the solution?
If you don’t need further explanation on this question, we can end the session.
I want to remind you this answer will always be saved in your profile. I’d really appreciate you letting me know how I did by rating our session after you exit. Thanks and have a great day!
(a)A circle has a radius of 12cm. If the radius is increased by a factor of 7, how's many times larger will the circle's circumference be? (b)What is the scale factor of the circumference of a circle with a radius of 3 when compared to the original circle? Write your answer as a decimal to the nearest hundredth.
The circumference of a circle is found using the formula,
[tex]C=2\pi r[/tex]Where
C is the circumference
r is the radius
A circle has radius 12 cm, so its circumference is
[tex]\begin{gathered} C_1=2\pi r \\ C_1=2\pi(12) \\ C_1=24\pi \end{gathered}[/tex]When the radius (12 cm) is increased by a factor of 7, we mean the radius is 7 times the original, so, the new radius is
[tex]7\times12=84[/tex]So, the circumference of this circle will be >>>>
[tex]\begin{gathered} C_2=2\pi r \\ C_2=2\pi(84) \\ C_2=168\pi \end{gathered}[/tex]To find how many times larger this circumference is of the previous one, we divide,
[tex]\frac{C_2}{C_1}=\frac{168\pi}{24\pi}=7_{}[/tex]Answer7(b)Using the circumference formula, we can find the circumference of this circle,
[tex]\begin{gathered} C=2\pi r \\ C=2\pi(3) \\ C=6\pi \end{gathered}[/tex]The original circle had a circumference of 24π
The question basically asks "how many times is the circumference of this circle compared to the circumference of the original circle?"
Of couse, it will be less than 1 since this circle is smaller than the original one.
So,
[tex]\begin{gathered} \frac{6\pi}{24\pi} \\ =\frac{1}{4} \end{gathered}[/tex]So, the scale factor is 1/4, or 0.25
Answer0.25What are the coordinates of the point? Responses (−2, 4) begin ordered pair negative 2 comma 4 end ordered pair (4, −2) begin ordered pair 4 comma negative 2 end ordered pair (−4, −2) begin ordered pair negative 4 comma negative 2 end ordered pair (2, 4) begin ordered pair 2 comma 4 end ordered pair A coordinate grid with a dot placed in the second quadrant. The dot is to the left of positive 4 on the y axis and above negative 2 on the x axis Skip to navigation
The coordinates of the point are (-2,4)
A coordinate grid has two lines perpendicular to each other referred to as the Axis, labeled a bit like number lines. The horizontal axis is ordinarily called the x-axis. The vertical axis is ordinarily called the y-axis. The origin is the point where the x- and y-axis meets. The numbers on a coordinate lattice are utilized to find points. Each point can be identified by a requested combination of numbers; that's, a number on the x-axis called an x-coordinate, and a number on the y-axis called a y-coordinate. The requested sets are composed in enclosures (x-coordinate, y-coordinate).
For the given point, the x-coordinate is -2 on the negative x-axis, and y - coordiante is 4 on the positive y-axis.
To know more about coordinates refer to the link https://brainly.com/question/27749090?referrer=searchResults.
#SPJ1
(b) The area of a rectangular pool is 8075 m².If the length of the pool is 95 m, what is its width?Width of the pool: ]m
The area of a rectangle is:
[tex]A=wl[/tex]where w is the width and l is the length. Plugging the values we have and solving for w:
[tex]\begin{gathered} 8075=95w \\ w=\frac{8075}{95} \\ w=85 \end{gathered}[/tex]Therefore the width is 85 meters.
magine,... L Free Games Online. Online Voice Recon What is the circumference of a circle with a radius 5 square un 50 m square units quare units
The distance around a circle is known as the circumference, by definition.
Rita, Goran, and Kareem have a total of $93 in their wallets. Rita has $7 more than Goran. Kareem has 2 times what Rita has. How much do they have in their wallets?
Goran has $18 in his wallet. Rita has $25 and Kareem has $50 in his wallet.
What is basic algebra?Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical formulas. Mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z are needed to construct a valid mathematical expression. Coordinate geometry, calculus, and trigonometry are just a few of the mathematics topics that involve algebra. A simple algebraic equation is 2x + 4 = 8. Algebraic expressions are the result of performing operations on variables and constants, such as addition, subtraction, multiplication, division, etc.
Let the amount Goran have = X
Then, the amount Rita have= x+7
Then, Kareem has the amount = 2(x+7)
According to question
The total money three of them have = $93
Therefore,
x+x+7+2(x+7) = 93
2x + 7 + 2x + 14 = 93
4x+21= 93
4x= 93-21
4x= 72
x= 18
So,
Goran has $18 in his wallet
Rita have $ 18 +37= $25 in her wallet
Kareem has 2 × 25 = $50 in his wallet
To learn more about basic algebra visit :
brainly.com/question/15167098
#SPJ10
You are designing a rectangular poster to contain 70 cm2 of printing with a 2 cm margin at the top and bottom and a 4 cm margin on the left and right. Determine, to two decimal places, the length of the poster required so as to minimize the amount of paper used.
The dimension of minimum paper size would be 18 inches by 9 inches.
What dimensions will minimize the amount of paper used?Let the paper size be x inches in length and y inches in width.
The length of the printed space would be x-8 inches and width would be y-4 inches.
Print area would thus be (x-8)(y-4)=50.
From this [tex]$y=4+\frac{50}{x-8}=\frac{4 x+18}{x-8}$[/tex]
Also from the same equation on simplifying, it is x y-8 y-4 x+32=50.
Since the area of the paper of size x inches by y inches is xy, let it be denoted as A.
Thus
[tex]$A-8 y-4 x=18$[/tex] Or [tex]$A=8 y+4 x+18$[/tex]
[tex]$A=\frac{32 x+144}{x-8}+4 x+18$[/tex].
For minimum paper size [tex]$\frac{d A}{d x}$[/tex] must be =0, hence,
[tex]$\frac{d A}{d x}=\frac{32(x-8)-(32 x+144)}{(x-8)^2}+4=0$[/tex]
[tex]$\frac{-400}{(x-8)^2}+4=0$[/tex]
(x-8)² = 100
x-8 = 10
[tex]$\mathrm{x}=18$[/tex], hence [tex]$\mathrm{y}=4+\frac{50}{x-8}=9$[/tex]
Dimension of minimum paper size would be 18 inches by 9 inches.
The complete question is:
You are designing a rectangular poster to contain 50 in^2 of printing with a 4-in. margin at the top and bottom and a 2-in margin at each side. What overall dimensions will minimize the amount of paper used?
To learn more about decimal places refer to:
https://brainly.com/question/1827193
#SPJ13
m multipled by the square of n
Answer:
mn²
Step-by-step explanation:
the square of n is n² and m multiplied by this is
mn²
Which number is greater than 555,621,000?A.5.0 x 10*6B.6.2 x 10*7C.5.55621 x 10*7D.9.99 x 10*6
Given:
[tex]555,621,000[/tex]Consider the individual options and compare them with the given number.
A.
[tex]5.0\times10^9[/tex][tex]\text{Use }10^9=1,000,000,000.[/tex][tex]5.0\times10^9=5.0\times1,000,000,000[/tex][tex]5.0\times10^9=5,000,000,000[/tex]We know that
[tex]5,000,000,000>555,621,000[/tex]This option is correct.
B.
[tex]6.2\times10^7[/tex][tex]\text{Use }10^7=10,000,000.[/tex][tex]6.2\times10^7=6.2\times10,000,000[/tex][tex]6.2\times10^7=62,000,000[/tex]We know that
[tex]62,000,000<555,621,000[/tex]This option is not correct.
C.
[tex]5.55621\times10^7[/tex][tex]\text{Use }10^7=10,000,000.[/tex][tex]5.55621\times10^7=5.55621\times10,000,000[/tex][tex]5.55621\times10^7=55,562,100[/tex][tex]55,562,100<555,621,000[/tex]This option is not correct.
D.
[tex]9.99\times10^6[/tex][tex]\text{Use }10^6=1,000,000.[/tex][tex]9.99\times10^6=9.99\times1,000,000[/tex][tex]9.99\times10^6=9,990,000[/tex][tex]9,990,000<555,621,000[/tex]This option is not correct.
Final answer:
[tex]5.0\times10^9\text{ is greater than 555,621,000.}[/tex]Option A is correct.
Flan- servers 10 people; $10.85 per person 1/8 teaspoon salt.1(12 fluid once) 1 teaspoon vanilla1/4 cup brown sugar
Filling with the information given, we have:
Multiply the original recipe by 10 (Since we have to serve 10 people)
New recipe:
Salt: 1/8 x 10 = 10/8 = 5/4 (Multiplying fractions and simplifying)
5/4 = 1 1/4 ( Converting the fraction to a mixed number)
Evaporated milk : 1 x 10 = 10 cans.
Vanilla: 1 x 10 = 10 teaspoons.
Brown sugar: 1/4 x 10 = 10/ 4 = 5/2 (Multiplying fractions and simplifying)
5/2 = 2 1/2 (Converting the fraction to a mixed number)
The values of the new recipe are:
Salt: 1 1/4
Evaporated milk: 10 cans
Vanilla: 2 1/2 teaspoons
Brown sugar: 2 1/2 cups
The mass of a bull is 325 kg. This is 175 kg more than the mass of a calf. The mass of a calf is 107 kg less than the mass of a cow.
Calculate the mass of a cow
Answer:
257 kg
Step-by-step explanation:
Hello!
Given Info:Bull = 325 kgCalf = 175 kg less than BullCow = 107 kg more than the calfCalf:325 - 175150Cow:150 + 107257The mass of the cow is 257 kg.
need help assap look in the picture
Answer:
8
Step-by-step explanation:
To find the perimeter, you must add the lengths of all sides.
In this question the perimeter is given, which is 63.
63 = 12 + 12 + 3x + 2x + 1 + x + 2
1. Add the numbers
63 = 12 + 12 + 3x + 2x + 1 + x + 2
12 + 12 + 1 + 2 = 27
63 = 27 + 3x + 2x + x
2. Combine Like Terms
63 = 27 + 3x + 2x + x
x = 1
3x + 2x + 1x = 6x
63 = 27 + 6x
3. Move Variable to the left
63 = 27 + 6x
63 = 6x + 27
4. Subtract 27 from both sides, the opposite of adding 27
63 = 6x + 27
63 - 27 = 6x + 27 - 27
36 = 6x
5. Divide by the same factor, the opposite of multiplying 6
36 = 6x
36/6 = 6x/6
6. Cancel out the 6s but leave the x
36/6 = 6x/6
x = 6
So, now that we know that x = 6 we can solve the expression, x + 2, to find out the length of the side BC.
6 + 2 = 8
Supposed that you purchased an old property for $120,000. You decide to mark
up the value by 40% before you put it on the market. If your real estate agent
charges 5.5% commission on the sale, how much did you make on the sale?
Answer:
158,760$
Step-by-step explanation:
120,000$ + 40%=168,000$-5.5%=158,760$
An investment grows by 4% per year for 5 years. By what percent does it increase over the 5-year period?
ill give brainliest if i can have help, i am having trouble turning on axis, can someone explain? (refer to image somewhere lol)
Answer:
a=2,-2 b=-5,-1 c=-1,-2
Step-by-step explanation:
you just put the shape the opisite way
Find the volume of the solid to the nearest unit. 13 A 6 A drawing not to scale 3 O 546 ft 3 O 1092 ft 3 O 273 ft 3 O 422 ft
Volume = Area of the base * height
Area of the base = (7 * 6) / 2
Area of the base = 42/2
Area of the base = 21ft^2
Volume of the prism = 21 * 13
Volume of the prism = 273 ft^3 The thi
A car travels for 15km in a city at a Certain speed-Dutside the city it travels 72km at twice its former speed. If the total travelling time is 1hour 8minutes find the average speed .
If the total traveling time is 1 hour 8 minutes f the average speed is 45 km/h.
This is a problem from time and distance. We can solve this equation by following a few steps.
Let's assume the car travel in the city for t minutes and the average speed is v.
According to the question, the car travel outside the city for, (68- t) minutes as 1 hour 8 minutes is equal to 68 minutes.
Therefore, the average speed (v) in the city = 15/t km/minute as v = s/t where v represents the speed, t represents the taken time and s represents the distance.Hence, the speed outside the city = 72/(68- t) km/minute.As per the question, Outside the city, it travels at twice its former speed v.
Now, we can form an equation, 2 (15/t) = 72/(68- t).
Let's simplify the given equation. 30/t = 72/(68- t)
Or, 72t = 30(68- t) [cross multiplication]
Or, 72t = 2040 - 30t
Or, 102t = 2040 [add with +30t both sides]
Or, t = 2040/102
Or, t = 20 [dividing by 102 both sides]
Therefore we can conclude that the average speed ( km/h) is (15×60) / 20 = 45 km/h.
To learn more about distance and time visit,
brainly.in/question/23588569
#SPJ9
Multiple choice triangle. im pretty sure its pythagorean theorem but please let me know
To solve this triangle, we cannot use either the Pythagorean Theorem or the Law of Cosines. We need more information.
Conversely, we can use SOHCAHTOA, in the sense that we can use the SOH part of this (Sine = opposite side over hypotenuse), that is, we can use angle 33 as the reference angle, and we have a right triangle here. Then, using trigonometric ratios, we can use:
[tex]\sin (\theta)=\frac{opp}{hyp}\Rightarrow\sin (33)=\frac{x}{29}\Rightarrow x=29\cdot\sin (33)\Rightarrow x=15.7945[/tex]We also can use the Law of Sines to solve it:
[tex]\frac{x}{\sin(33)}=\frac{29}{\sin(90)}\Rightarrow\frac{x}{\sin(33)}=\frac{29}{1}\Rightarrow x=29\cdot\sin (33)\Rightarrow x=15.7945[/tex]Therefore, we can solve this triangle using both Law of Sines and SOHCAHTOA. (We can select two options: c and d.)
please help me again )))))))))
Answer: -14/5, -2.25, 1 1/4, 3/2
Step-by-step explanation:
Answer:
-14/5, -2.25, 1 1/4, 3/2
Step-by-step explanation:
I double-checked, and I believe it's correct.
P.S, if I could get Brainliest, it'd mean a lot to me! Thanks!
John is a software salesperson. His base salary is $2300 and he makes $70 more for every copy of English is Fun he sells. His total pay, P (in dollars), after selling c copies is given by the following.
P=70c+2300
(a) If john’s total pay is $4750, how many copies did he sell?
(b) What is john’s total pay if he sells 25 copies?
Answer:
A - 35 copies
B - $4050
Step-by-step explanation:
A-
2300 + 70c = 4750
70c = 4750 - 2300
70c = 2450
c = 35
He sold 35 copies
B-
P = 2300 + 70(25)
P = 2300 + 1750
P = $4050
Total if he sold 25 copies: $4050
A fisher finder shows a large fish at 13 ft below the surface and a smaller fish 4 ft below surface. what is the expressions that are equivalent to the distance between the fish
Answer:
Distance = 9 ft
Explanation:
We can represent the position of the large fish with the number -13 because it is 13ft below the surface. In the same way, we can represent the position of the smaller fish with the number -4.
Then, the distance between the fish will be the absolute value of the difference between their positions. So, the expressions that are equivalent to the distance between the fish are:
| - 13 - ( - 4) | = | - 13 + 4| = 9
or
| -4 - (- 13) | = | - 4 + 13 | = 9
Therefore the distance between the fish is 9 ft
for which values of (A) the system has at least one solution
Answer
The values of a that ensures that the system has at least one solution is
a > (21/127)
Explanation
We are told to find the values of a that ensures that the system has at least one solution. The system of equations include
3 (a - 5x) < 1 + x
2 - (x/2) > 3 + 5 (x - a)
To do this, we need to solve the expressions
3 (a - 5x) < 1 + x
3a - 15x < 1 + x
We can rewrite this as
1 + x > 3a - 15x
x + 15x > 3a - 1
16x > 3a - 1
Divide both sides 16
[tex]\begin{gathered} \frac{16x}{16}>\frac{3a-1}{16} \\ x>\frac{3a}{16}-\frac{1}{16} \end{gathered}[/tex]We then solve the second one. But to do this, let's multiply through by 2
2 - (x/2) > 3 + 5 (x - a)
4 - x > 6 + 10 (x - a)
we can rewrite as
6 + 10 (x - a) < 4 - x
6 + 10x - 10a < 4 - x
10x + x < 10a - 6 + 4
11x < 10a - 2
Divide both sides by 11
[tex]\begin{gathered} \frac{11x}{11}<\frac{10a-2}{11} \\ x<\frac{10a}{11}-\frac{2}{11} \end{gathered}[/tex]The two solutions are
x > (3a/16) - (1/16)
x < (10a/11) - (2/11)
To find a lasting solution, we need the inequality sign to be the same, so, we need to multiply through one of the equations by -1
x > (3a/16) - (1/16)
-x < (-3a/16) + (1/16)
So, the system of equations become
-x < (-3a/16) + (1/16)
x < (10a/11) - (2/11)
We can then add the two equations
-x + x < (-3a/16) + (1/16) + (10a/11) - (2/11)
0 < (-3a/16) + (10a/11) + (1/16) - (2/11)
0 < -0.1875a + 0.9091a + 0.0625 - 0.1818
0 < 0.7216a - 0.1193
Rewrite
0.7216a - 0.1193 > 0
0.7216a > 0.1193
Divide both sides by 0.7216
(0.7216a/0.7216) > (0.1193/0.7216)
a > 0.1653
a > (21/127)
Hope this Helps!!!
Give a formular on how to calculate growth rate
Answer:
Straight-line percent change method example
Growth rate = (489 - 402) / 402. Absolute change = 87 (489 - 402) Growth rate = 0.2164 (87 / 402) Percent change = 21.64% (0.2164 x 100)
The graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the range of the function.
The range of the function is determined as 1 ≤ M ≤ 6.5 kg.
What is range of a function?The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Also we can defined a domain of a function as all the possible values that go into a function.
From the graph the range of the function of the mass of the bucket is calculated as follows;
The minimum value of the mass of the bucket = 1
The maximum value of the mass of the bucket = 6.5 kg
The range of the function (mass, M of the bucket) = {1, 2, 3, 4, 5, 6.5 kg}
1 ≤ M ≤ 6.5 kg
Thus, the range of the function includes numbers ranging from 1 to 6.5 kg. That is {1, 2, 3, 4, 5, 6.5 kg}.
Learn more about range of a function here: https://brainly.com/question/7644636
#SPJ1
The net of a square pyramid is shown below. What is the surface area of the pyramid?
Answer:
qt 456u8u64t3544
Step-by-step explanation:
for wicks watchful warships x