The resulting equation after the first step in the solution is:
2v + 4 = 8.
What is Equation?An equation is a mathematical statement that asserts the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, or exponentiation.
we have the Equation v + 4 + v =8
Now, simplifying we get
2v + 4= 8
2v = 4
v =2
To obtain this equation, we combined the like terms "v" on the left side of the equation, which gives us 2v. The rest of the equation remains unchanged.
Therefore, the correct answer is : 2v + 4 = 8.
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A scale drawing of a rectangular playground has a length of 20 inches and a width of 10 inches as shown.The scale is 1 inch = 15 feet.
Write a scale that relates the area of the drawing to the area of the actual playground. Show or explain your work and write your answer in the space provided.
Answer:
4:9
Step-by-step explanation:
Find the area in inch first:
20 inch × 10 inch = 200 inch
Area in feet:
(20×15) + (10×15) = 450 inch
Area of the drawing : Area of the actual playground
200:450
Simplify it by dividing by 5
Last answer =4:9
A number is chosen at random from 1 to 50. Find the probability of see tiny multiples of 12
Answer:
4/50
Step-by-step explanation:
12,24,36,48 are multiples of 12
Kim is earning money for a trip. She has saved $60 and she earns $10 per hour babysitting. The total amount of money earned
(y) after (x) number of hours worked is given by the equation y = 10x + 60.
How many hours will she need to work in order to earn $300 for her trip?
Answer:
x=24
Step-by-step explanation:
you need 300.
10x + 60?
10 x 3 = 300
300 - 60 = 240
300 = (10 x 24) + 60
These are Questions/answers for #1, 2, 3, 17, 18, 19 & 20 if you can't see what it says in the picture (Please answer all questions in correct order)
#1.Given w = −96i −180j, what are the magnitude and direction of −4w? Round the answers to the nearest whole number.
204; 62°
816; 62°
204; 242°
816; 242°
# 2. A basketball player shoots a free throw, where the position of the ball is modeled by x = (24cos 48°)t and y = 6.1 + (24sin 48°)t − 16t 2. What is the height of the ball, in feet, when it is 13 feet from the free throw line? Round to three decimal places.
10.053
10.292
10.673
11.025
#3.Vectors u and v are shown on the graph.
vectors u and v share an initial point and vector u points down 8 units and vector v points to the right 6 units
Which of the following vectors represents u + v? (Please put/show a graph if you can)
17.What are the magnitude and direction of u + v + w? Round the magnitude to three decimal places and the direction to the nearest degree.
53.241; 355°
52.822; 355°
53.241; 5°
52.822; 5°
#18. Which point represents z1 + z2?
P
Q
R
S
Question 19. A barge is being towed by two tugboats, using ropes with force vectors as shown.
Two vectors named F sub 1 and F sub 2 that share an initial point from the barge each pointing to a different tugboat
Given vector F sub 1 equals open angled bracket 12000 comma 7000 close angled bracket and vector F sub 2 equals open angled bracket 14500 comma negative 5000 close angled bracket comma what is the angle between the ropes? Round to the nearest degree.
31°
33°
49°
54°
Question 20.Given v = 8i − 3j and w = −12i + 4j, find 7v − 2w.
−80i − 29j
−80i + 29j
80i − 29j
80i + 29j
Answer:
See below for answers and explanations (along with a graph for #3)
Step-by-step explanation:
Problem #1
Applying scalar multiplication, [tex]-4w=-4\langle-96,-180\rangle=\langle384,720\rangle[/tex].
Its magnitude would be [tex]||-4w||=\sqrt{384^2+720^2}=816[/tex].
Its direction would be [tex]\displaystyle\theta=tan^{-1}\biggr(\frac{720}{384}\biggr)\approx61.927^\circ\approx62^\circ[/tex].
Thus, B) 816; 62° is the correct answer
Problem #2
Find the time it takes for the ball to cover 13ft:
[tex]x=(24\cos48^\circ)t\\13=(24\cos48^\circ)t\\t\approx0.8095[/tex]
Find the height of the ball at the time it takes for the ball to cover 13ft:
[tex]y=6.1+(24\sin48^\circ)t-16t^2\\y=6.1+(24\sin48^\circ)(0.8095)-16(0.8095)^2\\y\approx10.053[/tex]
Thus, A) 10.053 is the correct answer
Problem #3
We have [tex]u=\langle0,-8\rangle[/tex] and [tex]v=\langle6,0\rangle[/tex] as our vectors. Thus, [tex]u+v=\langle0+6,-8+0\rangle=\langle6,-8\rangle[/tex]. Attached below is the correct graph. You can also solve the problem visually by using the parallelogram method where the resultant vector is the diagonal of the parallelogram.
Problem 4 (#7)
[tex]\displaystyle t \cdot v=(7)(-10)+(-3)(-8)=-70+24=-46[/tex]
Thus, C) -46 is the correct answer
Problem 5 (#8)
Find [tex]r[/tex] and [tex]\theta[/tex]:
[tex]r=\sqrt{x^2+y^2}=\sqrt{2^2+(-8)^2}=\sqrt{4+64}=\sqrt{68}=2\sqrt{17}\approx8.246[/tex]
[tex]\displaystyle\theta=tan^{-1}\biggr(\frac{y}{x}\biggr)=tan^{-1}\biggr(\frac{-8}{2}\biggr)\approx-75.964^\circ[/tex]
Find the true direction angle accounting for Quadrant IV:
[tex]\theta=360^\circ-75.964^\circ=284.036^\circ[/tex]
Write the complex number in polar/trigonometric form:
[tex]z=8.246(\cos284.036^\circ+i\sin284.036^\circ)[/tex]
Thus, C) 8.246(cos 284.036° + i sin 284.036°) is the correct answer
Problem 6 (#12)
Eliminate the parameter and find the rectangular equation:
[tex]x=3t\\\frac{x}{3}=t\\ \\y=t^2+5\\y=(\frac{x}{3})^2+5\\y=\frac{x^2}{9}+5\\9y=x^2+45\\0=x^2-9y+45\\x^2-9y+45=0[/tex]
Thus, D) x^2-9y+45=0 is the correct answer
Problem 7 (#13)
Find the magnitude of the vector:
[tex]||v||=\sqrt{(-77)^2+36^2}=85[/tex]
Find the true direction of the vector accounting for Quadrant II:
[tex]\displaystyle \theta=tan^{-1}\biggr(\frac{36}{-77}\biggr)\approx-25^\circ=180^\circ-25^\circ=155^\circ[/tex]
Write the vector in trigonometric form:
[tex]w=85\cos155^\circ i+85\sin155^\circ j[/tex]
Thus, D) w=85cos155°i+85sin155°j is the corrwect answer
Problem 8 (#15)
[tex]\frac{z_1+z_2}{2}=\frac{(3-7i)+(-9-19i)}{2}=\frac{-6-26i}{2}=-3-13i=(-3,-13)[/tex]
Thus, C) (-3,-13) is the correct answer
Problem 9 (#16)
Treat the golf ball and wind as vectors:
[tex]u=\langle1.3\cos140^\circ,1.3\sin140^\circ\rangle[/tex] <-- Golf Ball
[tex]v=\langle1.2\cos50^\circ,1.2\sin50^\circ\rangle[/tex] <-- Wind
Add the vectors:
[tex]u+v=\langle1.3\cos140^\circ+1.2\cos50^\circ,1.3\sin140^\circ+1.2\sin50^\circ\rangle\approx\langle-0.225,1.755\rangle[/tex]
Find the magnitude of the resultant vector:
[tex]||u+v||=\sqrt{(-0.225)^2+1.755^2}\approx1.769[/tex]
Find the true direction of the resultant vector accounting for Quadrant II:
[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{1.755}{-0.225}\biggr)\approx-82.694^\circ\approx-83^\circ=180^\circ-83^\circ=97^\circ[/tex]
Thus, B) 1.769 m/s; 97° is the correct answer
Problem 10 (#17)
Identify the vectors and add them:
[tex]u+v+w=\langle50\cos20^\circ,50\sin20^\circ\rangle+\langle13\cos90^\circ,13\sin90^\circ\rangle+\langle35\cos280^\circ,35\sin280^\circ\rangle=\langle50\cos20^\circ+13\cos90^\circ+35\cos280^\circ,50\sin20^\circ+13\sin90^\circ+35\sin280^\circ\rangle=\langle53.062,-4.367\rangle[/tex]
Find the magnitude of the resultant vector:
[tex]||u+v+w||=\sqrt{53.062^2+(-4.367)^2}\approx53.241[/tex]
Find the true direction of the resultant vector accounting for Quadrant IV:
[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{-4.367}{53.062}\biggr)\approx-4.705^\circ\approx-5^\circ=360^\circ-5^\circ=355^\circ[/tex]
Thus, A) 53.241, 355° is the correct answer
Problem 11 (#18)
We observe that [tex]z_1=-8-6i[/tex] and [tex]z_2=4-4i[/tex], hence, [tex]z_1+z_2=(-8-6i)+(4-4i)=-4-10i[/tex]
Thus, Q is the correct answer
Problem 12 (#19)
Find the dot product of the vectors:
[tex]F_1\cdot F_2=(12000*14500)+(7000*-5000)=174000000+(-35000000)=139000000[/tex]
Find the magnitude of each vector:
[tex]||F_1||=\sqrt{12000^2+7000^2}=1000\sqrt{193}\\||F_2||=\sqrt{14500^2+(-5000)^2}=500\sqrt{941}[/tex]
Find the angle between the two vectors:
[tex]\displaystyle \theta=\cos^{-1}\biggr(\frac{F_1\cdot F_2}{||F_1||||F_2||}\biggr)\\ \theta=\cos^{-1}\biggr(\frac{139000000}{(1000\sqrt{193})(500\sqrt{941})}\biggr)\\\theta\approx49.282^\circ\approx49^\circ[/tex]
Thus, C) 49° is the correct answer
Problem 13 (#20)
Using scalar multiplication, [tex]7v-2w=7\langle8,-3\rangle-2\langle-12,4\rangle=\langle56,-21\rangle-\langle-24,8\rangle=\langle56-(-24),-21-8\rangle=\langle80,-29\rangle=80i-29j[/tex]
Thus, A) -80i - 29j is the correct answer
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 5 child bikes and 15 adult bikes in a week. No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Answer:
C
Step-by-step explanation:
PLEASE HELP ME WITH THIS!!
Otis measured the heights of several sunflowers. He found that their heights were 1, 4, 6, 9, and 10 feet. Otis found that the mean was 6 feet and the range was 9 feet. Which numbers describe the center and spread of this data set?
Answer: 6 feet describes the center, and 9 feet describes the spread
Step-by-step explanation:
The center of a data set is mostly considered as the median or the mean
Here mean is 6 (given). And median is also 6. As 6 is exactly at the middle of the data set. (When arranged in ascending order)
Now, one of the way of calculating the spread is calculating the range, here it's given that the range is 9.
Therefore, 6 feet describes the center, and 9 feet describes the spread is correct.
Can you help me with the top question please I’ll give brainliest
Answer:
C
Step-by-step explanation:
Find the domain and range.
Answer:
Domain is all real #s
Range is (-∞, 4] or y < 4
Step-by-step explanation:
1. Dr. Orchid has 9 paintings she wants to hang side by side on her wall.
(a) In how many ways can she arrange all 9 paintings? Show your work.
(b) If she only wants to display 4 of the paintings, in how many ways can she choose the paintings she
wishes to display? Show your work.
Answer:
The number of ways to arrange the 9 paintings is 362880, and there are 126 ways to display only 4 out of the 9 paintings
Part A: The number of arrangements.The number of paintings is given as:
n = 9
The number of arrangement is then calculated using:
n! = 9!
Evaluate the factorial
n! = 362880
Part B: The number of selectionTo select 4 paintings from a total of 9, we make use of the following combination formula
Ways = 9C4
Evaluate the above expression using a calculator
Ways = 126
Hence, there are 126 ways to display only 4 out of the 9 paintings
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Simplify these expressions.
a. 6ab + (–3x) + 2ab
b. 12x + 4y + (–3x)
c. 6w + (–2y) + 3w
d. 4abc + (–9abc) + 10d
Answer:
a. 6ab +( - 3x) + 2ab
=6ab - 3x +2ab
=6ab + 2ab - 3x
=8ab - 3x
Step-by-step explanation:
Eliminated the brackets first
Collected like terms
Then I solved
A customer spent no more than $500 for a television
and a mounting kit. The customer expected to pay a
minimum of $300 for the television but actually paid
at least $75 more than that. What is the maximum
amount, in dollars, the customer could have spent for
the mounting kit after purchasing the television?
(Disregard the $ sign when gridding your answer.
The maximum amount, in dollars, the customer could have spent for the mounting kit after purchasing the television is $125.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let's suppose the customer spend $x on television, and $y on mounting kit.
x + y = 500
x = 300 + 75 = 375
y = 500 - 375 = $125
Thus, the maximum amount, in dollars, the customer could have spent for the mounting kit after purchasing the television is $125.
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HELP ASAP PLEAse!!! HOW DO YOU FIND THE LATERAL AREA OF THE TRIANGLE, (ALREADY GOT SURFACE AREA CORRECT), PLEASE ROUND IT TO THE NEAREST HUNDRETH
HELP! Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the
rounded values to calculate the next value. Round your final answer to the nearest tenth.
Answer:
b
Step-by-step explanation:
Volume of a Cylinder
The volume is 54,437.52.
Answer:
54,437.52 ( fifty four thousand four hundred thirty seven and fifty two thousanths.)
Step-by-step explanation:
Volume of rectangle and triangle problem. The one that has no answer
Answer:
6825 in^3
Step-by-step explanation:
First break the shape into two shapes a square prism and triangular prism
the volume of a square prism is equal to s^2 * h
and the volume of a triangular prism is 1/2 b * l *h
square prism:
v = s^2 * h
v = 13^2 * 30
v = 5070 in^3
triangular prism:
v = 1/2 b * l * h
v = 1/2 * 9 * 30 * 13
v = 1755 in^3
then you add the two volumes to get the total volume
5070 + 1755 = 6825 in^3
what is the distance between (7, -7) and (9,-9)
Answer: 2,-2
Step-by-step explanation: 9-7 is 2 and -9 minus -7 is minus 2.
Need some help please
A cube has a volume of 216 cubic inches. What is the width of the cube?
Answer:
6
Step-by-step explanation:
Find the cube root of 216
A student incorrectly determined that the length of DE is 29 cm explaining that 12-7 = 5 and 36-7 = 29 explain what mistake the student may have made and why this is not correct way to determine the length of a DE what is the actual length of DE
Answer:
The length of the hypotenuse ≈ 39.7 cm
Explanation:
Since the given triangle is a right-angled triangle, this means that we can apply the Pythagorean theorem.
The equation for Pythagorean calculation is:
(hypotenuse)² = (first leg)² + (second leg)²
In the given, we have:
first leg = 30 cm
second leg = 26 cm
Substitute with the givens in the above equation to get the hypotenuse as follows:
(hypotenuse)² = (30)² + (26)²
(hypotenuse)² = 1576
This means that:
either hypotenuse = √1576 = 39.69 ≈ 39.7 cm ..........> accepted
or hypotenuse = -√1576 = -39.69 ......> rejected as length can't be negative
Hope this helps :)
help me please…………….
Answer:
The answer is e. (x - 10 * y^2 * z) (x + 10 *y^2 *z)
Step-by-step explanation:
To explain it test all the options by distributing them.
Using an online website that I plugged into the calculator to factory gets answer e.
Mrs. Reynolds has $153. She buys a bicycle for $105.
Then, she finds $20 at the bottom of her purse.
How much money does she have now? Use the bar diagrams to help you.
Step 1:
Step 1: a bar diagram shows 105 and m, the money left after buying a bike. Together 105 and m are equal to 153.
Step 2:
Step 2: a bar diagram shows that 20 and m is equal to s, the money now.
Enter your answer in the box.
Mrs. Reynolds has $
now.
The total amounts of money which Mrs. Reynolds now has according to the descriptions in the task content is; $68.
How much does Mrs. Reynolds have now?It follows from the task content that;
Together 105 and m are equal to 153.20 and m is equal to s.On this note;
105 + m = 153m = 153 -105 = 48Hence, it follows that the amount of money, s she has now is;
s = 48 + 20 = $68Read more on addition and subtraction;
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f(x) = e^-x . Find the equation of the tangent to f(x) at x=-1
Answer:
The equation of the tangent line is given by the following equation:
[tex]\displaystyle y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg)[/tex]
General Formulas and Concepts:
Algebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinatey₁ - y coordinatem - slopeCalculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
*Note:
Recall that the definition of the derivative is the slope of the tangent line.
Step 1: Define
Identify given.
[tex]\displaystylef(x) = e^{-x} \\x = -1[/tex]
Step 2: Differentiate
[Function] Apply Exponential Differentiation [Derivative Rule - Chain Rule]:Step 3: Find Tangent Slope
[Derivative] Substitute in x = 1:∴ the slope of the tangent line is equal to [tex]\displaystyle \frac{-1}{e}[/tex].
Step 4: Find Equation
[Function] Substitute in x = 1:∴ our point is equal to [tex]\displaystyle \bigg( 1, \frac{1}{e} \bigg)[/tex].
Substituting in our variables we found into the point-slope form general equation, we get our final answer of:
[tex]\displaystyle \boxed{ y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg) }[/tex]
∴ we have our final answer.
---
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---
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Find the Volume. 4 1/2 ft 3 ft 7 1/5
Answer:
97.2 ft
Step-by-step explanation:
4 1/2*3*7 1/5=13.5*7.2=
97.2
Round 2566.36 to the nearest tenth
Can someone help please
Answer:
24sq.ft
Step-by-step explanation:
Area of a parallelogram = Base*HeightHere,
→Base = 6ft, Height = 4ft
→ 6*4ft
→24sq.ft
While writing area of a figure, we have to express the area in sq which means square ThankYouPlease mark me as brainliest
1) Find the circumference and Area
2) Find the Perimeter and Area
Thank you so much!
Answer:
See below.
Step-by-step explanation:
1) We know that the circumference of a circle can be found using the formula [tex]c=\pi d[/tex], so for this circle the circumference will be [tex]c=3.14 \times 40=125.6 \text{ yards}[/tex]. The formula for the area of a circle is [tex]A=\frac{1}{4}\pi d^2[/tex], so the area of this circle will be [tex]A=\frac{1}{4} \times 3.14 \times 40^2=1256 \text{ yards}[/tex].
2) First we'll work out the length of the curved side of the shape. That's [tex]\frac{1}{2}\times\pi d =\frac{1}{2} \times 3.14 \times 12=18.84 \text{ mm}[/tex]. Then, we'll add the length of the other two straight sides to get [tex]10.82 \times 2 + 18.84=40.48 \text{ mm}[/tex]. Next: the area of the semi-circle is [tex]\frac{1}{2} \times \frac{1}{4} \pi d^2 = \frac{1}{8} \times 3.14 \times 144 = 56.52 \text{ mm}[/tex]. Adding this to the areas of the two triangles: [tex]56.52+2 \times \frac{1}{2}bh=56.52+(\sqrt{10.82^2-9^2)}\times9 \approx 110.57 \text{ to 2 d.p.}[/tex]
Example: I am shopping for school supplies at Target and I have $130 extra. I see air pods on sale for
$120. / want to determine if I have enough money to cover the total purchase price, including tax,
before i get to the register. Here's how I would organize the problem in my head (or on paper) to get
an accurate calculation...
To determine if you have enough money to buy this product, calculate the sales tax and the final price of the product.
How to calculate sales tax?Sales tax is usually expressed as a percentage. Moreover, this percentage can slighly change depending on the state where you live.
Here is an example:
Sales tax in texas: 6.25%Price of the product / 100 x 6.25130/ 100 = 1.3 x 6.25 = 8.12Final price = 138.12
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Can someone explain why this equation equals 2?
Answer:
bc it dose
Step-by-step explanation:
Type The Correct Answer.
Answer:
6.3
Step-by-step explanation:
151.2/24 in order to find out how many miles he drove per day
the answer is 6.3 miles per day
Answer:
6.3 Miles
Step-by-step explanation:
just divide 151.2 by 24.