Answer:
Exactly One Solution
Step-by-step explanation:
4x + 2 = x + 8
3x = 6 Simplify.
x = 2 Divide by 2.
Answer:
One solution, x = 2
Step-by-step explanation:
4x + 2 = x + 8 (Given)
4x = x + 6
(The 2 is subtracted from the right side, therefore the left side is also subtracted. 8 becomes 6.)
3x = 6
(The x is subtracted from the right side to the left side. Thus turning the 4x into 3x)
x = 2
(The 3 is divided out to get x alone. So, the 6 has to be divided by 3 as well, turning it into 2)
A farmer decides to make three identical pens with 88 feet of fence. The pens will be next to each other sharing a fence and will be up against a barn. The barn side needs no fence. What dimensions for the total enclosure (rectangle including all pens) will make the area as large as possible?
Answer:
The long fence, AC = 44 feet
4 shorter segments at 11feet each = 44 feet
Area = 484 ft^2
Step-by-step explanation:
The three pens will share one fence section parallel to the barn, we'll call it AB. Each pen will need two side fence segments, from the front fence to the barn. We'll call those portions AC. We need four of them: two for the outer sides and two more to divide up the space equally among the three pens. The total area would be AB*AC.
We know that AC + 4AB = 88 feet.
or AC = (88feet - 4AB)
Area = AB(88feet - 4AB)
Area = 88AB - 4AB^2
To maximize the area, we can take the first derivative and set it equal to zero:
Area' = 88 - 8AB
0 = 88 - 8AB
AB = 11 feet
AC = (88 - 4AB)
AC = (88 - 44)
AC = 44 feet
The fours segments of fence:
AC + 4AB = 88 feet
(44) + 4(11 feet) = 88feet
Area = 44' x 11 ft' = 484 ft^2
8. If the measure of one side of a square is increased by 2 centimeters and the measure of
the adjacent side is decreased by 2 centimeters, the area of the resulting rectangle is
32 square centimeters. Find the measure of one side of the square (the original figure).
Answer:
6 cm
Step-by-step explanation:
If the original side length is x, then the modified square has an area of ...
A = LW
32 = (x +2)(x -2) = x^2 -4
36 = x^2 . . . . . . . . add 4
6 = x . . . . . . . . . . take the square root
The original figure has a side length of 6 cm.
__
Check
The modified figure is 8 cm by 4 cm = 32 cm^2.
can somebody please tell me if this is correct or not
Answer:
I would have done it the same way. Believing it is correct.
Step-by-step explanation:
Answer: Looks precise
Step-by-step explanation:
Jack was the science Museum in sabotage the recycling plant had an average speed of 26KM/H. Sometime later Aaliyah love traveling in the opposite direction with an average speed of 57KM/H. After Jack had traveled for four hours they were 332KM a part. How long did Aaliyah travel?
Which point would not be a solution to the system of linear inequalities shown below?
Answer:
C
Step-by-step explanation: looks right
dont trust it though
The angle of elevation to a nearby tree from a point on the ground is measured to be
73°. How tall is the tree if the point on the ground is 28 feet from the tree? Round
your answer to the nearest tenth of a foot if necessary.
Answer:91.6
Step-by-step explanation:
The height of the tree if the point on the ground is 28 feet from the tree is 91.5 ft.
The angle of elevation is given 73°. The distance between the point on the ground and the tree is 28 feet.
What is a trigonometric function?In mathematics, the trigonometric function is a function that deals with the sides of the right-angled triangle and angles.
sin, cos, tan, cosec, sec, and cot are the basic function of trigonometric.
We know that tan Ф = perpendicular / Base
tan 73° = h / 28
tan 73° × 28 = h
3.27 × 28 =h
h = 91.5 ft
Therefore, the height of the tree if the point on the ground is 28 feet from the tree is 91.5 ft.
Learn more about a trigonometric function;
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Find the area of triangle ABC. Give your answer correct to 1 decimal place. A 9 cm 8 cm 10 cm B
HELP PLEASE HAHAHA
(03.04 MC)The youth group is going on a trip to the state fair. The trip costs $58. Included in that price is $12 for a concert ticket and the cost of 2 passes, one for the rides and one for the game booths. Each of the passes costs the same price. Write an equation representing the cost of the trip, and determine the price of one pass. Solve your equation by showing your work and steps.
Answer:
58= 2x +12
each pass is 23 dollars
Step-by-step explanation:
let x represent the cost of the passes
58= 2x + 12
solve for x
58-12 = 2x +12 -12
46 = 2x
46/2 =2x/2
23 = x
Find a solution to the inequality x > 4.
A. 8
B. 3
C. 4
D. 0
Answer:
8
Step-by-step explanation:
Isn't it simple because all other numbers are less than 4?
The corner store sells pairs at a rate of $2.50 for per pair if Fiona has $15 how many pairs can if you fiona buy?
Answer: Fiona can buy six pairs.
15/2.5 = 6
Answer:
Fiona can buy 6 pairs
Step-by-step explanation:
2.50x 6
x-(2x+3)
how to solve and why you change the sign for the +3?
Answer:
-x - 3
Step-by-step explanation:
x-(2x + 3)
=> x-1(2x + 3)
=> x - 2x - 3
=> -x - 3
Therefore, this is the solution. Hoped this helped.
[tex]GeniusUser[/tex]
Answer:
Step-by-step explanation:
x-(2x+3)
Notice that we can't further simplify the things in the bracket so we should multiply by -1
Technically this is like:
x - 1(2x+3)
-1 times 2x = -2x , -1 times 3 is -3
= x - 2x - 3
= -x - 3
15 minutes how many students read the book in an hour
Answer:
Your reading speed will increase if you're reading a book you're familiar with than one you barely know. So, on average, you can read 40 to 50 pages of a book in an hour.
Step-by-step explanation:
What is the equation of g(x)? g(x) = 10x â€"" 3 g(x) = 10x 3 g(x) = 10x â€"" 3 g(x) = 10x 3.
The equation of g(x) is [tex]\rm g(x) = 10^{x-3}[/tex].
Given that,
The graphs of f(x) = 10x and its translation, g(x), are shown.
We have to determine,
What is the equation of g(x)?
According to the question,
The given graphs of two functions f(x) and g(x).
The function f(x) is an exponential function and is given by:
[tex]\rm f(x) = 10^x[/tex]
To find the equation for the transformed function g(x).
We could see that the graph of the function g(x) passes through points (3,1), (4,10), (5,100), and so on.
This means that the equation or the expression for the function g(x) is given by:
[tex]\rm g(x) = 10 ^{x-3}[/tex]
Substitute the value of x = 3 in the function g(x),
[tex]\rm g(x) = 10 ^{x-3}\\\\g(3) = 10^{3-3}\\\\g(3) = 10^0\\\\g(3) = 1[/tex]
Substitute the value of x = 4 in the function g(x),
[tex]\rm g(x) = 10 ^{x-3}\\\\g(4) = 10^{4-3}\\\\g(3) = 10^1\\\\g(3) = 10[/tex]
Hence, The equation of g(x) is [tex]\rm g(x) = 10^{x-3}[/tex].
For more details refer to the link given below.
https://brainly.com/question/13148696
Answer:
the answer is a g(x)= 10x^-3
Step-by-step explanation:
Tina rolls a dice what is the probability that she rolls a 1 b3 c4 d 3 or 4
Using the probability concept, it is found that there is a [tex]\mathbf{\frac{1}{6}}[/tex] probability that she rolls a 1.
A probability is the number of desired outcomes divided by the number of total outcomes.In a dice, there are 6 sides, one of which is a roll is 1, then:
[tex]p = \frac{1}{6}[/tex]
There is a [tex]\mathbf{\frac{1}{6}}[/tex] probability that she rolls a 1.
For more on probabilities, you can check https://brainly.com/question/24437717
May I please receive help?
Answer:
4.8 feet
Step-by-step explanation:
a² + b² = c²
a² + 11² = 12²
a² + 121 = 144
a² = 23
a = [tex]\sqrt{23}[/tex]
a, or the height of the kite ≈ 4.8
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
What is the range of function g?
Answer:
C
Step-by-step explanation:
This function starts at point (1, 2), so 2 is inclusive. Therefore the range of this function is:
[tex]y \geq 2[/tex]
What is the length of leg y of the right triangle? (1 point)
A right triangle with hypotenuse 37 and legs 35 and y
A)2
B)8
C)12
D)35
Answer:
C)12
Step-by-step explanation:
[tex] {y}^{2} = {37}^{2} - {35}^{2} [/tex]
[tex] {y}^{2} = 1369 - 1225[/tex]
[tex] {y}^{2} = 144[/tex]
[tex]y = 12[/tex]
Is the system of equations consistent and independent, consistent and dependent, or inconsistent?
y=3x+4
y=3x+3
Select the correct answer from the drop-down menu.
Answer:
y=3x+4 I think I am correct hola amigo señorita a person in my class is called adiola adiola adiola hah
Answer:
Its inconsistent
Step-by-step explanation:
If you are doing 5.11 Unit Test: Systems of Equations - Part 1 from K12, this is your answer
The graphs of the lines do not intersect, so the graphs are parallel and there is no solution. Since there are no solutions, its inconsistent.
If it has at least ONE solution, its consistent.
If it has EXACTLY ONE solution, its consistent in dependable
If it has INFINITE AMOUNT of solutions, its consistent dependable
I'm having trouble. Can someone answer?
Answer:
okay wait
Step-by-step explanation:
What is the equation of the line.
Answer:
y = 1/2x - 1
slope = 1/2
y-intercept is
(0,-1)
37. Briefly explain how the use of credit helped increase the average
American's standard of living in the 20th century.
Answer: If a person has a better credit, they have better chances of getting the job they had applied for. Getting the job means they get a stable income. Having a stable income helps a person to buy all essential needs.
Step-by-step explanation:
1
6 cm
Diagram NOT
accurately drawn
9cm
Scm
11 cm
2
6 cm
18 cm
The diagram shows a shape.
All of its corners are right angles.
Work out the area of the shape.
The area of the shape is 110 square centimeters
From the diagram, the shape can be subdivided into rectangles of the following dimensions:
6cm by 11cm5cm by 6cm7cm by 2cmSo, the area of the shape is the sum of the areas of the three rectangles.
This gives
[tex]Area = 6cm \times 11cm + 5cm \times 6cm + 7cm \times 2cm[/tex]
Evaluate the products
[tex]Area = 66cm^2 + 30cm^2 + 14cm^2[/tex]
Add the terms
[tex]Area = 110cm^2[/tex]
Hence, the area of the shape is 110 square centimeters
Read more about areas at:
https://brainly.com/question/8408690
Tim is an elementary school art teacher. His students are sculpting a replica of a shark out of clay. Tim has given them one block of clay to make 20 conical shark teeth for the sculpture. The block contains 81 cm3 of clay. If each tooth is solid and has a 2. 5 cm base diameter, what is the maximum height each tooth can be? Assume that the students use all the clay. A. 1. 25 cm B. 2. 27 cm C. 2. 47 cm D. 3. 57 cm E. 4. 50 cm.
The maximum height each tooth is 2.47cm.
The first step is to determine the maximum volume of a tooth.
Maximum volume of a tooth = volume of the block / number of teeth
81 cm³ / 20 = 4.05cm³
The formula to determine the height of a cone is:
Height = volume ÷ [tex]\frac{1}{3}[/tex]πr²
Where:
π = pi = 22/7 r = radius = 2.5 / 2 = 1.25cmHeight = 4.05 ÷ [tex]\frac{1}{3}[/tex] x [tex]\frac{22}{7}[/tex] x 1.25² = 2.47 cm
To learn more about the volume of a cone, please check: https://brainly.com/question/1315822
Which graph shows the solution to the system of linear inequalities?
y ≥ 2x + 1
y ≤ 2x – 2
Answer:
See belowStep-by-step explanation:
Given system:
y ≥ 2x + 1 y ≤ 2x – 2The solution is the common area shaded by the inequalities.
The lines are parallel because of same slope.
Both lines are solid because of equal sign in both inequalities.
The first inequality has a y-intercept of 1 and shaded area is to the left of the line since the value of y is greater as x increases.
The second inequality has a y-intercept of -2 and shaded area is to the right of the line since the value of y is greater as x increases.
The matching graph is the second picture (or attached below) and there is no solution.
From the given inequalities we have boundaries (0, -1) and (0, 2). Therefore, option B is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given system of inequalities are y ≥ 2x + 1 and y ≤ 2x – 2.
The solution is the common area shaded by the inequalities.
The lines are parallel because of same slope.
Both lines are solid because of equal sign in both inequalities.
The first inequality has a y-intercept of 1 and shaded area is to the left of the line since the value of y is greater as x increases.
The second inequality has a y-intercept of -2 and shaded area is to the right of the line since the value of y is greater as x increases.
Therefore, option B is the correct answer.
To learn more about the inequalities visit:
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A company needs to package 2,400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container can hold 80 pencils. Each box costs the company $0. 50, while each cylindrical container costs $0. 75. Which packaging should the company use to minimize cost? Explain. The rectangular prism boxes should be used because they will cost the company $2. 50 less than using the cylindrical containers. The cylindrical containers should be used because they will cost the company $2. 50 less than using the rectangular boxes. The rectangular prism boxes should be used because they will cost the company $5. 00 less than using the cylindrical containers. The cylindrical containers should be used because they will cost the company $5. 00 less than using the rectangular boxes.
The true statement is (a) The rectangular prism boxes should be used because they will cost the company $2. 50 less than using the cylindrical containers.
The given parameters are:
[tex]Pencils = 2400[/tex] --- the pencils needed
The number of pencils the prism can hold is:
[tex]Prism =60[/tex]
Divide the number of pencils needed by the number of pencils in 1 rectangular prism, to calculate the number of prisms needed (n1)
[tex]n_1 = \frac{Pencils}{Prism}[/tex]
So, we have:
[tex]n_1 = \frac{2400}{60}[/tex]
[tex]n_1 = 40[/tex]
A rectangular prism costs $0.50.
So, the total cost is:
[tex]Total\ cost = 40 \times 0.50[/tex]
[tex]Total\ cost = \$20[/tex]
The number of pencils the cylinder can hold is:
[tex]Cylinder=80[/tex]
Divide the number of pencils needed by the number of pencils in 1 cylinder box, to calculate the number of cylinders needed (n2)
[tex]n_2 = \frac{Pencils}{Cylinder}[/tex]
So, we have:
[tex]n_2 = \frac{2400}{80}[/tex]
[tex]n_2 = 30[/tex]
A cylinder costs $0.75.
So, the total cost is:
[tex]Total\ cost = 30 \times 0.75[/tex]
[tex]Total\ cost = $22.5[/tex]
By comparison, the rectangular prism costs $2.5 less than the cylinder
Hence, the true statement is (a)
Read more about volumes at:
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Evaluate 5−1/−90. Write your answer as a fraction in simplest form.
Answer:
2/-45
Step-by-step explanation:
5-1 = 4
4/-90 = 2/-45
Hope that helps
Solve.
−1.3=x−(−13.2)
What is the solution to the equation?
Enter your answer in the box.
x =
x= -14.5
Step-by-step explanation:
-1.3=x-(-13.2)
the two - signs cross eachother out, making it a +.
making the equation -1.3=x-(-13.2) turn into -1.3=x+13.2.
so you should automatically know your x is going to have to be negative.
What I did:
13.2+1.3=14.5,
but since the 1.3 was actually negative, (-1.3) the 14.5 will turn negative, making it -14.5
Evaluate the function for = and =.
()=−
Answer:Example: evaluate the function f(x) = 2x+4 for x=5
Just replace the variable "x" with "5":
f(5) = 2×5 + 4 = 14
Answer: f(5) = 14
Step-by-step explanation:
Miranda bought oranges which are sold in a bag of 5 for $2. The next day she bought 20 oranges which was $8. What is the table for this problem? (Create a table with the information above with at least 5 ordered pairs)
Answer:
I think the answer is $170
Solve for x 18 Х 16 24 0 15 O 12 0 24 o 17
Answer:
Look it up
Step-by-step explanation:
