Answer:
The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol
A collection of nickels, dimes, and quarters consist of 15 coins with a total of $2.00. If the number of dimes is equal to the number of nickels, find the number of each type of coins.
Number graph ranging from negative four to four on the x and y axes. A line with a positive slope is drawn on the graph, passing through the labeled point A at (zero, two) and the labeled point B at three, three). What is the slope of the line passing through points A and B? Responses −3 − 3 , −15 − 1 5 14 1 4 13
The slope of the line passing through points A and B is 1/3.
The formula for the slope of a line to find the slope passing through points A and B. The formula is:
slope = (change in y) / (change in x)
Let's label the coordinates of point A as (x₁, y₁) and the coordinates of point B as (x₂, y₂).
Then, substitute the values and calculate the slope:
slope = (y₂ - y₁) / (x₂ - x₁)
slope = (3 - 2) / (3 - 0)
slope = 1 / 3
Therefore, the slope of the line passing through points A and B is 1/3.
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Ali, Basti and Cian stand at three points A, B and C respectively. Suppose that the measure of angle ABC is 50 degrees , the measure of angle BAC is 60 degrees and Ali is exactly 150 ft away from Basti. Find the distance between Basti and Cian.
The distance between Basti and Cian is approximately 138.2 ft. Option D
To find the distance between Basti and Cian, we can use the Law of Sines, which relates the lengths of sides to the sines of their opposite angles in a triangle.
Let's label the points: A, B, and C. Ali is at point A, Basti is at point B, and Cian is at point C.
Given:
Angle ABC = 50 degrees (angle opposite side AC)
Angle BAC = 60 degrees (angle opposite side BC)
Ali is 150 ft away from Basti (side AB)
We want to find the distance between Basti and Cian, which is side BC.
Using the Law of Sines, we have:
BC/sin(50) = AB/sin(60)
Substituting the known values:
BC/sin(50) = 150/sin(60)
To find BC, we can rearrange the equation:
BC = (150/sin(60)) * sin(50)
Using a calculator to evaluate the expression:
BC ≈ 138.2 ft
Option D is correct.
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What is the distance between -3 and 2 on the
number line?
A.-5
B.-1
C.1
D.5
Answer:
D. 5
Step-by-step explanation:
distance between -3 and 2 on the number line is given as as:
\(2 - ( - 3) = 2 + 3 = 5 \: units\)
smb help w this pls asap
Answer:
Step-by-step explanation:
-35x+85x-4=26 what is x
. What is the value of x in the diagram below?
(1 point)
36
20
Х
Ox= 12v5
Ox=12/14
Ox=4170
O not enough information
Answer:
C. x = 4√70
Step-by-step explanation:
To find x, we would apply the leg rule.
Leg rule is:
Hypotenuse/leg = leg/part
Hypotenuse = 36 + 20 = 56
Leg = x
Part = 20
Plug in the values into the equation
Thus, we would have:
56/x = x/20
Cross multiply
x*x = 56*20
x² = 1,120
x = √1,120
x = √(16*70)
x = 4√70
The correct answer is c.
What is the measure of one exterior angle of a 15-sided regular polygon?
O 12 degrees
O 168 degrees
O24 degrees
O 156 degrees
Answer:
24°
Step-by-step explanation:
For an n-sided regular polygon, the sum of internal angles = (n-2)×180°
Since all internal angles are equal, the internal angle can is given as:
Here, it is given that the polygon has 15 sides.
So n = 15
So each internal angle is 156°.
Internal and external angles are always supplementary. So the sum of the internal and external angles is 180°.
So external angle = 180° - 156° = 24°.
The measure of each external angle is 24°.
6(3x+4)+2(2x+2)+2=22x+31 solve the equation for the given variable
The equation 6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31 has no solution for the variable x.
What is the solutuon to the given equation?Given the equation in the question:
6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31
To solve the equation 6(3x + 4) + 2(2x + 2) + 2 = 22x + 31 for the variable x, we will simplify and solve for x.
Apply distributive property:
6 × 3x + 6 × 4 + 2 × 2x + 2 × 2 + 2 = 22x + 31
18x + 24 + 4x + 4 + 2 = 22x + 31
Collect and combine like terms on both sides:
22x + 30 = 22x + 31
Next, we want to isolate the variable x on one side.
22x - 22x + 30 = 22x - 22x + 31
30 = 31
However, we notice that the x terms cancel out when subtracted:
30 ≠ 31
This means that there is no solution.
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The area of a rectangle is 125 square yards. If the perimeter is 60 yards, find the length and width of the rectangle.
Answer:
25 yards long, 5 yards wide
Step-by-step explanation:
The given parameters can be used with the area and perimeter formulas for a rectangle to form an equation that can be solved for the dimensions.
SetupThe length and width can be represented by x and y. The formulas for area and perimeter give two equations relating these two variables:
A = LW ⇒ 125 = xy
P = 2(L+W) ⇒ 60 = 2(x +y)
Using the second equation to write an expression for y, we have ...
y = 30 -x
Substituting into the first equation gives ...
125 = x(30 -x)
SolutionThis suggests we can find x by looking for factors of 125 that total 30.
125 = 1(125) = 5(25)
Factor totals are 126 and 30. This means we have ...
x = 5, y = 30-5 = 25
or
x = 25, y = 30 -25 = 5
The rectangle dimensions are 5 yards by 25 yards.
__
Additional comment
The two equations can also be solved graphically, as in the attachment.
The rectangle will be 25 yards long, and 5 yards wide.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
The given parameters can be used with the area and perimeter formulas for a rectangle to form an equation that can be solved for the dimensions.
The length and width can be represented by x and y. The formulas for area and perimeter give two equations relating to these two variables:
A = LW ⇒ 125 = xy
P = 2(L+W) ⇒ 60 = 2(x +y)
Using the second equation to write an expression for y, we have ...
y = 30 -x
Substituting into the first equation gives ...
125 = x(30 -x)
This suggests we can find x by looking for factors of 125 that total 30.
125 = 1(125) = 5(25)
Factor totals are 126 and 30. This means we have.
x = 5, y = 30-5 = 25
x = 25, y = 30 -25 = 5
Therefore, the rectangle will be 25 yards long, and 5 yards wide.
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give me answer ........................................................
The bottom row and right column are representing totals of previous cells and the grand total is 82 as indicated in the question.
Find the missing numbers in the following order:
Teachers/Apples = 24 - 22 = 2Teachers/Oranges = 25 - 24 = 1Total/Total = 82 (given)Teachers/Total = 2 + 4 + 1 = 7Students/Total = 82 - 7 = 75Students/Grapes = 75 - 24 - 22 = 29Totals/Grapes = 29 + 4 = 33PLSSS! Fast! I will give 5 stars! At noon, the temperatures in Portland, Maine and Phoenix, Arizona had opposite values. The temperature in Portland was lower than in Phoenix. What was the temperature in each city? Explain your reasoning.
Opposite values are those values which on the number line has the same distance between them and zero. The temperature in each city is PoT=-PhT and PhT =+PoT.
What are opposite values?Opposite values are those values which on the number line has the same distance between them and zero. Although the sign on the values may be difference. For example if the first value is 4, then its opposite value is -4.
In general, the temperature equation for Portland, Maine is stated mathematically as
PoT=-PhT
As it is given in the question that the Portland, Maine and Phoenix, Arizona had opposite values. Also, the temperature in Portland is lower than in Phoenix. Therefore, the temperature in each city can be written as,
PoT=-PhT
PhT =+PoT
Hence, the temperature in each city is PoT=-PhT and PhT =+PoT.
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A Poker club has 10 members. A president and a vice-president are to be selected. In how many ways can this be done if everyone is eligible?
Answer:
90 different ways
Step-by-step explanation:
We have a total of 10 members, and we want to find how many groups of 2 members we can have, where the order of each member in the group of 2 is important, so we have a permutation problem.
To solve this problem, we need to calculate a permutation of 10 choose 2.
The formula for a permutation of n choose p is:
\(P(n, p) = n! / (n - p)!\)
So we have:
\(P(10, 2) = 10! / (10 - 2)!\)
\(P(10, 2) = 10! / 8!\)
\(P(10, 2) = 10*9 = 90\)
So there are 90 different ways of choosing a president and a vice-president.
i need help can anyone please help
Answer:
vertically opposite angle
Step-by-step explanation:
Suppose
p
varies directly with
q
and that
p
=
96
when
q
=
12
. What is the value of
p
when
q
=
3
?
Answer:
p= 24
Step-by-step explanation:
1) p ∝ q
p=kq
when p=96 and q =12
96=k×12
96=12k
k=96/12
k=8
the equation connecting p and q is
p=8q
2) when p=?,q=3
p=8q
p=8×3
p=24
rate as brainliest
Hi, simplify the following rational expression, if possible: x + 2/ x^2 = 4x + 4
Given:
\(\frac{x+2}{x^2-4x+4}\)To simplify the given rational expression, we first factor x^2-4x+4 by applying Perfect Square Formula as shown below:
\(\begin{gathered} a^2-2ab+b^2=(a-b)^2 \\ \end{gathered}\)Hence,
\(x^2-4x+4=x^2-2x(2)+2^2=(x-2)^2\)Now, we simplify the given expression:
\(\frac{x+2}{x^{2}-4x+4}=\frac{x+2}{(x-2)^2}\)Therefore, the answer is:
\(\frac{x+2}{(x-2)^{2}}\)The time X (minutes) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A = 20 and B = 30. a. Write the pdf of X and sketch its graph. b. What is the probability that preparation time exceeds 27 minutes? c. Find the preparation mean time, then calculate the probability that preparation is within 2 minutes of the mean time? d. For any a such that 20 < a < a + 2 < 30, what is the probability that preparation time is between a and a + 2 minutes?
the probability that preparation is within 2 minutes of the mean time is 0.134.
What is probability distribution?An illustration of a probability distribution shows the anticipated results of potential values for a specific data generation procedure.
What are the types of probability?Axiomatic, theoretical and experimental are the three types of probability.
P(35-2<X<35+2)= P(33<X<37)= P(X<37)-P(X<32)
Using cumulative functi0n we get
P(35-2<X<35+2)= P(33<X<37)= P(X<37)-P(X<32)
=\(\frac{37-20}{50-20}-\frac{33-20}{50-20}\\ =0.567-0.433\\=0.134\)
Thus the probability that preparation is within 2 minutes of the mean time is 0.134.
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NEED THE ANSWERS FAST PLEASE
In Exercises 13 and 14, find a possible pair of integer values for a and c so that
the quadratic equation has the given number and type of solution(s). Then write
the equation.
13. ax² − 3x + c = 0; two real solutions
-
14. ax² + 10x + c = 0; two imaginary solutions
15. Determine the number and type of solutions to the equation 2x² - 8x = -15.
A. two real solutions
B. one real solution
C. two imaginary solutions
D. one imaginary solution
In Exercises 16 and 17, use the Quadratic Formula to write a quadratic equation
that has the given solutions.
16. x
10 ± √√-68
14
17. x =
-3±i√√7
8
In Exercises 18-21, solve the quadratic equation using the Quadratic Formula.
Then solve the equation using another method. Which method do you prefer?
Explain.
18. 7x² + 7 = 14x
20. x² + 2 = -x
19. x² + 20x = 8
21. 8x² - 48x + 64 = 0
22. The quadratic equation x² + x + c = 0 has two imaginary solutions. Show that
the constant c must be greater than 1.
Answer:
Step-by-step explanation:
the degree of a polynomial determines 1:1 the number of solutions.
a quadratic equation (degree 2) has 2 solutions.
the general solution is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = -4
b = -4
c = -1
so,
x = (4 ± sqrt((-4)² - 4×-4×-1))/(2×-4)
when we look at the square root
16 - 16
we see that it is 0.
the square root of 0 is 0, and there is no difference between -0 and +0.
so, we get only one (real) solution : 4/-8 = -1/2
but : formally, there are still 2 solutions (as this is a quadratic equation). they are just identical.
so, I am not sure what your teacher wants to see in this case as answer.
my answer would be 2 real identical solutions. did this help?
1. A taxi charges $2.00 for up to and including the first mile and $1.60 for each mile thereafter. Which equation best fits this situation, where x
represents the miles after the first mile and y is the total amount.
A)y=1.602 - 2.00
B)y=2.002 -1.6
C)y =2.00x + 1.60
D)y=1.60x+2.00
Answer:
D
Step-by-step explanation:
The taxi charges $2.00 for any distance less than or up to 1 mile.
Then for every mile after the taxi will charge you a fee of $1.60 dependent upon how many miles you go.
This can be modeled as:
y = 2.00 +1.60(x)
where x is the number of miles after the first mile.
Thirty is what percent of 90?
Statement True False There are whole numbers that are not integers.
True!
your very welcome
What is the vertical distance between the points C(2, -0.8) D(2,1.2)
Answer:
2 units
Step-by-step explanation:
vertical distance will be the magnitude of the difference in the 'y' coordinates
| -.8 - 1.2| = 2 units
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Answer:
2x(7×3)+(7×6)+(3×6)= 162ft
HELP PLEASE DUE IN 4 MINUTES
Answer:
8/3
Step-by-step explanation:
Answer:
C. 2/3
Step-by-step explanation:
this is the correct answer
Which arrangement shows 27/5, 5.36, 5 3/5, 33/6 in order from least to greatest?
Answer:
5.36 < 27/5 < 33/6 < 5 3/5 or 5.36, 27/5, 33/6, 5 3/5
Step-by-step explanation:
(a) Find the lateral area (in square inches) of the prism.
(b) Find the total area (in square inches) of the prism.
(c) Find the volume (in cubic inches) of the prism.
Answer:
c
Step-by-step explanation:
A police officer invested $5,000 in a treasury bond paying 4.75% interest compounded quarterly. After 25 years, the value of the bond will be $16,280.08. If the police officer's investment was compounded continuously instead of four times per year, what would be the difference in the account balances after 25 years?
Answer:
114.29
Step-by-step explanation:
The volume of a tree stump can be modeled by considering it as a right cylinder. Lauren measures it’s height as 0.7ft and it’s radius as 20in find the volume of the stump in cubic inches. Round your answer to the nearest tenth if necessary
The volume of the tree stump is approximately 1005.3 cubic inches when rounded to the nearest tenth.
To calculate the volume of the tree stump, we can use the formula for the volume of a cylinder, which is given by:
Volume = π * r^2 * h
Given:
Radius (r) = 20 inches
Height (h) = 0.7 feet
First, let's convert the height from feet to inches since the radius is already in inches. There are 12 inches in 1 foot, so:
Height (h) = 0.7 feet * 12 inches/foot = 8.4 inches
Now, we can substitute the values into the volume formula:
Volume = π * (20 inches)^2 * 8.4 inches
Calculating the volume:
Volume = 3.14159 * (20 inches)^2 * 8.4 inches
≈ 3.14159 * 400 inches^2 * 8.4 inches
≈ 1005.3096 cubic inches
Rounding the volume to the nearest tenth:
Volume ≈ 1005.3 cubic inches
Therefore, the volume of the tree stump is approximately 1005.3 cubic inches when rounded to the nearest tenth.
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Please help me with this question
What value of n makes the equation true?
1/2(n + + 4) = 6
4,2,8,-1
Answer:
8
Step-by-step explanation: