An equilateral triangle and a square have the same perimeter of 12 inches. what is the ratio of the side length of the triangle to the side length of the square? express your answer as a common fraction.
Find the radius of a circle with an area of 615.75 sq kilometers?
area = pi x r^2
615.75 = 3.14 x r^2
r^2 = 615.75/3.14 =196.0987 round to 196.1
r = sqrt(196.1) = 14.00357 round to 14
radius = 14 kilometers
The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is the number of photos printed, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem?
Part B: Determine the x-intercepts. What do these values mean in the context of the problem?
Rewrite the formula to find the radius of a sphere. The volume (V) of a sphere is given by the formula V=4/3 pi r^2
Which expression is equivalent to (2x^4y)^3
The equivalent expression to the given expression is [tex]8x^12y^3[/tex].
We have given that,
The expression (2x^4y)^3
We have to determine the,
Which expression is equivalent to (2x^4y)^3
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
The answer is D.
2^3 is 8.
(x^4)^3 is x^12 and y^3 is simply y^3.
Put them together to get the final answer.
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Thank you very much for your help!
Half of the population of cool town owns a bicycle, and 25% of the population owns a car. if 10% of the population owns both a car and a bicycle, what is the probability that a person chosen at random from cool town owns either a car or a bicycle or both?
Solve 2x2 + 5x + 5 = 0. Round solutions to the nearest hundredth.
Rounded to the nearest hundredth, they are:
[tex]\[x_1 \approx -0.63 + 1.35i\][/tex]
[tex]\[x_2 \approx -0.63 - 1.35i\][/tex]
To solve the quadratic equation [tex]\(2x^2 + 5x + 5 = 0\)[/tex], we can use the quadratic formula:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
where [tex]\(a = 2\), \(b = 5\)[/tex], and [tex]\(c = 5\)[/tex].
Substituting the values into the quadratic formula:
[tex]\[x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 2 \cdot 5}}}}{{2 \cdot 2}}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{{25 - 40}}}}{{4}}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{{-15}}}}{{4}}\][/tex]
Since the discriminant [tex](\(b^2 - 4ac\))[/tex] is negative, the solutions will involve imaginary numbers.
Using the imaginary unit [tex]\(i\)[/tex], where [tex]\(i^2 = -1\),[/tex] we can rewrite [tex]\(\sqrt{{-15}}\)[/tex] as [tex]\(i\sqrt{{15}}\):[/tex]
[tex]\[x = \frac{{-5 \pm i\sqrt{{15}}}}{{4}}\][/tex]
So, the solutions to the equation [tex]\(2x^2 + 5x + 5 = 0\)[/tex] are complex numbers. Rounded to the nearest hundredth, they are:
[tex]\[x_1 \approx -0.63 + 1.35i\][/tex]
[tex]\[x_2 \approx -0.63 - 1.35i\][/tex]
These solutions represent the points where the graph of the quadratic equation intersects the x-axis. They lie on the complex plane.
What's the slope of the line that passes through (2,14) and (-1,-1)?
The amount of an ordinary $7,500.00 annuity for 3 years at 12 percent compounded quarterly is
Answer:
$180,997.50.
Step-by-step explanation:
1. On TABLE 14-1 Future Value of $1.00 Ordinary Annuity, select the periods row corresponding to the number of interest periods.
2. Select the rate-per-period column corresponding to the period interest rate.
3. Locate the value in the cell where the periods row intersects the rate-per-period column.
4. Multiply the annuity payment by the table value from step 3.
Future value = annuity payment × table value
FV = $7500.00 * 24.133 = $180,997.50
Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589.
how many solutions does this system have -3x+6y=10 -3x+6y= -4
Which has a greater area, a square with sides that are x - 1 units long or a rectangle with a length of x units and a width of x - 2 units?
The base of the parallelogram, b, can be found by dividing the area by the height. If the area of the parallelogram is represented by 6x2 + x + 3 and the height is 3x, which represents b, the length of the base
Answer:
[tex]2x+\frac{1}{3}+\frac{1}{x}=Base[/tex]
Step-by-step explanation:
Given: The area of the parallelogram is [tex]6x^2+x+3[/tex] and the height is 3x.
To find: The base of the given parallelogram.
Solution: It is given that The area of the parallelogram is [tex]6x^2+x+3[/tex] and the height is 3x.
Now, area of parallelogram is given as:
[tex]A=b{\times}h[/tex] where b is the base and h is the height of teh gievn parallelogram.
Substituting the given values, we have
[tex]6x^2+x+3=b{\times}3x[/tex]
⇒[tex]\frac{6x^2+x+3}{3x}=Base[/tex]
⇒[tex]\frac{6x^2}{3x}+\frac{x}{3x}+\frac{3}{3x}=Base[/tex]
⇒[tex]2x+\frac{1}{3}+\frac{1}{x}=Base[/tex]
which is the required expression for the base of the given parallelogram.
A triangle has measurements of 39, 52, and 65 units. Is it a right triangle?
Yes
No
Not enough information to tell
I need help learning how to do these problems some how whenever I do them I always get it wrong please help I have a test Wednesday!
Which side has an equal measure to BC?
A.DE
B.AB
C.EF
D.DF
PLEASE HELP
In the given diagram, we are given two triangles, triangle ABC and triangle DEF.
And we are given a line or reflection l.
Triangle DEF is the mirror image of triangle ABC.
Therefore, all sides of the triangle ABC would be congruent to sides of triangle DEF.
AB = DF
AC = DE and
BC = EF.
We can see than BC is the smallest side of triangle ABC and EF is the smallest side of triangle DEF.
Therefore, correct option is C option.C.EFWhich symbol creates a true sentence when x equals 6? 42 + (x – 3)2 __ 28
Y varies jointly as x and z, and y = 32 m, x = 6 m, and z = 8 m. what is the value of y when x = 5 m and z = 12 m?
a. 90 m
b. 4 m
c. 40 m
d. 9 m
Find the value of two numbers if their sum is 12 and the difference is 4
x+y=12
x-y=4
x=y-4
y-4+y=12
2y-4=12
2y=16
y=8
x=8-4=8
8+4=12
the 2 numbers are 8 & 4
Shyla used a probability simulator to pull 3 colored marbles from a bag and flip a coin 50 times. The results are shown in the tables below:
16 blue
20 green
14 yellow
heads 18
tails 32
Using Shyla's simulation, what is the probability of pulling a blue marble and the coin landing tails up?
Answer:
512/2500
Step-by-step explanation:
The length l of a rectangle is 4 inches greater than its width w. The area of the rectangle is 252 square inches.Using the method of completing the square, what are the length and width of the rectangle? Show your work.
Mike wants to make meatloaf. His recipe uses a total of 6 pounds of meat. If he uses a 3 to 1 ratio of beef to pork how much pork will he use? Enter your answer as a mixed number in simplest terms
Mike will use 1 1/2 pounds of pork for his meatloaf recipe, which calls for a 3 to 1 ratio of beef to pork and a total of 6 pounds of meat.
Mike's meatloaf recipe has a total of 6 pounds of meat and uses a 3 to 1 ratio of beef to pork. To find out how much pork he will use, we can express the total amount of meat as the sum of beef and pork parts.
First, we know that there are 3 + 1 = 4 parts in total because of the given ratio. Since the ratio is 3 to 1, for every 4 parts of meat, 1 part is pork. Therefore, we calculate the weight of each part by dividing the total weight by the number of parts:
6 pounds ÷ 4 parts = 1.5 pounds per part
Since one part is pork, Mike will use 1.5 pounds of pork for his meatloaf. Expressed as a mixed number, that's 1 1/2 pounds of pork in simplest terms.
The number of hours (H) that a candle will burn increases when the length of the candle (L) increases. Write the correct equation for this scenario, and solve for the number of hours when the length is 2. Length Hours 15 3 20 4
Answer:
H = .2L; H = .4
Step-by-step explanation:
A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23/fts. The ball's height h (in feet) after t seconds is given by the following.
h=7+23t-16t^2
Find all values of t for which the ball's height is 15 feet.
Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)
As per quadratic equation, all values of 't' for which the ball's height is 15 feet are 33.25 and (- 31.813).
What is a quadratic equation?"Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x)."
Given, [tex]h = 15[/tex] feet.
Therefore, the quadratic equation for [tex]h = 15[/tex] will be:
A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23 feet per second.
The ball's height h (in feet) after t seconds is:
[tex]h = 7+23t-16t^{2}[/tex]
[tex]15 = 7+23t-16t^{2}[/tex]
⇒ [tex]15-7-23t+16t^{2} = 0[/tex]
⇒ [tex]16t^{2} -23t - 8 = 0[/tex]
⇒ [tex]t = [- (-23)[/tex] ± [tex]\sqrt{(23)^{2} - 4(16)(- 8)}[/tex] ]/(2 × 16)
⇒ [tex]t =[/tex] [23 ± 1041]/32
⇒ [tex]t =[/tex] [23 + 1041]/32, [23 - 1041]/32
⇒ [tex]t =[/tex] 33.25, - 31.813
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HELP PLEASE! Which of these shows the following expression factored completely? 6x^2-13x=5
a (3x-1)(2x+5)
b (3x-5)(2x-1)
c (3x-1)(2x-5)
d (3x-5)(2x+1)
The solution is: the following expression factored completely,
6x^2-13x=5 is: c (3x-1)(2x-5)
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Here, we have,
we have,
6x² - 13x = +5
6x² - 13x - 5 = 0
6x² - 15x + 2x - 5 =0
so, we get,
(3x-1)(2x-5) = 0
The sign of the constant term is the product of the signs of the constants in the binomial factors: (+1)·(+5). We want a positive sign for the constant, so both binomial factor constants must have the same sign.
When the signs of the binomial factor constants are the same, the x-term constant will match them. Thus, for a positive x-term constant, both binomial factor constants must be positive.
The signs of the x-term and the constant term are both positive, so the signs of the constants in the binomial factors must be the same and must both be positive. The only offering that meets that requirement is
... C (3x-1)(2x-5)
Hence, The solution is: the following expression factored completely, 6x^2-13x=5 is: c (3x-1)(2x-5)
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Solve the following equation by transforming it into a perfect square trinomial. x2 – 4x = 5 will mark as brilliant
The solution of the given equation is -1 or 5
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example, 3x + 5 = 15.
Given is an equation, x²-4x = 5,
we need to transform it into a perfect square,
The equation is =
x²-4x = 5
Add 4 to each side,
x²-4x+4 = 5+4
x²-4x+4 = 9
(x-2)² = 9
Solving for x,
x-2 = √9
x-2 = ±3
x = -1 or x = 5
Hence, the solution of the given equation is -1 or 5
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PLEASE HELP ASAP ILL GIVE BRAINLIEST IF YOURE RIGHT!!
Find the greatest possible error for each measurement.
9 g
a.
1/2 g
b.
1/4 g
c.
1/6 g
d.
1/8 g
gpe = 1/2 of the unit measures
since 9 is a whole number the gpe would be 1/2 g
Ue can wash a car in 1 hour. steve can wash a car twice as fast as sue. how long will it take them to wash a car if they work together, but sue starts 30 minutes before steve?
. The total cost of gasoline varies directly with the number of gallons purchased. Gas costs $1.77 per gallon. Write a direct variation to model the total cost c for g gallons of gas.
A . c=g/1.77
B. c=1.77g
C. g=1.77c
D. c=g+1.77