Final answer:
The perimeter of the isosceles triangle with a base of 20 meters and height of 24 meters is 60 meters.
Explanation:
The formula for the area of a triangle is 1/2 × base × height.
In this case, the base of the isosceles triangle is given as 20 meters and the corresponding height is given as 24 meters.
Using the formula, we can calculate the area: Area = 1/2 × 20 × 24 = 240 square meters.Next, we need to calculate the length of the two equal sides of the triangle.Since the triangle is isosceles, the length of the base is equal to the length of the two equal sides.So, each equal side of the triangle is equal to 20 meters.Finally, to find the perimeter of the triangle, we add up the lengths of all three sides.Perimeter = 20 + 20 + 20 = 60 meters.what is a equivalent fraction of 10/25, 6/8, 3/5, 1/10
Answer:
Step-by-step explanation:
10/25=20/50=40/100
6/8=3/4=12/16
3/5=6/10=60/100
1/10=10/100
A 9-sided die is rolled. The die's faces are labeled with the numbers 1 through 9, and each number is equally likely to be rolled. Find the probability of rolling an even
number
Final answer:
The probability of rolling an even number on a 9-sided die is 4/9.
Explanation:
To find the probability of rolling an even number on a 9-sided die, we need to determine the number of favorable outcomes (even numbers) and divide it by the total number of possible outcomes.
In this case, there are 4 even numbers on the die: 2, 4, 6, and 8. The total number of possible outcomes is 9 (since there are 9 sides on the die).
Therefore, the probability of rolling an even number is 4/9.
Point A(2, 2) and point B(4, −3) are located on the grid. Which measurement is closest to the distance between point A and point B in units?
A) 5.2 units
B) 5.4 units
C) 5.6 units
D) 5.8 units
Answer:
b
Step-by-step explanation:
5 ft
3 ft
3 ft
2 ft
2 ft
2 ft
3 ft
4 ft
find the area
Answer:
multiply all together
Step-by-step explanation
the sum of one-half t and one third s
Answer:
5/6
Step-by-step explanation:
Add the fractions by finding the common denominator.
1/2 + 1/3
3/6 + 2/6
5/6
if y varies inversely as x² and x varies directly as z. find the relationship connecting y and z if c is a constant
Answer:
y = c/z²
Step-by-step explanation:
(1) y ∝ 1/x²or
y = a/x² where a is a constant
x ∝ z or x = bz, where b is a constant
Substitute x into (1)
y ∝ a/(bz)² = a/(b²z²) = (a/b²)/z²
a is a constant and b is a constant, so a/b² is a constant.
Let c = a/b². Then
y = c/z²
2 Construct a rational function that will help solve the problem. Then, use a calculator to answer the question.
An open box with a square base is to have a volume of 500 cubic inches. Find the dimensions of the box that will have
minimum surface area. Let x = length of the side of the base.
Show your work:
Answer:
Dimension of box:-
Side of square base = 10 in
Height of box = 5 in
Minimum Surface area, S = 300 in²
Step-by-step explanation:
An open box with a square base is to have a volume of 500 cubic inches.
Let side of the base be x and height of the box is y
Volume of box = area of base × height
[tex]500=x^2y[/tex]
Therefore, [tex]y=\dfrac{500}{x^2}[/tex]
It is open box. The surface area of box, S .
[tex]S=x^2+4xy[/tex]
Put [tex]y=\dfrac{500}{x^2}[/tex]
[tex]S(x)=x^2+\dfrac{2000}{x}[/tex]
This would be rational function of surface area.
For maximum/minimum to differentiate S(x)
[tex]S'(x)=2x-\dfrac{2000}{x^2}[/tex]
For critical point, S'(x)=0
[tex]2x-\dfrac{2000}{x^2}=0[/tex]
[tex]x^3=1000[/tex]
[tex]x=10[/tex]
Put x = 10 into [tex]y=\dfrac{500}{x^2}[/tex]
y = 5
Double derivative of S(x)
[tex]S''(x)=2+\dfrac{4000}{x^3}[/tex] at x = 10
[tex]S''(10) > 0[/tex]
Therefore, Surface is minimum at x = 10 inches
Minimum Surface area, S = 300 in²
Write 5 over 15 in simplest form.
Answer: 1/3
Step-by-step explanation:
5/15 divided both by 5 is 1/3
5xy —9cs (-)-3xy + cs simplify
Answer:
Step-by-step explanation:
2 • (xy - 4cs)
Which exponential function has an initial value of 2? f(x) = 2(3x) On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 0.5) and goes through (2, 2). f(x) = 3(2x) A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries one-eighth, one-fourth, one-half, 1, 2.
Answer:
The correct answer is A. f(x)= 2(3^x)
Step-by-step explanation:
The exponential function y = 2(3)ˣ, has an initial value of 2
Exponential functionAn exponential function is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplicative rate of change
Given the exponential function y = 2(3)ˣ, has an initial value of 2
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Carol buys a house for £234 900
She pays a 10% deposit
Work out the deposit made by carol
Answer:
23,490
Step-by-step explanation:
10% = 0.1
234900 x 0.1 = 23490
9-4 (3+6*2)=__+1=
(need answer asap please)
Find a numerical value of one trigonometric function of x for cos^2x+ 2sin x-2=0
Answer:
x = 90°
Step-by-step explanation:
We are given a trigonometric function of x from which we have to a solution for x.
The function is [tex]\cos^{2} x + 2\sin x - 2 = 0[/tex]
⇒ [tex]1 - \sin^{2} x + 2\sin x - 2 = 0[/tex]
{Since we know the identity [tex]\sin^{2} \alpha + \cos^{2} \alpha = 1[/tex]}
⇒ [tex]\sin^{2} x - 2 \sin x + 1 = 0[/tex]
⇒ [tex](\sin x - 1)^{2} = 0[/tex]
{Since we know the formula (a - b)² = a² - 2ab + b²}
⇒ [tex](\sin x - 1) = 0[/tex]
⇒ [tex]\sin x = 1 = \sin 90[/tex]
⇒ x = 90° (Answer)
To solve cos^2 x + 2sin x - 2 = 0, we convert cos^2 x to 1 - sin^2 x and solve the quadratic equation sin^2 x - 2sin x + 1 = 0, finding that sin x equals 1. Thus, the numerical value of the trigonometric function is sin x = 1.
To find a numerical value of one trigonometric function of x for the equation cos2x + 2sin x - 2 = 0, let's start by expressing everything in terms of sin x:
Using the Pythagorean identity, we know that cos2x = 1 - sin2x. So, we can write:
(1 - sin2x) + 2sin x - 2 = 0
Simplifying, we get:
1 - sin2x + 2sin x - 2 = 0
-sin2x + 2sin x - 1 = 0
This is a quadratic equation in terms of sin x. Let's solve it:
sin2x - 2sin x + 1 = 0
We recognize this as a perfect square trinomial:
(sin x - 1)2 = 0
So, we have:
sin x - 1 = 0
Therefore:
sin x = 1
So, the numerical value of one trigonometric function of x from the given equation is sin x = 1.
Marquise is 9 years old. In two years, Marquise will be 1/3 of his mother’s age. What is his mother’s age?
Answer:
33
Step-by-step explanation:
9+2=1/3x
11=1/3x
x=11/(1/3)=(11/1)(3/1)=33/1=33
#1
Suppose g(a) = 7.6 cos(0.5a).
a. What is the argument of the cosine function? (Enter an expression.)
Answer:
[tex]0.5a[/tex]
Step-by-step explanation:
We have been given a trigonometric function [tex]g(a)=7.6\text{ cos}(0.5a)[/tex]. We are asked to find the argument of the cosine function.
We know that a trigonometric equation is solved for an unknown angle and that unknown angle is known as the argument of the trigonometric function. For example: [tex]\text{cos}(\theta)=0[/tex]. In this equation [tex]\theta[/tex] is the argument of the equation.
Upon looking at our given function, we can see that [tex]0.5a[/tex] is the argument.
Neptune has a gravitational pull 1.2 times that on earth if an object weights 15.3 pounds on earth how much would it weigh on Neptune
Answer:
the object would weigh 18.36
since it is 1.2 times as much you multiply the weight of the object on earth by 1.2 and that's the answer
Step-by-step explanation:
Train A and Train B leave the station at 2 P.M. The graph below shows the distance covered by the two trains. Compare the speeds of the two trains.
Answer:
Train b is moving faster than a by 45 units an hour
Step-by-step explanation:
what does x = -6(4x+3) = 6(-4x-3)
Answer:
Infinitely many solutions
Step-by-step explanation:
-6(4x+3)=6(-4x-3)
-24x-18=-24x-18
infinitely many solutions
HELP!!!! What is-15=(3x-10)-5x
Answer:
x = 2.5Step-by-step explanation:
[tex]-15=(3x-10)-5x\\\\-15=3x-10-5x\qquad\text{combine like terms}\\\\-15=(3x-5x)-10\\\\-15=-2x-10\qquad\text{add 10 to both sides}\\\\-15+10=-2x-10+10\\\\-5=-2x\qquad\text{divide both sides by (-2)}\\\\\dfrac{-5}{-5}=\dfrac{-2x}{-2}\\\\2.5=x\to x=2.5[/tex]
Answer:
exact form x=5/2 decimal form2.5 mixed number form 2 1/2
Step-by-step explanation:
Find the range and standard deviation for the set of numbers.
111, 122, 134, 146, 150, 159, 193
Answer:
For this set of numbers, we have a range of 82, a mean of 145, a variance of 618.86 and a standard deviation of 24.88.
Step-by-step explanation:
1. Let's find the range for the set of numbers given:
Don't forget that range is a measure of dispersion and is the difference between the lowest and highest values in this set of numbers.
Range = 193 - 111
Range = 82
2. For calculating the standard deviation, we should calculate first the mean and the variance, this way:
Mean = Sum of all the terms / Number of the terms of the set
Mean = (111 + 122 + 134 + 146 + 150 + 159 + 193)/ 7
Mean = 1,015/7
Mean = 145
Now, we proceed to calculate the variance this way:
Variance= Sum of the squared distances of each term in the set from the mean/ Number of terms of the set or sample
Let's calculate the squared distances of each term in the set from the mean:
111 - 145 = - 34 ⇒ - 34² = 1,156
122 - 145 = - 23 ⇒ - 23² = 529
134 - 145 = - 11 ⇒ - 11² = 121
146 - 145 = 1 ⇒ 1² = 1
150 - 145 = 5 ⇒ 5² = 25
159 - 145 = 14 ⇒ 14² = 196
193 - 145 = 48 ⇒ 48² = 2,304
Now replacing with the real values:
Variance = (1,156 + 529 + 121 1+ 25 + 196 + 2,304)/7
Variance = 4,332/7
Variance = 618.86 (Rounding to two decimal places)
Finally, we can calculate easily the standard deviation:
Standard deviation = √Variance
Standard deviation = √ 618.86
Standard deviation = 24.88 (Rounding to two decimal places)
The graph represents this system of equations y equals 4 - x y equals x - 2 what is the solution to the system of equations
The solution to the system of equations is (3,1)
Step-by-step explanation:
The system of equations represented by graph are:
[tex]y=4-x\\y=x-2[/tex]
Solving the system of equations
Let:
[tex]y=4-x\,\,\,eq(1)\\y=x-2\,\,\,eq(2)[/tex]
Putting value of y from eq(2) into eq(1):
[tex]x-2=4-x\\Simplifying:\\x+x=4+2\\2x=6\\x=6/2\\x=3[/tex]
So, Value of x = 3
Putting value of x into eq(2)
[tex]y=x-2\\y=3-2\\y=1[/tex]
So, value of y= 1
So, The solution to the system of equations is (3,1)
Keywords: System of equations
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Grace is comparing cell phone plans. A prepaid phone plan costs $0.20 per minute and has no monthly fee. A contracted phone plan costs $50 per month and $0.02 per minute. How will the graphs of the monthy costs of the two cell phone plans compare where x represents minutes purchased in a month?
The prepaid phone plan will have a steeper line and lower y-intercept.
The contracted phone plan will have the same steepness and a higher y-intercept.
The prepaid phone plan will have a less steep line and the same y-intercept.
The contracted phone plan will have a steeper line and same y-intercept.
Answer:
The prepaid phone plan will have a steeper line and lower y-intercept.
I hope this is right
Step-by-step explanation:
prepaid phone plan y = .20x
contracted phone plan y = .02x + 50
The prepaid and the contracted plans are illustrations of linear functions, where the prepaid phone plan has a steeper line and lower y-intercept.
We have:
Prepaid
[tex]Rate = 0.20[/tex]
[tex]Monthly = 0[/tex]
Contracted
[tex]Monthly = 50[/tex]
[tex]Rate = 0.02[/tex]
For both plans, the cost function (y) is:
[tex]y =Monthly + Rate \times x[/tex]
Where:
[tex]x \to[/tex] Number of minutes
[tex]Rate \to[/tex] Steepness
So, we have:
Prepaid
[tex]y =0 + 0.20 \times x[/tex]
[tex]y =0.20x[/tex]
The y intercept (i.e. when x = 0) is
[tex]y = 0.20 \times 0 = 0[/tex]
The steep of the function is 0.20The y-intercept is 0Contracted
[tex]y = 50 + 0.02 \times x[/tex]
[tex]y = 50 + 0.02x[/tex]
The y intercept is:
[tex]y = 50 + 0.02 \times 0 = 50[/tex]
The steep of the function is 0.02The y-intercept is 50By comparing the steepness and the y-intercepts,
The prepaid plan is steeper (0.20 > 0.02)The prepaid plan has a smaller y-intercept (0 < 50)Hence, (a) is correct
See attachment for the graphs of both plans
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what is the slope of the line that contains the points (-2,5) and 6,-3)
Answer:
slope = - 1
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (6, - 3)
m = [tex]\frac{-3-5}{6+2}[/tex] = [tex]\frac{-8}{8}[/tex] = - 1
- Suppose y varies directly as x. If y = -7 when x = -14, find x when y = 10.
Answer:
[tex]x=20[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
in this problem
For x=-14, y=-7
Find the value of the constant of proportionality k
[tex]k=y/x[/tex]
substitute
[tex]k=-7/-14=0.5[/tex]
so
The linear equation is
[tex]y=0.5x[/tex]
Find x when the value of y=10
substitute the value of y in the equation
[tex]10=0.5x[/tex]
solve for x
Multiply by 2 both sides
[tex]x=20[/tex]
Final answer:
In direct variation relationship 'y = kx', using the given y = -7 when x = -14, the constant of variation 'k' is found to be 0.5. To find x when y = 10, we use 'y = kx' to get x = 20.
Explanation:
The student's question revolves around the concept of a direct variation, which is a fundamental topic in algebra. The direct variation relationship between two variables 'x' and 'y' can be expressed as 'y = kx', where 'k' is the constant of variation. To determine the constant 'k', we can use the given condition, which states that when x = -14, y = -7. This equation simplifies to 'k = y/x', so 'k = (-7)/(-14)' which equals 0.5.
Now, we need to find 'x' when y is 10. Using the direct variation equation 'y = kx' and our calculated 'k' value of 0.5, we can set up the equation '10 = 0.5x'. Solving for 'x', we get 'x = 10/0.5' which simplifies to 'x = 20'. Thus, when y equals 10, the corresponding value of x is 20.
Which value is needed in the expression below to create a perfect square trinomial?
x2+8x+______
Answer:
Step-by-step explanation:
The answer is 16
The y-intercept is 4 and the line is parallel to the line whose equation is 6x+y=5
Answer:
[tex]\displaystyle 6x + y = 4[/tex]
Step-by-step explanation:
In the Linear Standard Formula [Ax + By = C], C represents the y-intercept, and since the instructions say "parallel line", you keep your '6' the same, and just alter 5 to 4.
* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], which was why 6 remained the way it was.
I am joyous to assist you anytime.
Jacob has $1,000 in a checking account and withdraws $40 each week. His account requires a minimum balance of more than $400. Write an inequality to model the number of weeks, x, that he can withdraw $40 to maintain the minimum balance requirement.
Answer:
[tex]1000-40x>400[/tex]
Step-by-step explanation:
Let's call B the balance of Jacob's checking account. Each week he withdraws $40 from his actual balance of $1000, so if x is the number of weeks, the account's balance is
B=1000-40x
The balance must be more than $400, which means
[tex]1000-40x>400[/tex]
That is the inequality to model the situation. If we wanted to know the limit for x, we can solve the inequality. Operating:
[tex]1000-400>40x[/tex]
600>40X
[tex]x<\frac{600}{40}[/tex]
Or x<15
Which means Jacob can withdraw $40 14 times at most to maintain the minimum balance requirement
there are 125 students in your class 75 of them are girls what percent all boys percent
Answer:
40%
Step-by-step explanation:
125 - 75= 50
50 ÷ 125 = 0.4
0.4 = 40%
25(M-2)=650 what is M ?
Answer:M=24
Step-by-step explanation:
There are 2 ways to do this
---------------------------------------------------
Method 1) Divide both sides by 25, then add 2 to both sides
25(M-2) = 650
M-2 = 650/25
M-2 = 26
M = 26+2
M = 28
---------------------------------------------------
Method 2) Distribute the 25 through to each term inside the parenthesis. Then isolate for M by adding 50 to both sides, and then dividing both sides by 2.
25(M-2) = 650
25M - 50 = 650
25M = 650+50
25M = 700
M = 700/25
M = 28
---------------------------------------------------
Either way the answer is 28EASY MATH FROM THE BEGINNING OF 6th GRADE MATH BUT THIS WAS A REVIEW FROM BACK IN 5TH GRADE!!!!GETS BRAINILIST!!The figure below shows the quotient of fraction 1 over 2 divided by fraction 1 over 6. Rectangle divided into six equal parts, where the first part is shaded dark representing one-sixth, the next two parts are shaded light to complete the one-half, and the last three parts are not shaded. The quotient is ____. Numerical Answers Expected! Answer for Blank 1:
Answer:
=3
Step-by-step explanation:
Okay so you 1/2 divided by 1/6
Answer:
3
Step-by-step explanation:
1/2÷ 1/6
=
1/2×6/1
=
1 × 6
2 × 1
=
6/2
=
6 ÷ 2
2 ÷ 2
= 3
Just Divide 1/6 by 1/2