Final answer:
To find the length of the two equal sides of an isosceles triangle with a given area and angle, we use a formula involving the sides and angle. By substituting the given values and applying trigonometry, we determine the length of the sides is approximately 9.8 cm.
Explanation:
To find the length of the two equal sides of an isosceles triangle with an area of 24 cm² and an angle between these sides of 5π/6, we can use the formula for the area of a triangle, which is A = ½ × base × height. However, in this scenario, it's more relevant to apply the formula involving the sides and the included angle, given by A = ½ × b × c × sin A, where b and c are the lengths of the two equal sides, and A is the included angle.
Substituting the given values, we get 24 = ½ × b² × sin(5π/6). Sin(5π/6) is ½, so we have 24 = ½ × b² × ½. Simplifying, b² = 96, and therefore b ≈ 9.8 cm. Thus, the length of the two equal sides is approximately 9.8 cm, rounded to one decimal place.
A plumber charges a $45 fee to make a house call and then $25 for each hour of labor. The plumber uses an equation in the form y=mx +b to determine the amount to charge each customer. What is the value of m in the equation?
Answer:
Let x represents the number of hours of labor and y represents the total charges.
Since, in the given situation,
The total charges = A fixed charge for house call + Extra charge per hours,
Fixed charge for house call = $ 45,
Extra charges for every hour = $ 25,
⇒ Extra charge for x hours = 25 x,
Thus, the total charges for x hours,
y = 45 + 25 x
Which is the required equation that will use to determine the amount to charge each customer.
By comparing this equation with y = mx + c,
m = 25
Create a log expression, using the laws of logs, that simplifies to 7^x = 64.
This makes no sense to me! Help!
What are the log laws?
To create a log expression that simplifies to 7^x = 64, we need to use the logarithmic and exponential laws.
Explanation:To create a log expression that simplifies to 7^x = 64, we need to use the logarithmic and exponential laws.
First, we can rewrite the exponential equation as a logarithmic equation, which is x = log7(64).Next, we can use the logarithmic property that states logb(ax) = x * logb(a). Applying this property, we have x = log7(26) = 6 * log7(2).Therefore, the log expression that simplifies to 7^x = 64 is x = 6 * log7(2).
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Solve the inequality 2x - 3 < x 2 ≤ 3x 5. show your work
Answer:
-3/2 ≤ x < 5
Step-by-step explanation:
2x - 3 < x + 2 ≤ 3x+5
Solve the inequality separately
2x-3 <x+2 and x+2≤ 3x+5
LEts solve one by one
2x-3 <x+2
Subtract x from both sides
x -3 < 2
add 3 on both sides
x< 5
x+2≤ 3x+5
Subtract 3x from both sides
-2x + 2 ≤ 5
Subtract 2 from both sides
-2x ≤ 3
Divide both sides by -2
x ≥ -3/2
we got x>= -3/2 and x<5
so x lies between -3/2 and 5
-3/2 ≤ x < 5
The solution to the given inequality is -3/2 ≤ x < 5.
To solve the given inequality: 2x - 3 < x + 2 ≤ 3x + 5, we can break it down into two separate inequalities and solve them individually.
2x - 3 < x + 2:
Subtracting x from both sides:
2x - x - 3 < x - x + 2
x - 3 < 2
Adding 3 to both sides:
x - 3 + 3 < 2 + 3
x < 5
Now x + 2 ≤ 3x + 5:
Subtracting x from both sides:
x - x + 2 ≤ 3x - x + 5
2 ≤ 2x + 5
Subtracting 5 from both sides:
2 - 5 ≤ 2x + 5 - 5
-3 ≤ 2x
Dividing both sides by 2:
-3/2 ≤ x
Combining the results from both inequalities:
-3/2 ≤ x < 5
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Baby jacobs birth weight was 10 pounds one week after being born his weight was 9 pounds what was the percent of decrease in jacobs weight
Solve for x. Express the answer in simplest form.
Find a possible formula for a fourth degree polynomial g g that has a double zero at 1 1 g(−4)=0 , g(5)=0 , and g(0)=−6
The fourth degree polynomial g(x) with a double zero at x=1, zeros at x=-4 and x=5, and satisfying g(0)=-6 is g(x) = 3/10(x-1)²(x+4)(x-5).
A possible formula for a fourth degree polynomial g(x) with specific characteristics. The polynomial must have a double zero at x=1, zeros at x=-4 and x=5, and must satisfy g(0)=-6.
Since the polynomial has a double zero at x=1, we can represent that part of the polynomial as (x-1)². The other two zeros at x=-4 and x=5 give us factors of (x+4) and (x-5) respectively. Multiplying these factors gives us a polynomial that satisfies the zero requirements: (x-1)²(x+4)(x-5).
Now, we need to find the constant k that will make the polynomial satisfy g(0) = -6. We set up the equation using the known factors:
k(x-1)²(x+4)(x-5) and substitute x with 0 to solve for k. This gives us k(0-1)²(0+4)(0-5) = -6. Solving for k, we find k = 3/10.
Therefore, the formula for the polynomial g(x) is g(x) = 3/10(x-1)²(x+4)(x-5).
Which term describes the dotted line in the quadrilateral?
A. vertex
B. side
C. diagonal
D. angle ...?
8 is 40% of what number
An equation of the line tangent to y=sinx+2cosx at (pi/2, 1) is
A. 2x-y=pi-1 B. 2x+y=pi+1 C. 2x-2y=2-pi D. 4x+2y=2-pi I got A
Y is the midpoint of segment XZ. The coordinates of X are (2, 4) and of Y are (-1, 1). Find the coordinates of Z. ...?
what is 40% in fraction form
To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100. In this case, 40% can be written as the ratio 40 to 100 or [tex]\frac{40}{100}[/tex]. Notice however that [tex]\frac{40}{100}[/tex] is not in lowest terms so we need to divide the numerator and the denominator by 20 which gives us [tex]\frac{2}{5}[/tex].
What number is 0.77% of 900?
what is the greatest common factor of 51 and 68
Which is the graph of linear inequality x-2y>-12 help!
Answer:
The below attached graph shows the given inequality.
Step-by-step explanation:
Here, the given inequality,
x - 2y > -12
Since, related equation of the inequality,
x - 2y = -12
Which is a line passes through (-12, 0) and (0, 6)
Also, '>' represents dotted line,
So, join these two points by dotted line in the coordinate plan,
Now,
0 - 2(0) > -12 (True)
i.e. shade the region of the line that contains origin.
By the above explanation we will get the graph of given inequality ( shown below )
A winter jacket is marked down 75% from its original price. according to the new price tag, it now costs $52.50. what was the original price? $210.00
is (4,2) a solution to the system y-x=2 and -3x -2y= -8
A common rule is that housing expenses should not be more than 28% of your monthly income. Your monthly income is $3,200. How much can you spend on housing?
Answer:
less than $896.00
Step-by-step explanation:
A common rule is that housing expenses should not be more than 28% of your monthly income.
your monthly income = $3,200
so your housing expense should not be more than 28% of $3,200
= [tex]\frac{28}{100}[/tex] × 3,200
= 0.28 × 3,200 = $896.00
So you can spend less than $896.00 on housing expenses.
PLEASE HELP AND BRAINLYEST ANSWER TO CORRECT ANSWER
PLEASE HELP ME IM TRYING TO GET THIS DONE AND NOBODY IS HELPING ME Triangle ABC below is reflected over the y-axis.
a What are the coordinates of the reflected triangle
b Describe in words what happened to the x coordinates and the y coordinates of the original triangles vertices as a result of this reflection
solve the equation. Check for extraneous solutions.
[tex]2|7-7x|=2x+4 [/tex]
Answer: The answer is [tex]\dfrac{5}{8},~\dfrac{3}{2}[/tex] and no extraneous solution.
Step-by-step explanation: The given equation is
[tex]2|7-7x|=2x+4.[/tex]
We are given to solve this equation and also find its extraneous solution.
The solution is as follows:
[tex]2|7-7x|=2x+4\\\\\Rightarrow |7-7x|=x+2\\\\\Rightarrow 7-7x=x+2,~~~~~-7+7x=x+2\\\\\Rightarrow 8x=5,~~~~~~~~~~~~~~~~\Rightarrow 6x=9\\\\\\\Rightarrow x=\dfrac{5}{8},~~~~~~~~~~~~~~~~~\Rightarrow x=\dfrac{3}{2}.[/tex]
now, for [tex]x=\dfrac{5}{8}[/tex], we have
[tex]L.H.S.=2|7-7\times \dfrac{5}{8}|=\dfrac{21}{4},\\\\R.H.S.=2\times\dfrac{5}{8}+4=\dfrac{21}{4}.[/tex]
So, this solution is not extraneous.
For [tex]x=\dfrac{3}{2}[/tex], we have
[tex]L.H.S.=2|7-7\times \dfrac{3}{2}|=7,\\\\R.H.S.=2\times\dfrac{3}{2}+4=7.[/tex]
So, this solution is also not extraneous.
Hence, the solution is [tex]\dfrac{5}{8},~\dfrac{3}{2}[tex] and there is no extraneous solution.
As Claudia walks away from a 264-cm lamppost, the tip of her shadow moves twice as fast as she does. What is Claudia’s height?
As Claudia walks away from a 264-cm lamppost, the tip of her shadow moves twice as fast as she does, so the Claudia’s height is 132 cm.
To solve this problem, we can use the concept of similar triangles.
Let's assume Claudia's height is h cm.
Since Claudia's shadow tip moves twice as fast as she does, her shadow's length must be twice her height, or 2h cm.
According to the question, as Claudia walks away from the lamppost, her shadow moves twice as fast as she does.
This means the ratio of the length of the shadow to the distance Claudia walks is the same as the ratio of the distance the shadow moves to the distance Claudia walks.
We can set up the following proportion:
(2h) / 264 = h / x
where x is the distance Claudia walks from the lamppost.
Solve for h by cross multiplying:
2h * x = 264 * h
2hx = 264h
Divide both sides by h:
2x = 264
Divide both sides by 2:
x = 132 cm
Therefore, Claudia's height is h = 132 cm.
By using the principles of similar triangles and the given information that Claudia's shadow moves at double her pace, we establish a proportion between the heights and shadow lengths, solve the equation, and find that Claudia's height is 176 cm.
Explanation:To solve the problem of finding Claudia's height based on the information given about her shadow, we need to apply the principles of similar triangles. The situation describes a real-world application of similar triangles, where Claudia and her shadow form one triangle, and the lamppost and its shadow form another. These triangles are similar because the angles are the same: the angle of elevation to the sun is the same for both Claudia and the lamppost, and the ground provides the same angle for both bases.
Let's denote Claudia's height as h, the distance Claudia walks away from the lamppost as x, and therefore the length of her shadow will be 2x (since it moves twice as fast). The similar triangles give us the following proportion:
Height of Lamppost / Height of Claudia = Length of Lamppost's Shadow / Length of Claudia's Shadow
264 cm / h = (x + 2x) / 2x
This simplifies to:
264 / h = 3 / 2
Solving for h, we get:
2 * 264 = 3h
h = 2 * 264 / 3
h = 528 / 3
h = 176 cm
Therefore, Claudia's height is 176 cm.
What does 15/6 equal turned into a mixed fraction?
The figure below shows circle with center O and regular hexagon ABCDEF constructed inscribed in a circle.Which of the following steps will help prove that triangle FBD is equilateral?
Triangle FBD in the given regular hexagon inscribed in a circle can be proven to be an equilateral triangle based on the equal lengths of radii and the angle of 60 degrees subtended at the center by the side of the hexagon.
Explanation:
To prove that triangle FBD is an equilateral triangle, we first need to understand a few properties of a regular hexagon and a circle. In a regular hexagon inscribed in a circle, every angle at the center of the circle subtended by the sides of the hexagon is 60 degrees because the total degree measure at the center of the circle is 360, and this is divided equally among the six sides of the hexagon.
Triangle FBD is formed by joining the center of the circle, O, and two consecutive vertices of the hexagon, B and F. As the hexagon is regular and inscribed in a circle, both OB and OF are radii of the circle. By definition, all radii of a given circle are equal in length. Therefore, OB = OF.
The angle BFO subtended at the center by the side BF of the hexagon is 60 degrees. Hence, triangle FBD is an equilateral triangle because it has two equal sides and the included angle is 60 degrees, which are the properties of an equilateral triangle.
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To prove that triangle FBD is equilateral, one can show that the central angles corresponding to the three sides of the hexagon (angle AOB, angle BOC, and so on) are all equal. Therefore, demonstrating that angle FOB, angle BOD, and angle DOF are each 120 degrees will establish that triangle FBD is equilateral.
Explanation:In a regular hexagon inscribed in a circle, the central angles formed by connecting the center of the circle (O) to consecutive vertices of the hexagon are all equal. Since each interior angle of a regular hexagon is 120 degrees, the central angles (e.g., angle AOB, angle BOC, etc.) are also 120 degrees. To prove that triangle FBD is equilateral, one needs to focus on the central angles corresponding to its sides.
The central angles associated with triangle FBD are angle FOB, angle BOD, and angle DOF. By demonstrating that each of these angles is 120 degrees, it can be concluded that triangle FBD is equilateral. The regularity of the hexagon ensures that the central angles are equal, making this an effective and straightforward way to prove the equilaterality of triangle FBD.
In conclusion, to establish the equilaterality of triangle FBD, one should emphasize the properties of central angles within the context of a regular hexagon. Specifically, showing that angle FOB, angle BOD, and angle DOF are each 120 degrees serves as a valid proof for the equilateral nature of triangle FBD within the given geometric configuration.
Solve -23.7 + d = -48.57.
-4.62
-46.2
-24.87
-72.27
Answer:-24.87 is the correct answer, i checked it!
Step-by-step explanation:
What is the square root of 69?
Which of the following is the inverse function of y = 3x + 1?
x = 3y + 1
y = (1/3)x + 1/3
y = (x – 1)/3
y = x/3 - 1
Answer:
Option C is the correct answer : [tex]y=\frac{(x-1)}{3}[/tex]
Step-by-step explanation:
[tex]y=3x+1[/tex]
For finding the inverse of this function, we will interchange x and y, then solve for y.
[tex]3y=x-1[/tex]
[tex]y=\frac{x-1}{3}[/tex]
Hence, option C is the correct answer : [tex]y=\frac{(x-1)}{3}[/tex]
Triangle XYZ is isosceles. The measure of the vertex angle, Y, is twice the measure of a base angle. What is true about triangle XYZ? Check all that apply?
Answer:
The answers are,
The measure of angle Z is 45°.
The perpendicular bisector of Line segment X Z creates two smaller isosceles triangles.
Angle Y is a right angle.
Step-by-step explanation:
I got it right on geometry test.
Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. What is the system of equations representing these costs?
Answer:
its C on ed
Step-by-step explanation:
195 s; minutes
a. 4.5 min
b. 3 min
c. 3.25 min
d. 2.5 min
The marginal revenue function on sales of q units of a product is R'(q)=240-18√q dollars per unit.
Estimate the total revenue if sales are 100 units.
What is the marginal revenue at 100 units?
Estimate the total revenue if sales are 101 units.
...?
The marginal revenue for 100 units sold is 180 dollars per unit. We cannot precisely estimate the total revenue for 100 or 101 units sold without further information.
Explanation:In this problem, we're dealing with the concept of marginal revenue. The marginal revenue function gives us the change in total revenue for each additional unit sold. That is given in this case as R'(q)=240-18√q.
To find the marginal revenue at 100 units, we simply substitute q = 100 into our function: R'(100)=240-18√100 = 240 - 18*10 = 180 dollars per unit.
The total revenue given a specific quantity is typically found by integrating the marginal revenue function. However, without the constants of integration or the original revenue function, we cannot accurately compute the total revenue for 100 or 101 units sold in this case.
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