A rhombus exists. This rhombus has 2 diagonals. The diagonals touch the side forming angles. These angles are in the ratio 4:5. Solve for all the angles in this rhombus based on the theorems for rhombuses and parallelograms.
What is the area of a sector with a central angle of π3 radians and a radius of 12.4 m? Use 3.14 for π and round your final answer to the nearest hundredth.
Answer:
80.47
Step-by-step explanation:
This is correct! :D
jake plans to use a ramp to make it easier to move a piano out of the back of his truck the back of the truck is 33 inches tall and the ramp is 65 inches long. what is the horizontal distance from the end of the ramp to the back of the truck
Answer:
56 inches is the horizontal distance from the end of the ramp to the back of the truck.
Step-by-step explanation:
Height of the back of the truck =33 inches
Length of the ramp = 65 inches
Length of the end of ramp to the back of the truck =?
In triangle ABC:
AB = 33 inches
BC = ?
AC = 65 inches
[tex]AB^2+BC^2=AC^2[/tex] (Pythagoras theorem)
[tex](33 inches)^2+(BC)^2=(65 inches)^2[/tex]
BC = 56 inches
factor the following polynomial completely 30y^6+25y^5-10y^4
Please solve these for me. I need them for a quiz.
A clock is constructed using a regular polygon with 60 sides. The polygon rotates everybody minute. How much has the polygon rotated after 7 minutes
•14 degrees
•21 degrees
•35 degrees
•42 degrees
maxine hosted a dinner party at her favorite restaurant. she had to pay $12 per guest. the restaurant took $72 off the bill due to a mistake in the order. if the finale bill is $300, which equation will help the restaurant determine the number of guests at the dinner party
A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 6% of 80%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation.
6) Ethan uses the function f(x) = 2x2 + 2x + 4 to track the temperature of a substance over 8 hours. You know that f(3) = 28 meaning that the temperature of the substance is 28°C when you plug in a 3 for x. What is the domain of Ethan’s function?
The domain of Ethan's function f(x) = 2x² + 2x + 4 is all real numbers as it is a quadratic function.
Explanation:The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value). In this case, the function f(x) = 2x² + 2x + 4 represents the temperature of a substance over time. Since temperature is a physical quantity and cannot be negative, the domain of the function must be restricted to non-negative values of x.
To determine the exact domain of the function, we can analyze the expression 2x² + 2x + 4. This expression is always non-negative for any real number x. Therefore, the domain of f(x) = 2x² + 2x + 4 is all real numbers x ≥ 0.
In mathematical notation, the domain of the function can be expressed as:
{x ∈ ℝ | x ≥ 0}
This indicates that the function is defined for all real numbers (ℝ) as long as the value of x is greater than or equal to 0 (x ≥ 0).
Which rule describes a translation that is 8 units to the right and 2 units up?
x, y (x + 8, y + 2)
Ninas car exponentially depreciates at a rate of 7 percent per year. If nina bought the car when it was 6 years old for 12000, what was the original price of the car
Answer:
[tex] A(6) = 12000 = A_o e^{-0.07 *6}[/tex]
And solving for the initial amount [tex] A_o[/tex] we got:
[tex] A_o = \frac{12000}{e^{-0.07*6}}= 18263.539[/tex]
So then the original price for the car would be approximately 18263.539$
Step-by-step explanation:
For this case we can use the exponential model given by:
[tex] A(t) = A_o e^{bt}[/tex]
Where:
[tex]A_o[/tex] represent the initial amount for the car
[tex]b=-0.07[/tex] represent the exponential growth/decay rate
t represent the number of years. With t =0 at the begin
After 6 year we have that t =6, and we know this condition:
[tex] A(6) = 12000[/tex]
So then we can use the exponential model formula and the condition given and we have this:
[tex] A(6) = 12000 = A_o e^{-0.07 *6}[/tex]
And solving for the initial amount [tex] A_o[/tex] we got:
[tex] A_o = \frac{12000}{e^{-0.07*6}}= 18263.539[/tex]
So then the original price for the car would be approximately 18263.539$
help me plsss i really need did that but still dont get it
What is log5(4*7)+log5^2 as a single log?
Answer with explanation:
The four options are
(A) log5 21 (B) log5 26 (C) log5 30 (D) log5 56
[tex]\rightarrow\log_{5}(4\times 7) +\log_{5}(2)\\\\ \rightarrow \log_{5}28+\log_{5}2\\\\\rightarrow \log_{5}(28 \times 2)\\\\=\log_{5}(56)\\\\ \text{Used this property of log}\\\\ \log_{m} a+\log_{m} b=\log_{m} ab[/tex]
Option D
HELP QUICK PLEASE!!!!!
A proof for the Corresponding Angles Theorem is shown below. Next to each reason, choose the statement to which it applies.
How many sets of 7 questions can be chosen from a file of 25 questions?
I need Geometry help!!!
Find the nth term of the sequence
-3, 0, 5, 12
Work out the reciprocal of 2 x 10(9,as a power). Give your answer in standard form.
The perimeter of the rectangle is 34 cm. Find the value of x.
A. 2
B. 17
C. [tex] \frac{34}{33} [/tex]
D. 20
PLZ HELP!!!!!!! Can a kite be formed by drawing a triangle and then reflecting one or more times? Explain.
Select one:
a. Yes. Draw any triangle ABC. Reflect this triangle across the perpendicular bisector of line AB, creating triangle A'B'C' for which A'=B and B'=A. By the definition of a reflection, sides A'C and B'C' are congruent. In addition, sides B'C and A'C' are congruent. The quadrilateral CC'B'A' has two pairs of consecutive sides that are congruent and no congruent opposite sides. By definition, this is a kite.
b. Yes. Draw any triangle ABC. Reflect this triangle across the line AB, creating triangle A'B'C' for which A'=A and B'=B. By definition of a reflection, sides B'C and B'C' are congruent. In addition, sides A'C and A'C' are congruent. The quadrilateral CA'C'B' has two pairs of consecutive sides that are congruent and no congruent opposite sides. By definition, this is a kite.
c. No. Since the reflection of a triangle is always another triangle, there is no way to create a quadrilateral using a triangle or its reflection.
d. No. It is not possible to reflect a triangle in such a way that the result is quadrilateral with any consecutive sides that are congruent.
The answer is (B).
Draw any triangle ABC. Reflect this triangle across the line AB, creating triangle A'B'C' for which A'=A and B'=B. By definition of a reflection, sides B'C and B'C' are congruent. In addition, sides A'C and A'C' are congruent. The quadrilateral CA'C'B' has two pairs of consecutive sides that are congruent and no congruent opposite sides. By definition, this is a kite.
Hi guys can you help me factor these two equations?
5x^2-13x-6
4x^4 – 28x^3 + 48x^2
please show your work on both of them, and thank you so much!
Verify that △ABC∼△DEF. Find the scale factor of △ABC to △DEF.
△ABC: AB = 10, BC = 16, CA = 20
△DEF: DE = 25, EF = 40, FD = 50
I really need someone to explain to me how to do this because i am so confused my teacher didn't give us notes and didn't explain this very well.
Answer:
2/3 i got it right
Step-by-step explanation:
Final answer:
To find the scale factor between △ABC and △DEF, compare their corresponding side lengths and calculate the scale factor as 2.5 or 5/2.
Explanation:
To verify that two triangles △ABC and △DEF are similar, you need to check if their corresponding angles are congruent and their corresponding sides are proportional.
Calculate the scale factor using the corresponding sides of the triangles: AB/DE = BC/EF = CA/FD.
Substitute the values: 10/25 = 16/40 = 20/50. Simplify to find the scale factor.
Therefore, the scale factor of △ABC to △DEF is 2.5 or 5/2.
How are the functions y=x and y=x+5 related? How are their graphs related?
Final answer:
The functions y=x and y=x+5 have the same slope but different y-intercepts. Their graphs are straight lines.
Explanation:
The functions y=x and y=x+5 are related in that they have the same slope of 1. This means that for every increase of 1 in the value of x, the value of y will also increase by 1. However, they have different y-intercepts. The function y=x has a y-intercept of 0, while the function y=x+5 has a y-intercept of 5.
Their graphs are related in that they are both straight lines. The graph of y=x is a line passing through the origin (0,0), while the graph of y=x+5 is a line shifted upward by 5 units compared to the graph of y=x.
Eight more than the quotient of a number and 4 equals 5
What is 6/7 as a recurring decimal?
Which algebraic expression is equivalent to the expression below? (3x + 12) + 8x
A.
(3x + 8x) + 12
B.
(3x - 8x) + 12
C.
23x
D.
(3x + 12x) + 8
If the circumference of a circle is 11inches, which is closest to its area?a.380 square inchesb.95 square inchesc.17 square inchesd.35 square inches
Write an expression to show the sum of fourteen and triple eight.
Write an equation for the translation of y = 4 x that has the given asymptotes. 15. x = 0, y = 3
helppppppppppppppppppppppppppppppppp
If the radius of the circle is doubled, by what number is the circumference multiplied?
The number by which the circumference is multiplied is:
2
Step-by-step explanation:We know that the circumference of the circle in terms of the radius r is given by:
[tex]\text{Circumference}=2\pi r[/tex]
Now, if the radius is doubled.
i.e.
[tex]r'=2r[/tex]
Hence, the circumference of the new circle is given by:
[tex]\text{Circumference of new circle}=2\pi (2r)\\\\i.e.\\\\\text{Circumference of new circle}=2(2\pi r)[/tex]
i.e.
[tex]\text{Circumference of new circle}=2\times \text{Circumference of original circle}[/tex]
The constant by which the circumference is multiplied is: 2