solve for x. round your answer to two decimal places. show your work for full credit. a right triangle is shown with the hypotenuse labeled x. one angle has a measure of thirty degrees, and the opposite leg has a length of ten.
The value of x is 20 when right triangle is with the hypotenuse labeled x , one angle has a measure of thirty degrees, and the opposite leg has a length of ten.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Right ∆ with Hypotenuse is x, Opposite is 10
Reference angle = 30°.
We need to find the value of x
Since we are given a reference angle with opposite length, and we are to find the hypotenuse length, x, apply the following trigonometric ratios formula:
sin(theta)=opposite side/hypotenuse
Plug in the values into the equation
sin 30 = 10/x
1/2=10/x
Apply cross multiplication
x=20
Hence, the value of x is 20 when right triangle is with the hypotenuse labeled x , one angle has a measure of thirty degrees, and the opposite leg has a length of ten.
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true or false Volume can be measured in liters or cubic meters.
Sixteen is 64% of what number?
A.12
B.25
C.32
D.48
Put these numbers in order from least to greatest 11, 7, 8, 3, 6, three, 16, 10, 16
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f of x equals eight divided by x and g of x equals eight divided by x
Multiply.
Express your answer as a simple fraction or improper fraction.
7 · 3/4 = n
Rasheed needs to save $231. To earn money,he plans to wash cars and charge $12 per car.Write two estimates Rasheed could use to determine how many cars he needs to wash
slope -2 and passes through (1, 1)
There are 6 quarters in a jar. Jill adds 2 quarters to the jar every day. Which linear equation represents the total amount of quarters in the jar after x days?
y = 6x + 2
y = 1/6x + 2
y = 2x + 6
6y = 2x
Answer: [tex]y = 2x + 6[/tex]
Step-by-step explanation:
Let x represents the number of days .
Given : There are 6 quarters in a jar.
Jill adds 2 quarters to the jar every day.
Then, the number of quarters added in x days = 2x
Now, the total number of quarters in the jar after x days = 2x+6
Hence, the linear equation represents the total amount of quarters in the jar after x days will be:-
[tex]y = 2x + 6[/tex]
Olivia must earn 475 points out of 550 to receive a b in math. so far she had earned 240 test points 85 quiz point and 40 homework points. how many points p must she score on her final exam to earn at least a b in math
Answer: Olivia needs 110 points on her final exam in order to earn at least a B in Math.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
Here, given that,
Olivia must earn 475 points out of 550 to receive a b in math.
so far she had earned 240 test points
85 quiz point
and 40 homework points.
Solution: 240 + 85 + 40 = 365
Now, we get,
475 - 365 = 110
Hence, Answer: Olivia needs 110 points on her final exam in order to earn at least a B in Math.
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Paul has 2/3 as many postcards as shawn . the number of postcards shawn has is 3/5 of the number of postcards tim has. if the three boys have 280 postcards altogether,how many more postcards does tim have than paul ?
Heather writes the equations below to represent two lines drawn on the coordinate plane.
–6x + 18y = 0
4x – 12y = 20
After applying the linear combination method, Heather arrived at the equation 0 = 60. What conclusion can be drawn about the system of equations?
The equation has no solution; therefore, the system of equations has no solution.
The equation has a solution at (0, 60); therefore, the system of equations has a solution at (0, 60).
The equation has infinite solutions; therefore, the system of equation as infinite solutions.
The equation has a solution at (0, 0); therefore, the system of equations has a solution at (0, 0).
Answer:
its A if you are taking the unit test
Step-by-step explanation:
You have $6,500 to deposit. If you deposit the money in a savings account at your local bank, you will earn 1.45% annual interest and will be able to make ATM withdrawals at your bank's ATMs. If you deposit the money in an online savings account, you will earn 2.25% interest, but you will be charged $4 every time you make an ATM withdrawal. Assuming that your ATM withdrawals do not reduce the amount of interest you earn, how many ATM withdrawals must you make in a year for the local savings account to be a better deal than the online savings account?
a.
5
b.
12
c.
14
d.
10
Answer:
C. 14
Step-by-step explanation:
I just answered it correct
How many pints are in 7.5 gallons?
a. 120 pt
b. 90 pt
c. 60 pt
d. 30 pt
A box of ground nutmeg weighs 1 1/3 ounce. If there are 20 teaspoons of nutmeg in the box, how much does one teaspoon of nutmeg weigh?
1/15 ounce
1/20 ounce
1/60 ounce
4/3 ounce
we know that
a) A box of ground nutmeg weighs [tex]1 1/3[/tex] ounces
b) There are [tex]20[/tex] teaspoons of nutmeg in the box
Step 1
Convert mixed number to an improper fraction
[tex]1\frac{1}{3} \ ounces= \frac{1*3+1}{3}= \frac{4}{3}\ ounces[/tex]
Step 2
By proportion
Find the weight of one teaspoon
[tex]\frac{(4/3)}{20} \frac{ounces}{teaspoons} =\frac{x}{1} \frac{ounces}{teaspoon} \\ \\x= \frac{4}{20*3}\\ \\x= \frac{4}{60}\ ounces\\\\x=\frac{1}{15}\ ounces[/tex]
therefore
the answer is the option
[tex]\frac{1}{15}\ ounces[/tex]
lim x->1 (x^n-1)/(x^m-1) =?
is 48/72 and 6/9 Proportional or Nonproportional
The fractions (48/72) and (6/9) are proportional as, (8/8)(6/9) is equal to (48/72).
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
Given, A fraction 48/72.
Now, If we simplify the fraction by factoring out some common terms we'll have,
24/36.
= 12/18.
= 6/9.
So, They are proportional.
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Match Term Definition
Line Segment A) a series of points that extend in two directions without end
Plane B) two lines that intersect at 90° angles
Perpendicular Lines C) lines that lie in the same plane and do not intersect
Line D) a flat surface that extends infinitely and has no thickness
Parallel Lines E) part of a line that has two endpoints
Answer:
Line segment: E
Plane: D
Perpendicular lines: B
Line: A
Parallel lines: C
Step-by-step explanation:
This middle school mathematics question asks for matches between geometric terms and their definitions. Line segments have two endpoints, planes extend infinitely without thickness, perpendicular lines intersect at 90 degrees, lines extend indefinitely in two directions, and parallel lines never intersect.
Explanation:
In the field of mathematics, particularly in geometry, we often deal with various foundational elements such as lines, line segments, planes, and the relationships between them. To understand these concepts, it is essential to know their definitions and how they relate to each other.
A line segment is best described as a part of a line that has two distinct endpoints. This means a line segment is contained and does not extend infinitely in any direction. An example of this is the edge of a ruler, which begins and ends at specific points. The correct match for a line segment in the provided list is E) part of a line that has two endpoints.
A plane in geometry is a flat, two-dimensional surface that extends infinitely in all directions. It's similar to a vast sheet of paper with no edges. It is defined by at least three noncollinear points and is often represented in drawings as a four-sided figure, but it continues without end. The correct definition for a plane is D) a flat surface that extends infinitely and has no thickness.
Perpendicular lines are two lines that intersect at an angle of 90 degrees. The point where they cross forms right angles, and the two lines are always at the same distance from each other at this point. The definition of perpendicular lines is B) two lines that intersect at 90° angles.
Regarding a line, it is an undefined term in geometry that represents a straight path that extends infinitely in both directions with no thickness. It is comprised of an infinite number of points. A simple description of a line is A) a series of points that extend in two directions without end.
Lastly, parallel lines are lines in the same plane that do not intersect, no matter how far they are extended on either side. This is because they are always the same distance apart, maintaining a consistent separation across their entire length. The correct match for parallel lines is C) lines that lie in the same plane and do not intersect.
answer that for me please i am very confused
What is the total interest on a ten-year. 6.1% loan with a principal of $32,000?
Final answer:
The total interest on a ten-year, 6.1% loan with a principal of $32,000 is $19,520.
Explanation:
To find the total interest, we need to use the formula:
Interest = Principal × Rate × Time
Given that the principal is $32,000, the interest rate is 6.1%, and the time is 10 years, we can substitute these values into the formula to calculate the total interest:
Principal: $32,000
Rate: 6.1%
Time: 10 years
Interest = $32,000 × 0.061 × 10 = $19,520
Therefore, the total interest on a ten-year, 6.1% loan with a principal of $32,000 is $19,520.
If adams plain travels at a speed of 375mph in 6hours ,how far did the plane travel
Which fraction is equivalent to 2/6?
help?
I don't want the answer, merely step by step instructions on how to solve it! Thanks x
Select the inequality that models the problem.
The length of a rectangle is twice its width. If the perimeter of the rectangle is less than 50 meters, what is the greatest width of the rectangle?
2*2w + 2w < 50
2 + 2w < 50
2w*w < 50
2w < 50 ...?
Solve for the equation. u + 3.5 = 5
What is the equation of the line –3x–2y=30 in slope-intercept form?
Enter your answer in the box.
The slope intercept form of the given equation of a line is y= -3/2 x -15.
The given equation of the line is -3x-2y=30.
What is the slope intercept form?The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.
The standard form of the slope intercept form is y=mx+c.
Now,
-3x-2y=30
⇒ -2y=3x+30
⇒ y= -3/2 x -15
Therefore, the slope intercept form of the given equation of a line is y= -3/2 x -15.
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Hector wrote the following proof for his geometry homework for the given problem:
Statements Reasons
segment LN is congruent to segment NP Given
∠1 ≅ ∠2 Given
∠N ≅ ∠N Reflexive Property
ΔLNO ≅ ΔPNM Angle-Angle-Side Postulate
∠NLO ≅ ∠NPM
Which of the following completes Hector's proof?
Angle Addition Postulate
Converse of Corresponding Angles Postulate
Corresponding Parts of Congruent Triangles Are Congruent
Triangle Proportionality Theorem
Answer:
∠ NLO ≅ ∠ NPM Corresponding Parts of Congruent Triangles Are Congruent
Step-by-step explanation:
It's on my chart on the test this is 100% right
Final answer:
Hector used the Angle-Angle-Side Postulate to show congruency between two triangles. Therefore, the corresponding angles are congruent with the CPCTC principle. Thus, option 3 is correct.
Explanation:
Hector claims that ΔLNO ≅ ΔPNM is based on the Angle-Angle-Side Postulate.
Since the triangles are congruent, their corresponding parts must also be congruent.
Therefore, the statement that ∠NLO ≅ ∠NPM is supported by the principle that Corresponding Parts of Congruent Triangles Are Congruent (CPCTC).
Carol sells candles and Yankee Candle. She earns $8.50 per hour plus 6% commission on sales. Last week Carol worked 40 hours. What was Carol’s weekly gross salary if her total sales were $250? *
$590.51
$352.16
$355.00
$340.00
Answer:$352.16
Im in a rush so cant add explaination
Ted and Robin each gave a basket of green apples to their friend Lily. Ted’s basket contains 5 apples, each weighing ounces. Robin’s basket contains 6 apples, each weighing ounces. Whose basket is heavier and by how much?
Robin's basket is heavier than Ted's basket by 2 ounces.
Explanation:To determine whose basket is heavier, we need to find the total weight of each basket.
Ted's basket contains 5 apples, each weighing 8 ounces. Therefore, the total weight of Ted's basket is 5 * 8 = 40 ounces.
Robin's basket contains 6 apples, each weighing 7 ounces. Therefore, the total weight of Robin's basket is 6 * 7 = 42 ounces.
Since Robin's basket weighs 42 ounces and Ted's basket weighs 40 ounces, Robin's basket is heavier by 2 ounces.
Find dy/dx and d2y/dx2. x = et, y = te−t
The question is about finding the first and second derivatives of y with respect to x. The first derivative dy/dx is found to be (1+t)e^-2t, and the second derivative d2y/dx2 is found to be -2e^-2t.
Explanation:The derivatives are found by differentiating each function with respect to t first, using the product and chain rules, respectively: the derivatives dy/dt and dx/dt are dy/dt = e^-t - te^-t and dx/dt = e^t. Then, dy/dx can be found as (dy/dt)/(dx/dt), and the second derivative d2y/dx2 can be obtained by differentiating dy/dx with respect to x, which will utilize the quotient rule. Specifically, dy/dx = (e^-t(1+t))/(e^t) which simplifies to (1+t)e^-2t, and after a relatively complex differentiation for d2y/dx2, we get -2e^-2t.
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