Solve the triangle, find m∠A and m∠C. Round angles to the nearest degree.
m∠A= __∘
m∠C= __∘
Answers
Answer:
\(m\angle A=63^\circ\\m\angle C=26^\circ\)
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of the triangle is called the hypotenuse and the other two sides are called the legs.
Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.
The cosine ratio is defined as:
\(\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}\)
Note the angle A of the figure has 17 as the adjacent leg and 38 as the hypotenuse, so we can directly apply the formula:
\(\displaystyle \cos A=\frac{17}{38}\)
\(\cos A=0.4474\)
Using a scientific calculator, we get the inverse cosine:
\(A=\arccos(0.4474)\)
\(A\approx 63^\circ\)
Since A+B+C=180°, we can solve for C:
C = 180° - A - B
C = 180° - 63° - 90°
C = 26°
Thus:
\(m\angle A=63^\circ\\m\angle C=26^\circ\)
In the given right triangle ABC, m∠A ≈ 26.44° and m∠C ≈ 63.56°.
To solve the right triangle ABC, we can use trigonometric ratios. In a right triangle, the three main trigonometric ratios are:
1. Sine (sin): \(\(\sin(\theta) = \frac{{\text{opposite side}}}{{\text{hypotenuse}}}\)\)
2. Cosine (cos): \(\(\cos(\theta) = \frac{{\text{adjacent side}}}{{\text{hypotenuse}}}\)\)
3. Tangent (tan): \(\(\tan(\theta) = \frac{{\text{opposite side}}}{{\text{adjacent side}}}\)\)
Given:
AC = 38
AB = 17
To find the angles m∠A and m∠C, we can use the sine and cosine ratios, respectively.
1. For m∠A:
\(\(\sin(m\angle A) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle A= \sin^{-1}\left(\frac{{17}}{{38}}\right)\)\)
2. For m∠C:
\(\(\cos(m\angle C) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle C = \cos^{-1}\left(\frac{{17}}{{38}}\right)\)\)
Let's calculate the angles:
\(1. \(m\angle A \approx \sin^{-1}\left(\frac{{17}}{{38}}\right) \approx 26.44^\circ\)\\\\2. \(m\angle C \approx \cos^{-1}\left(\frac{{17}}{{38}}\right) \approx 63.56^\circ\)\)
Therefore, m∠A ≈ 26.44° and m∠C ≈ 63.56° (rounded to the nearest degree).
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Related Questions
Multiply. Write each product in simplest form.
9. 3×11
10. //
13. 021-
12.
20
=
=
=
11. 2×4=
8 9
X
18 20
14.
=
Answers
Answer:
Te conozco y sé qué
Como Nuevo de fabrica el otro
Hannah can spend up to $40 on snacks and drinks at the movie theater. A snack costs $5 and a drink costs $3.50.
Use for the number of snacks
Use for the number of drinks
Which inequality represents this situation?
Answers
Answer:
5s + 3.50d < 40
Step-by-step explanation:
if you were to total up the costs of a snack and drink together you'll end up with $8.50
-multiply $8.50 until you reach $40 mark
i.e 8.50×2(means 2 of each item) = $17
8.50×3 = $25.5
8.50×4 = $34
8.50×5= $42.5
-if you look at it, the calculation for 5, the pricing is now over the budget therefore the answer is then 5s + 3.50d < 40 because she can only spend up to $34 at most
find the critical value(s) and rejection region(s) for the type of z-test with level of significance . include a graph with your answer. right-tailed test, a=0.03.
Answers
Answer:
c
Step-by-step explanation:
The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.
The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88 OR Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.
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plz guys help me with that questions plz
plz guys help me
Answers
Step-by-step explanation:
Issun Sengeki... Messatsu!
In my opinion, I'd say A and C aren't functions, but B is a function.
The reason being is because every "X" value has a "Y" value. For those that don't have exactly 1 "Y" value aren't functions.
A. has more "Y" values than "X" values, so that proves not to be a function.B. Has "X" values that are exactly appointed to a "Y" value.C. Has one "X" value that's missing, and a "Y" value that doesn't exist.Hope this helps!
Quote:
"The answer lies in the heart of battle."
- Ryu
Factor the expression 8x + 12 using the GCF.
8x + 12 =
Answers
Answer:
4(2x+3)
Step-by-step explanation:
Because 4 is the GCF
This track is made of a rectangle and two semicircles.
Find the perimeter of its outer edge, outlined in bold.
Answers
Answer:
the perimeter of thr outer breath is 34
Kareem says that the ratio 4:1 is equivalent to the ratio 12:9 because 4+8=12 and 1+8=9 is kareem correct? explain how you know.
Answers
No, Kareem is not correct because the ratio of 4:1 can never be equal to the ratio of 12:9.
Here,
Kareem says that the ratio 4:1 is equivalent to the ratio 12:9.
Because 4+8=12 and 1+8=9.
We have to find that Kareem is correct or not.
What is a ratio?
Ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.
Now,
Kareem says that the ratio 4:1 is equivalent to the ratio 12:9.
Calculate the ratio as;
12 / 9 = ( 3 x 4 ) / ( 3 x 3 ) = 4/3
So,
12 / 9 = 4 / 3
Hence, Kareem is incorrect because the ratio of 4:1 can never be equal to the ratio of 12:9.
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In how many ways can you put seven marbles in different colors into four jars? Note that the jars may be empty.
Answers
Answer: 16,384
Step-by-step explanation:
The seven marbles have different colours, so we can differentiate them.
Now, suppose that for each marble we have a selection, where the selection is in which jar we put it.
For the first marble, we have 4 options ( we have 4 jars)
For the second marble, we have 4 options.
Same for the third, for the fourth, etc.
Now, the total number of combinations is equal to the product of the number of options for each selection.
We have 7 selections and 4 options for each selection, then the total number of combinations is:
C = 4^7 = 16,384
Answer:
the answer is 16384
Step-by-step explanation:
have a nice day.
Cheryl is organizing her movie collection. If each movie case is 3/4 inch wide, how many movies can fit on a shelf 5 1/4 wide?
Answers
I believe she could fit 7 movies onto the shelf
Step-by-step explanation:
first what I did was I turned the 5 1/4 into 21/4. Then I divided 21 by 3 (5 1/4 ÷ 3/4) in order to get the amount of movies. That equaled 7
The answer would be that she could fit 7 movies on the shelf.
A school is looking to cater an event by having a food truck. Food truck A will charge $1.50 for each item sold and a fee of $50 to come to the school. Truck B will charge $2.75 per item but will not charge a fee to come to the school. How many items must the school purchase to have the cost of these two trucks be the same? Enter in your numerical answer.
Answers
Answer:
40 items
Step-by-step explanation:
I used the equation 1.5x+50=2.75x to find the answer. If the school were to buy 40 items from either truck, they would both amount to 110.
The diagram below shows two similar isosceles triangles. What is the length of ST in triangle RST?A. 6cmB. 4cmC. 12cm D. 16cm
Answers
ANSWER
ST = 4cm
EXPLANATION
We want to find the length of ST in triangle RST.
We are given that the two triangles are similar.
In similar triangles, the ratio of proportional sides of the two triangles are equal for all sides.
This means that:
\(\frac{OP}{RS}=\frac{PQ}{ST}=\frac{OQ}{RT}\)Therefore, to find the length of ST, we can apply the last two proportions. That is:
\(\begin{gathered} \frac{8}{ST}=\frac{4}{2} \\ \Rightarrow ST=\frac{8\cdot2}{4} \\ ST=4\text{ cm} \end{gathered}\)That is the length of ST.
3 If the formula y = x is changed by adding seven as shown in red below. Which of the following best describes the resulting change for each of the functions? Function f(0) = (x + 7)3 ] f(x) = x² +7 Transformation a. The +7 would directly affect the x-values, so the graph would shift horizonally. b. The +7 would directly affect the y-values, so the graph would shift vertically. c. The +7 would have no effect.
Answers
Notice that for the first altered function we have that:
\(x^3=(x-7+7)^3=f(x-7)\)Therefore the +7 would directly affect the x-values, so the graph would shift horizontally.
For the next function we have that:
\(x^3=x^3+7-7=f(x)-7\)Therefore the +7 would directly affect the y-values, so the graph would shift vertically.
Question 2(Multiple Choice Worth 2 points)
(Two-Column Tables MC)
The pharmacist has a 3.6 L bottle of cough syrup. If she fills a bottle that is 1,500 ml, how many ml of cough syrup does the pharmacist have left? (1 L = 1,000 ml)
21 ml
150 ml
1,360 ml
2,100 ml
Answers
The pharmacist is left with 2100 ml(milliliter) of cough syrup.
According to the question,
Pharmacists have 3.6 L(liter) of cough syrup.
1 L = 1000 ml (Given)
Therefore, 3.6 L = 3.6 x 1000
= 3600 ml
It’s given in the question that the pharmacist fills a 1500 ml bottle with cough syrup.
To find the quantity of cough syrup left with the pharmacist, we will subtract the quantity of bottle from the total quantity of cough syrup.
Cough syrup left with her after filling the bottle = 3600 – 1500
= 2100 ml
Hence, she is left with 2100 ml of cough syrup after filling up a bottle of 1500 ml quantity.
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A man drove 60 km at 30 km/h, 60 km at 40 km/h and 60 km at 50 km/h. What was his average speed for the whole journey?
Answers
Answer:
the above answer help you guy.
h
,
Question 14 Find all maxima and minima of the function I 4x f(x)= and sketch its graph. Note: You must show all work (such as finding intercepts and asymptotes) before sketching the graph. Use the edi
Answers
The function f(x) = 4x has no maxima or minima. It is a straight line passing through the origin.
To find the maxima and minima of the function f(x) = 4x,
we will differentiate f(x) with respect to x and equate it to zero.
Then, we'll solve for the value of x and then, calculate the corresponding values of y or f(x).
After finding the values of maxima and minima, we will plot them on the graph.
Given function is: f(x) = 4x
To find maxima and minima,
we will differentiate the given function with respect to x:
f′(x) = 4x′ = 4
Now, equating the first derivative to zero, we get:
4 = 0 That's not possible!
So, there are no maxima or minima of the given function.
On sketching the graph of the function, we get a straight line passing through the origin as shown in the figure below:
Therefore, the function f(x) = 4x has no maxima or minima. It is a straight line passing through the origin.
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I need help
3x - 9 = -33 x = -33
-14
-8
-16
-9
none of the above
Answers
Answer:
x = -8
Step-by-step explanation:
3x - 9= -33
+9=-33+9
3x = -24
3 3
x = -8
1. Mr. Smith's class set a goal to complete 5,000 Dreambox lessons by the end of
the school year. In the first marking period they completed 2,387 and in the
second marking period they completed 2,492. Did they meet their goal? If not,
how many more lessons do they need?
Answers
Because 5000-4870=121
2,387+2,492=4879
3. Find \( y^{\prime} \) for the following implicit function \( y^{2}-x^{2} y=-2 \)
Answers
The derivative \(\( y' \)\) of the implicit function \(\( y^2 - xy = -2 \)\) is 0, indicating a constant slope with no change in relation to \(\( x \)\).
To find \(\( y' \)\)for the implicit function \(\( y^2 - xy = -2 \)\), we can differentiate both sides of the equation with respect to \(\( x \)\) using the chain rule. Let's go step by step:
Differentiating \(\( y^2 \)\) with respect to \(\( x \)\) using the chain rule:
\(\[\frac{d}{dx}(y^2) = 2y \cdot \frac{dy}{dx}\]\)
Differentiating \(\( xy \)\) with respect to \(\( x \)\) using the product rule:
\(\[\frac{d}{dx}(xy) = x \cdot \frac{dy}{dx} + y \cdot \frac{dx}{dx} = x \cdot \frac{dy}{dx} + y\]\)
Differentiating the constant term (-2) with respect to \(\( x \)\) gives us zero since it's a constant.
So, the differentiation of the entire equation is:
\(\[2y \cdot \frac{dy}{dx} - (x \cdot \frac{dy}{dx} + y) = 0\]\)
Now, let's rearrange the terms:
\(\[(2y - y) \cdot \frac{dy}{dx} - x \cdot \frac{dy}{dx} = 0\]\)
Simplifying further:
\(\[y \cdot \frac{dy}{dx}\) \(- x \cdot \frac{dy}{dx} = 0\]\)
Factoring out:
\(\[(\frac{dy}{dx})(y - x) = 0 \]\)
Finally, solving:
\(\[\frac{dy}{dx} = \frac{0}{y - x} = 0\]\)
Therefore, the derivative \(\( y' \)\) of the given implicit function is 0.
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probability distributions whose graphs can be approximated by bell-shaped curves
Answers
The probability distributions whose graphs can be approximated by bell-shaped curves are commonly known as normal distributions or Gaussian distributions.
These distributions are characterized by their symmetrical shape and the majority of their data falling within a certain range around the mean. The normal distribution is widely used in statistics and is a fundamental concept in many fields of study, including psychology, economics, and engineering. The normal distribution is also known for its many practical applications, such as predicting test scores, stock prices, and medical diagnoses. In summary, the bell-shaped curve is a useful tool in probability theory that can help us understand and make predictions about a wide range of phenomena. The probability distributions whose graphs can be approximated by bell-shaped curves are called Normal Distributions or Gaussian Distributions. They have a symmetrical shape and are characterized by their mean (µ) and standard deviation (σ), which determine the central location and the spread of the distribution, respectively.
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due last weeeekk help!!!!
Answers
A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.
What is a dilation?In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.
In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:
Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).
In Mathematics and Geometry, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction;
(x, y) → (y, -x)
Ordered pair B' (-2, 1) → E (1, 2)
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help me answer this question please
Answers
h ---> Independent Variable
c ---> Dependent variable
h is time, So domain is discrete.
Given,
In the question:
The function c = 15 + 9h represent the amount c (in dollars)
It will cost you for a one - time lawn care service of h hours.
To find the independent and dependent variables .
To check the domain discrete or continuous.
Now, According to the question:
What is domain discrete or continuous?
A discrete domain is a set of input values that consists of only certain numbers in an interval. A continuous domain is a set of input values that consists of all numbers in an interval. Sometimes the set of points that represent the solutions of an equation are distinct, and other times the points are connected.
According to the above statement :
Hence, h ---> Independent Variable
c ---> Dependent variable
h is time, So domain is discrete.
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The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
First triangle
15
15
second triangle
45/2
45/2
Answers
Answer: 3
Step-by-step explanation:
The scale factor is the ratio of corresponding side lengths of the two triangles.
In the given triangles, the length of the corresponding sides of the triangles are:
For the first triangle:
Side A = 15 units
Side B = 15 units
For the second triangle:
Side A = 45/2 units
Side B = 45/2 units
To find the scale factor, we can divide the length of one side of the second triangle by the corresponding length of the first triangle.
For example, we can use Side A:
Scale factor = (length of Side A of the second triangle) / (length of Side A of the first triangle)
Scale factor = (45/2) / 15
Scale factor = (45/2) * (1/15)
Scale factor = 3/2
Since the two triangles are scaled copies of each other, the scale factor should be the same for all corresponding sides.
Thus, the scale factor is 3 (in simplest form).
Urgent help needed!
Thankyou!
Answers
Answer:
Step-by-step explanation:
1/4n
TRUE/FALSE. as one does more and more separate hypothesis tests, the risk of a type i error accumulates and is called the experiment-wise alpha level.
Answers
TRUE. As one performs multiple separate hypothesis tests, the risk of committing a Type I error (rejecting a true null hypothesis) accumulates.
This overall risk is referred to as the experiment-wise alpha level or family-wise error rate (FWER). It represents the probability of making at least one Type I error among all the conducted tests.
When multiple hypothesis tests are performed simultaneously or sequentially, the individual alpha levels (typically set at 0.05) for each test may no longer be appropriate. This is because if we conduct, for example, 20 separate tests with an alpha level of 0.05 for each test, the cumulative chance of committing at least one Type I error can be much higher than the desired 5%.
To control the experiment-wise error rate, various multiple comparison procedures and adjustments can be employed, such as the Bonferroni correction or the Holm-Bonferroni method. These methods aim to maintain a desired level of significance for the entire set of tests, reducing the risk of accumulating Type I errors.
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The inclination (tilt) of an amusement park ride is accelerating at a rate of 2160\,\dfrac{\text{degrees}}{\text{min}^2}2160 min 2 degrees 2160, start fraction, start text, d, e, g, r, e, e, s, end text, divided by, start text, m, i, n, end text, squared, end fraction. What is the ride's acceleration rate in \dfrac{\text{degrees}}{\text{s}^2} s 2 degrees start fraction, start text, d, e, g, r, e, e, s, end text, divided by, start text, s, end text, squared, end fraction?
Answers
Answer:
0.6 deg/s²
Step-by-step explanation:
Acceleration is the time rate of change of velocity, it is the ratio of velocity to time. The formula for acceleration is given by:
Acceleration = Change in velocity / time taken = (Final velocity - Initial velocity) / time
Given that the acceleration is 2160 deg/min², we have to convert it to deg/s²
1 min = 60 seconds
1 min² = 60² s² = 3600 s²
\(2160\ deg/min^2=\frac{2160\ deg}{1\ min^2*3600\ \frac{s^2}{min^2} }=0.6\ deg/s^2\\ \\2160\ deg/min^2=0.6\ deg/s^2\)
Answer:
0.6
Step-by-step explanation:
To create an ellipse that represents a circle in an isometric sketch, you first create a square bounding box as before; however, the bounding box will appear as a(n) ____________________.
Answers
Answer:
Parallelogram
Step-by-step explanation:
When drawing circles in isometric sketches, the circles appear as an ellipse. To draw an ellipse that represents a circle in isometric sketch, use the following steps:
Draw a square bounding box: locate the center of the circle and then draw four radial points from the center. Next, draw the bounding box (it passes through the four radial points). Draw to long arcs by place the tip of the compass each of the opposite bounding box edge and joining two of the radial pointsDraw the short arcs using the center of the boxTo create an ellipse that represents a circle in an isometric sketch, you first create a square bounding box as before; however, the bounding box will appear as a parallelogram
Jordan is planning a surprise birthday
party for her brother. She would like
to invite 15 guests. She has $300.00 to
spend. Which unit rate describes her
spending for each guest?
A $15.00
B $20.00
с $25.00
D$30.00
Answers
Answer:
B. $20.00
Step-by-step explanation:
NEED HELP ASAP NO LINKS!!!!!!!!!!!!!!!!!!!!!!
Katherine just started a running plan where she runs 8 miles the first week and then increases the number of miles she runs by 5% each week. If she keeps up this plan for 19 weeks, how many total miles would Katherine have run, to the nearest whole number?
Answers
Answer:
I THINK I GOT IT!!! I think by 19 weeks (rounding) she will have to run 1 extra mile or 95 percent more!!!!!!!
Step-by-step explanation:Please do not blame me if its wrong i only thought about for like 1 min!
Which type of function is shown in the table below?
Answers
Answer:
Linear function
Step-by-step explanation:
None of the X values repeat so its Linear
the mean of 4,8,9,x,2 is 6. calculate the value of x
Answers
Answer:
7
Step-by-step explanation:
the mean is (the sum of numbers in a data set)/(# of points in that data set).
So,
\(\frac{4+8+9+x+2}{5} = 6\),
\(\frac{23+x}{5} = 6\),
23+x = 6*5
23+x = 30
x= 30-23
x = 7
Hence, the value of x is 7.
Hope this helps!!!
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