Using the Law of Cosines,
[tex]c^{2}=2^{2}+4^{2}-2(2)(4)(\sin 30^{\circ})\\\\c^{2}=12\\\\c=2\sqrt{3}[/tex]
Using the Law of Sines,
[tex]\frac{\sin A}{a}=\frac{\sin C}{c}\\\\\frac{\sin A}{2}=\frac{\sin 30^{\circ}}{2\sqrt{3}}\\\\\frac{\sin A}{2}=\frac{1}{4\sqrt{3}}\\\\\sin A=\frac{1}{2\sqrt{3}}\\\\A=\boxed{\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)}[/tex]
So, as angles in a triangle add to 180 degrees,
[tex]B=180^{\circ}-30^{\circ}-\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)\\\\B=\boxed{150^{\circ}-\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)}[/tex]
Find the measure of
Answer:
h=70°
Step-by-step explanation:
h + 110° = 180° {linear pair angles}
h = 180° - 110°
h = 70°
Answer:
h=70
pa brainliest po kuya/ate
Step-by-step explanation:
pa brainliest po
Which statements are true about the graph of function f? f(x)=logx
The true statement about is the graph has a range of {y|-∞ < y < ∞} and decreases as x approaches 0.
What is a logarithm function?A logarithm function is a type of function that represents the inverse of an exponential function. Mathematically, a logarithmic function is written as [tex]y =log_ax[/tex].
The domain of the given logarithm function f(x) = logx is (x > 0) and its graph wouldn't touch the vertical axis but moves to the right.
Also, the logarithmic function increases as the value of x increases. Thus, this function would decrease when x approaches zero (0).
In conclusion, we can deduce that the range of this function is -∞ < y < ∞.
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Answer:
domain:
c. The graph has a domain of {x|0<x<∞} and approaches 0 as x decreases.
and pretty sure the range is:
b. The graph has a range of {y|-∞<y<∞}and decreases as x approaches 0.
because all real numbers
Step-by-step explanation:
hope this helped
10 less than 3 times a number is 25 what is that number
Answer:
-5
Step-by-step explanation:
10 - 3N = 25
Subtract 10 from both sides
-3N=15
Divide both sides by -3
N = -5
1 . A rope was 14.35 inches long. Megean cut the rope into 7 pieces of equal length. What was the length of each piece of rope in inches
2. Scott drank 3.5 bottles of water yesterday . Each bottle contained 1.2 pints of water. what was the number of pints of water Scott drank yesterday
Division is one of the four fundamental arithmetic operations. The number of pints of water Scott drank yesterday is 4.2 pints.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
A rope was 14.35 inches long. Megean cut the rope into 7 pieces of equal length. Therefore, the length of each piece of rope in inches will be,
Length of piece = 14.35 inches/7 = 2.05 inches
Scott drank 3.5 bottles of water yesterday . Each bottle contained 1.2 pints of water. Therefore, the number of pints of water Scott drank yesterday is,
Number of pints = 3.5 bottles × 1.2 pints = 4.2 pints
Hence, The number of pints of water Scott drank yesterday is 4.2 pints.
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Two airplanes leave Chicago at the same time and fly in opposite directions. If one travels at 450 miles per hour and the other at 550 miles per hour, how long will it take for them to be 4000 miles apart
450t+550t=4,000
1000t=4000
t=4000/1000
t=4 hours they will be 4,000 apart.
------------------------------------------
20t+12(4.5-t)=70
20t+54-12t=70
8t=70-54
8t=16
t=16/8
t=2 hours at 20 mph.
proof
20*2+12(4.5-2)=70
40+12(2.5)=70
40+30=70
70=70
What is the range of function g if g(x) =-2f(x-3)
Answer:
If you entered the function correctly there is not a range
Step-by-step explanation:
Answer: {y|-♾<y<0}
Step-by-step explanation: i’m taking this summer school class
Convert 3678 grams to kilograms
Answer:
3.678 Kilograms
Answer:
3678/1000
=3.678kg
the answer is 3.678kg
Solve the given inequality and graph the solution on a number line. -X/2 -3/2 = 5/2
No Links:
a) Work out the size of angle x. b) Give reasons for your answer. + A E C xº B F 105° G D H
Check the picture below.
May you please help with this, thanks!
Answer:
The standard form of the number will be written as 63 158
In the statement 10 +(-10) =0, how would you describe the -10?
Answer:
-10 is the opposite of 10
Step-by-step explanation:
-10 is the opposite of 10 ,because The sum of a number and its opposite equals to zero.
A trellis consists of overlapping wooden slats.
1.What is the position of the indicated angles?
2.What should the value of x be in order for the two slats to be parallel?
3. Which theorem or postulate will you use to prove the parallel slats?
4. Find the measure of the indicated angle
The position of the angles are corresponding angles.
The value of x should be 6 for the slats to be parallel.
The theorem use to prove the parallel slat is the corresponding angle theorem.
The measure of the indicated angles are 42 degrees.
How to know a corresponding angles?Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal.
Therefore, the position of the angles are corresponding angles
Since the angles are corresponding angles, they are congruent.
Therefore,
3x + 24 = 7x
24 = 7x - 3x
24 = 4x
x = 6
The theorem use to prove the postulate is the corresponding angle theorem.
The measure of the indicated angle can be calculated as follows:
7(6) = 42 degrees.
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I need help please help me and thank you :))
Answer:
see explanation
Step-by-step explanation:
∠ CZD = 90° , then
∠ CZF = 90° - ∠ FZD = 90° - 40° = 50°
∠ FZD and ∠ AZG are vertically opposite angles and are congruent , so
∠ AZG = 40°
∠ CZF and ∠ GZE are vertically opposite angles and are congruent , so
∠ GZE = 50°
E
∠ AZB + ∠ BZC = 90° , that is
3x - 2 + 32 = 90
3x + 30 = 90 ( subtract 30 from both sides )
3x = 60 ( divide both sides by 3 )
x = 20
5 less than a number b is 16
[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: 5 < b = 6 \: \: \: or \: \: \: b - 5 = 6 } \\ \end{gathered}[/tex]
Solution :-[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: b - 5 = 6 } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: b = 6 + 5 } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow \: \: \underline{ \boxed{\mathbf \red{ \: \: b = 11 \: \: }}} \\ \end{gathered}[/tex]
Hence,b is equal to 11 .▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Additional information[tex]\begin{gathered}\begin{gathered}\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \small \color{blue}{ \underline{\boxed{ \begin{array}{cc} \small \underline{\underline{\bf{ \color{red}{{ \orange \bigstar \: MᴏʀE \: IᴅᴇɴᴛɪᴛɪᴇS \: \orange \bigstar}}}}} \\ \\ \: \frak{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \: \frak{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \: \frak{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \: \frak{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \: \frak{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \: \frak{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \: \frak{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \: \frak{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \\ \: \end{array} }}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \: \: [/tex]
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
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Find the equation of a line that passes through the points (-4, -2) and (6, 3).
Answer:
[tex]y=\frac{1}{2} x[/tex]
Step-by-step explanation:
The equation of a line through two points can usually (except when the line is a vertical line) be written in slope intercept form, [tex]y=mx+b[/tex] , where "m" is the slope of the line, and "b" is the y-intercept of the line.
General outlineFind the slopeFind the y-interceptTo find "m", use the formula for slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{(3)-(-2)}{(6)-(-4)}[/tex]
[tex]m=\dfrac{3+2}{6+4}[/tex]
[tex]m=\dfrac{5}{10}[/tex]
[tex]m=\dfrac{1}{2}[/tex]
So, the slope is 1/2 and we know that the equation for the line that passes through these two points should look like: [tex]y=\frac{1}{2} x+b[/tex]
Step 2. Find the y-interceptTo find "b", substitute one of the known points, and solve for "b":
[tex]y=\frac{1}{2} x+b[/tex]
[tex](3)=\frac{1}{2} (6)+b[/tex]
[tex]3=3+b[/tex]
Subtracting 3 from both sides to isolate the "b"...
[tex](3)-3=(3+b)-3[/tex]
[tex]0=b[/tex]
So, the y-intercept is 0. Substituting into our line equation, [tex]y=\frac{1}{2} x+(0)[/tex] which simplifies to [tex]y=\frac{1}{2} x[/tex]
The band is raising money for their spring trip. they need to raise at
least $1500. earlier in the year, they made $575 on their annual fruit sale.
now they are selling donuts, where they will earn $5 profit for each box
of donuts they sell. which inequality could be used in order to
determine the number of boxes of donuts, d, they must sell in order to
meet their goal?
The inequality that can be used to determine the number of boxes of donuts, d, they must sell in order to meet their goal is $1500 ≥ $575 + $5d.
What is the inequality?Here are inequality signs and what they denote:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toTotal amount that needs to be raised ≥ amount made at the fruit sale + (profit per box x number of boxes)
$1500 ≥ $575 + $5d
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what is three and 2 fourths and minus two and three fourths
Answer:
The answer is 0.75
Hope this helps!
find the equation of the line:
The slope of AB is (0-4)/(-2-0)=2, so since perpendicular lines have negative reciprocal slopes, the slope of the perpendicular line is -0.5.
So, the equation of the line is:
y + 1 = -0.5(x - 5)
y + 1 = -0.5x + 2.5
y = -0.5x + 1.5
Which lists the steps in the correct order to find the median of this data set? 24, 16, 23, 30, 18, 29 O 1. Put the numbers in order. 2. Cross off high/low pairs. 3. Add the leftover numbers. 4. Divide the sum by 2. O1. Put the numbers in order. 2. Cross of high/low pairs. 1. Cross off high/low pairs. 2. Add the leftover numbers. 3.Divide the sum by 2. 1. Cross of high/low pairs.
Median is the central tendency of the data and always exists in the middle of the data set.
What is the median?The Median is the middlemost value of the numbers arranged in the ascending orders. Median is the central tendency of the data and always exists in the middle of the data set.
The process of finding the median if the number of data points is even is as follows:
Put the numbers or the data points in the order(increasing or decreasing i.e. ascending or descending order)Next cross of the high/ low pairsAdd the leftover numbersand divide the number( as obtained in the above step by 2)( if the number of data pints were even then we just need to arrange the numbers and cross the high/low pair and only one data point will be left which acts as the Median of the data set)
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What is the partial fraction decomposition, I know D is wrong
[tex]\dfrac{7x^2+14}{(x^2+3)^2}=\dfrac{7x^2+21-7}{(x^2+3)^2}=\dfrac{7x^2+21}{(x^2+3)^2}-\dfrac{7}{(x^2+3)^2}=\dfrac{7(x^2+3)}{(x^2+3)^2}-\dfrac{7}{(x^2+3)^2}=\\=\dfrac{7}{x^2+3}-\dfrac{7}{(x^2+3)^2}[/tex]
PLease HELP!!! 20 POINTS!!! WILL GIVE BRAINLIEST!!!
martina must choose a number between 49 and 95 that is multiple of 2,8 and 10. write all the numbers that she could choose.
Answer:
80
Step-by-step explanation:
10 limits it to 50, 60, 70, 80, and 90
2 eliminates none since 50=25, 60=30, 70=35, 80=40 and 90=45
8 divided by each number only leaves one option of 80. (80/8= 10) (80/10=8) (80/2=40)
plaese explain this exe i can't understand and tomorrow i have an exman of metahmatice
Answer:
B: 610; A: 202,000
D: 253; C: 2,007,000
Step-by-step explanation:
These are all expressions that can be calculated as is, or that can be simplified a little bit by taking advantage of the distributive property and other properties of addition and multiplication. The idea is to look for numbers that show up more than once, and rearrange the expression so they only show up once.
__
B = (597 -176) +(13 +176)This is a straight addition problem. The two "176" values have opposite signs, so cancel when they are added. Using the associative and commutative properties of addition, we can rearrange this to ...
597 +13 +(-176 +176)
= 597 +13
This can further be rearranged to ...
= (597 +3) +(13 -3)
= 600 +10
= 610
__
A = 2020×173 -2020×73The factor 2020 can be put outside parentheses using the distributive property:
= 2020(173 -73)
= 2020×100
= 202,000
__
D 17×15 -15 +13The value 15 is repeated. Terms using it can be combined using the distributive property.
= 15(17 -1) +13
= 15(16) +13
= 240 +13
= 253
Another way to look at this one is to use the factoring of the difference of squares.
= (16 +1)(16 -1) +(-15 +13)
= 16² -1² +(-2)
= 256 -3
= 253
__
C 2019×890 -(12000 -2019×110)Again, we can focus on rearranging so 2019 only needs to show up once.
= 2019(890 +110) -12000
= 2019×1000 -12×1000
= (2019 -12)×1000
= 2,007,000
Please solve this ASAP!!!
Select the correct answer.
A mistake was made in the steps shown to simplify the expression. Which step includes the mistake?
+3(41)
7+2³
Step 1: =
=
+ 3(3) - 7 + 23
Step 2:
=
+3(3) - 7 + 8
Step 3: =
(3) - 7+8
Step 4: =
Step 5: = 31+8
Step 6: =
= 47
A.
Step 4
B.
Step 1
C.
Step 5
D. Step 3
The mistake made in the step 3 option(D) step 3 is correct and the simplification form of the expression is 29/2,
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
The question is incomplete.
The complete question is in the picture please refer to the picture.
We have given an arithmetic expression:
[tex]=\dfrac{9}{2}+3\left(4-1\right)-7+2^3[/tex]
Step 1:
[tex]=\dfrac{9}{2}+3(3)-7+2^3[/tex]
Step 2:
[tex]=\dfrac{9}{2}+3(3)-7+8[/tex]
Step 3 should be:
[tex]=\dfrac{9}{2}(3)-7+8[/tex]
The mistake made in the step 3
Thus, the mistake made in the step 3 option(D) step 3 is correct and the simplification form of the expression is 29/2,
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Needing help with these 2 problems
Answer:
15) 3.2
17) 13.4
Step-by-step explanation:
To find the missing lengths, you need to use the Pythagorean theorem:
a² + b² = c²
In this form, "c" represents the length of the hypotenuse and "a" and "b" represent the lengths of the other two sides.
You are trying to find one of the side lengths (not the hypotenuse) in 15). To find the other length, you can plug the other values into the equation and simplify to find "b".
15) a = 4.1 c = 5.2
a² + b² = c² <----- Pythagreom Theorem
(4.1)² + b² = (5.2)² <----- Plug values in for "a" and "c"
16.81 + b² = 27.04 <----- Raise numbers to the power of 2
b² = 10.23 <----- Subtract 16.81 from both sides
b = 3.2 <----- Take the square root of both sides
You are trying to find the hypotenuse in 17). Since you have been given the lengths of the other sides, you can plug them into the equations and simplify to find "c".
17) a = 4.4 b = 12.7
a² + b² = c² <----- Pythagreom Theorem
(4.4)² + (12.7)² = c² <----- Plug values in for "a" and "b"
19.36 + 161.29 = c² <----- Raise numbers to the power of 2
180.65 = c² <----- Add
13.4 = c <----- Take the square root of both sides
1. What is the difference between the altitude rule and the leg rule?
Answer:
The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle
The Leg Rule (or Leg geometric mean theorem) relates the length of each leg of a right triangle with the segments projected by them on the hypotenuse.
Step-by-step explanation:
The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. Notice the triangle used with this rule. The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.
Drag the correct value into each box on the number line.
To identify the value that goes in each box, we must perform the corresponding operation and calculate the final result.
How to perform a mathematical operation?In mathematics there are procedures such as addition (+), subtraction (-), division (÷), and multiplication (×) to solve problems. These operations are the four basic operations of mathematics.
According to the above, what we must do is identify what operation we must perform with the given numbers and then identify the result and put it in the corresponding box.
Note: This question is missing because there is some information missing. Howeve i can answer it based on my general knowledge.
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What are the sides of ∠E?
Answer:
C. FE and ED
Step-by-step explanation:
The question is asking what are the sides of angle E. I've marked angle E along with its sides in the attached picture.
One side of the angle E has to be ED.
However we have multiple options for the other side. It can be called FE, CE or BE.
So the answers could be any of:
- ED and FE
- ED and CE
- ED and BE
The option that has one of the possible answers is option C: FE and ED.
A company provides snack-sized packages of nuts for its office employees.
employees can choose from among five kinds of nuts. which probabilities
correctly complete this probability distribution for 50 packages of nuts, in the
order listed?
nuts
almonds cashews mixed peanuts pecans
12
10
6
14
8
number of
packages
probability
a. probability 0.32 0.24 0.14 0.2 0.1
The probabilities that correctly complete this probability distribution for 50 packages of nuts will be 0.24, 0.2, 0.12, 0.28, and 0.16.
How to calculate the probability?From the information given, we have to find the probability for each fruit. This will be:
Almond = 12/50 = 0.24
Cashew = 10/50 = 0.2
Mixed = 6/50 = 0.12
Peanut = 14/50 = 0.28
Pecan = 8/50 = 0.16
Therefore, the probabilities that correctly complete this probability distribution for 50 packages of nuts will be 0.24, 0.2, 0.12, 0.28, and 0.16.
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