Given:
[tex]A=15^\circ, C=120^\circ,b=3[/tex].
To find:
The length of side c.
Solution:
According to the angle sum of property of a triangle, the sum of all interior angles of a triangle is 180 degrees.
[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex]
[tex]15^\circ+m\angle B+120^\circ=180^\circ[/tex]
[tex]m\angle B+135^\circ=180^\circ[/tex]
[tex]m\angle B=180^\circ-135^\circ[/tex]
[tex]m\angle B=45^\circ[/tex]
According to the Law of sines,
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
Using Law of sines, we get
[tex]\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]\dfrac{3}{\sin 45^\circ}=\dfrac{c}{\sin 120^\circ}[/tex]
[tex]\dfrac{3}{\dfrac{1}{\sqrt{2}}}=\dfrac{c}{\dfrac{\sqrt{3}}{2}}[/tex]
[tex]3\sqrt{2}\times \dfrac{\sqrt{3}}{2}=c[/tex]
On further simplification, we get
[tex]\dfrac{3\sqrt{6}}{2}=c[/tex]
[tex]3.674235=c[/tex]
[tex]c\approx 3.7[/tex]
Therefore, the length of side c is about 3.7 units.
Does anyone know how to solve this?
And please explain your answer
[tex] \huge \fbox{Answer : }[/tex]
The value of k for which
[tex] \sin(k - x) = \cos(x) [/tex]
is
[tex] \dfrac{\pi}{2} [/tex]
Line segment AB = 12, its image after a dilation is 36. What is the scale factor of the dilation?
The scale factor of the dilation is 3
How to determine the scale factor of the dilation?From the question, we have the following parameters that can be used in our computation:
Line segment AB = 12 units
After the dilation = 36 units
The scale factor of the dilation is then calculated as
Scale factor of the dilation = After the dilation/Line segment AB
Substitute the known values in the above equation, so, we have the following representation
Scale factor of the dilation = 36/12
Evaluate
Scale factor of the dilation = 3
Hence, the scale factor is 3
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Ina writes the expression below. [x + 5) - (x - 5] What is the value of Ina's expression for x= 10?
Answer:
10
Step-by-step explanation:
Given the expression below.
[x + 5) - (x - 5]
If x = 10, we will have to substitute x = 10 into the expression given as shown;
[x + 5) - (x - 5]
=[10 + 5) - (10 - 5]
= 15 - 5
= 10
Hence the required value is 10
1) A new phone costs $285. If the tax 5%, what is the total cost of the phone? Round to the nearest cent
if necessary. Show all work.
Answer:
299.25
Step-by-step explanation:
285x.05=14.25 tax
285 + 14.25=299.25 total cost
who is the father of mathematics
Answer:
Archimedes
Step-by-step explanation:
The father of Mathematics is known as Archimedes
-TheUnknownScientist
A matched pairs design involves: matching pairs of participants based on a variable and then randomly assigning one member of each pair to each group. randomly assigning participants to groups and then matching pairs of participants. matching pairs of participants based on a variable and then randomly assigning half the pairs of each group. an attempt to control for order effects.
Answer:
matching pairs of participants based on a variable and then randomly assigning one member of each pair to each group.
Step-by-step explanation:
A control experiment can be defined as an experiment in which a condition assumed to be a probable cause of the effect is being compared to the same situation by the scientist without involving or using the suspected condition.
A control group generally makes an experiment to work because they are not exposed to the variables and a neutral treatment.
On the other hand, an experimental group can be defined as a collection of participants that are subjected to the independent variable.
A matched pairs design involves matching pairs of participants based on a variable and then randomly assigning one member of each pair to each group. Thus, it's a process which typically involves pairing each individual in an experimental group with respect to another in the control group.
Generally, a matched pairs design is often times used when only a small group of participants are available for an experimental study or research.
Please help!!! Also do not put a link as your answer. Whoever answers this first with work shown will get Brainliest, and 30 points.
What is the equation of a parabola with (-3,3) as the focus, and y=5 as the directrix?
Remember no link! :)
Answer y = 1/4 (x+3)^2 + 4
Step-by-step explanation:
If the focus is (-3, 3) and the directrix is y=5, the vertex is at (-3, 4). a = 1/4p, p=1, a=1/4. (h,k) is the vertex.
y=a(x-h)^2 +k
y=1/4(x+3)^2+4
Nevaeh has $0.80 worth of nickels and dimes. She has a total of 11 nickels and dimes altogether. Graphically solve a system of equations in order to determine the number of nickels, x,x, and the number of dimes, y,y, that Nevaeh has.
Determine which binomial is a factor of 4x^3+17x^2+7x+12 A. X+12 B. x +4 C. x +7 D. X-4
Answer:
D is correct Answer. x-4. THANK YOU.
A lumber company is making boards that are 2578.0 millimeters tall. If the boards are too long they must be trimmed, and if they are too short they cannot be used. A sample of 20 boards is made, and it is found that they have a mean of 2580.2 millimeters with a variance of 64.00. Is there evidence at the 0.1 level that the boards are either too long or too short?
1. State the hypotheses.
2. Find the value of the t test statistic.
3. Specify if the test is one-tailed or two-tailed.
4. Determine the decision rule.
5. Determine the conclusion.
A) Reject Null Hypothesis
B) Fail to Reject Null Hypothesis
Answer:
-0.750
Step-by-step explanation:
Determining Which Measure
Check
Determine the appropriate measure for each description.
Amount of confetti stuffed in a tube
Volume
Surface Area
Amount of soup in a can
Amount of paper to cover a can
Amount of paint for outside of tube
Amount of cardboard to make a tube
Amount of dirt in a flower pot
5) Intro
Done
Tutoring
Activity
Answer:
VOLUME:
amount of confetti stuffed in a tube
amount of soup in a can
amount of dirt in a flower pot
SURFACE AREA:
amount of paper to cover a can
amount of paint for outside of tube
amount of cardboard to make a tube
Step-by-step explanation:
PLZ Hlp extra credit imma fail no link!!!
Answer:
B, C, and F
Step-by-step explanation:
You can double check my answers and it'll make sense.
2 to the power of 4 means you multiply 2 by itself 4 times.
The answer of that would be 16.
4 x 4 also equals 16 so therefore those three answers are equivalent.
Answer:
a and c
Step-by-step explanation:
it says equivalent to
What is 4 4/5 + 1 1/3?
Answer:
[tex] \frac{92}{15} [/tex]
Step-by-step explanation:
change to improper
[tex] \frac{24}{5} + \frac{4}{3} [/tex]
this gives us
[tex] \frac{92}{15} [/tex]
final answer
plz mark as brainliest
Answer:
[tex]\frac{92}{15} or 6\frac{2}{15}[/tex]
Step-by-step explanation
hope this helps have a good day :)
Please help I don’t understand this
On solving the provided question, we can say that - the area of the following rectangle is 200 cm sq.
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
here,
we have
L = 20 cm
and B = 10 cm
Area of rectangle, A =L X B = 20 X 10 = 200 cm sq.
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Write in scientific notation (multiply)
(5x10^18)(3x10^6)
Answer: 3 x [tex]10^{24}[/tex]
Step-by-step explanation:
Pllzzz help me with this!!!!
Solving the provided question, we can say that the quadratic equation is [tex]-16t^2 +vt +s[/tex] so answer is -16+48+3 = 35
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
the quadratic equation is
[tex]-16t^2 +vt +s[/tex]
v = 16
s =3
t =
so answer is -16+48+3 = 35
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Math To Do, Ready
login ready.com/student/dashboard/home
Park View Apartments has 2 buildings. Each building has 3 floors. Each floor has
16 windows. What is the total number of windows in the Park View Apartment
buildings?
Answer:
(probably) 96
Step-by-step explanation:
2 buildings, 3 floors, 16 windows.
first, 16x3=48
and then 48x2=96
So, the total number is 96.
Ellie brought 2 packs of hot dogs , 3 lbs of hamburger, and 2 lbs. of potato salad. How much did she spend?
Ellie spend of $37.8 for 2 packs of hot dogs , 3 lbs of hamburger, and 2 lbs. of potato salad
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The amount is not given for each hot dog, hamburger and potatos.
But Ellie brought 2 packs of hot dogs ,
3 lbs of hamburger, and
2 lbs. of potato salad
Let us consider each hot dog is $6
Hamburger is $5.6 and potatoes is $4.5
Total amount is 2(6)+3(5.6)+2(4.5)
12+16.8+9
$37.8
Hence, Ellie spend of $37.8 for 2 packs of hot dogs , 3 lbs of hamburger, and 2 lbs. of potato salad
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Identify each angle pair as Complementary, Supplementary, Adjacent, or Vertical. Select from the drop
down menu. Select the most specific choice.
Answer:
A. Adjacent
B. Complementary
C. Complementary
Step-by-step explanation:
An equilateral triangle with side length 2.5 is dilated with a scale factor of 6. What is the length of one side of the new figure?
Answer:
18
Step-by-step explanation:
What should Jayce conclude is the distance around the largest circle on the radar screen? Use pi = 3.14.
Step-by-step explanation:
plz mark as brainlist////
Can you please help me
Answer:
x=16
Step-by-step explanation:
the angle would be 1/2 of the arc so here's the steps
(2)7x+16=18x-32
14x+32=18x-32
+32 +32
14x+64=18x
-14x . -14x
64=4x
64/4=4x/4
x=16
Use Exponential Functions
From the table below, determine whether the data shows an exponential function. Explain why or why not.
a. Yes; the domain values are at regular intervals and the range values have a common factor 8.
b. Yes; the domain values are at regular intervals and the range values have a common factor 4.
c. No; the domain values are not at regular intervals.
d. No; the domain values are at regular intervals and the range values have a common factor 4.
Please select the best answer from the choices provided.
Answer:
B. Yes; the domain values are at regular intervals and the range values have a common factor 4.
Step-by-step explanation:
I calculated it logically
If ⅓y = 9; then y =?
Answer:
y = 27Eexplanation:
1/3y = 9
y/3 = 9
y = 9 × 3
y = 27
WHAT IS THE VOLUME OF THIS THING
Tip: Before finding a volume, you'll need to know the FORMULA of it. So the formula for a volume is Length x Width x Height. Then you should be able to solve any shape.
Two straight lines are perpendicular to each other at point M. One of the lines passes through (2, 6) and the equation of the other line is 2y + 3x -5 = 0. Calculate the co-ordinates of M.
Answer: The equation of a line in the form y = mx + b can be written as y - mx - b = 0. So we can rewrite the equation of the line as 2y - 3x + 5 = 0. This means that the slope of the line is -3/2.
The slope of a line perpendicular to this line would be the negative reciprocal of -3/2, which is 2/3. Let's call the point M (x, y). We know that the line passing through (2, 6) has a slope of 2/3. So we can write the equation of this line as:
y - (2/3)x - b = 0
Substituting the point (2, 6) into this equation, we get:
6 - (2/3)(2) - b = 0
b = 4
So the equation of the line passing through (2, 6) is:
y - (2/3)x - 4 = 0
To find the coordinates of point M, we need to find the point where these two lines intersect. Setting the two equations equal to each other and solving for x and y, we get:
2y - 3x + 5 = y - (2/3)x - 4
5 - 2y = y - (5/3)x + 4
(5/3)x = 3 - y
x = (3 - y) * (3/5)
Substituting this expression for x into one of the original equations, we can solve for y:
2y - 3((3 - y) * (3/5)) + 5 = 0
2y - (9 - 3y)(3/5) + 5 = 0
(10/5)y - (9/5) + 5 = 0
y = (9/5) + (5/5)
y = 2
Substituting this value for y back into the expression for x, we get:
x = (3 - 2) * (3/5)
x = 1
So the coordinates of point M are (1, 2).
Step-by-step explanation:
A=1/2(b+c)h
Rearrange the formula to highlight the height.
Evaluate 5+6x,when x is 4
A right triangle with coordinates A (-2,5), B (-2, 9) and C (4,5) is first rotated 90 degrees counterclockwise and
then translated 2 units left and 3 units down to form triangle A'B'C'. What is the measure of angle B'A'C',
in degrees, in the resulting figure?
Answer:
90 degree
Step-by-step explanation:
since the original angle BAC is 90 degree, no matter the triangle is rotated or translated, the angle remain unchanged
what is the first step to solve the system using substitution?
2y+x=4 3y=2x+6
A. Isolate a variable in one of the equations
B. Set one of the equations equal to zero
Answer:
A.
Step-by-step explanation:
just put it i swear it will help lollllll