Answer:
1001 ways
Step-by-step explanation:
Total number of people who applied for the job = 8 + 6 = 14
Number of people to be chosen = 4
This is a combination problem because the order of selection does not matter. A group selection involves the combinations. So here we have to find the combinations of 14 people taken 4 at a time. The formula for the combination is:
[tex]^{n}C_{r} = \frac{n!}{r!(n-r)!}[/tex]
Here, n is the total number of objects which is 14 in this case.
r is the number of objects to be chosen which is 4 in this case.
Using these values, we get:
[tex]^{14}C_{4}=\frac{14!}{4!(14-4)!}\\\\ = \frac{14!}{4! \times 10!}\\\\ =1001[/tex]
Thus, there are 1001 ways to select 4 applicants from 8 men and 6 women for the second interview.
What is the factored form Of
6x^2 -4x + 15x - 10
Answer:
(3x-2)(2x+5)
or
(2x+5)(3x-2) by commutative property
Step-by-step explanation:
Let's try factoring by grouping.
[tex]6x^2-4x+15x-10[/tex]
I'm going to group the first two terms together and the second two terms together.
[tex](6x^2-4x)+(15x-10)[/tex]
Now I'm going to factor what I can from each pair:
[tex]2x(3x-2)+5(3x-2)[/tex]
Now if you look at the terms 2x(3x-2) and 5(3x-2) you should see they have a common factor of (3x-2) so we can factor that out now.
(3x-2)(2x+5)
Factoring by grouping was a successful here.
Answer:
(3x - 2)(2x + 5)
Step-by-step explanation:
Given
6x² - 4x + 15x - 10 ( factor the first/second and third/fourth terms )
=2x(3x - 2) + 5(3x - 2) ← factor out (3x - 2) from each term
= (3x - 2)(2x + 5) ← in factored form
if 1/2 of a gallon of paint covered 1/4 of the wall how much does it take to cover the whole wall???
Answer:
2 gallons
Step-by-step explanation:
If you use one whole gallon, you will have covered 2/4.
When you simplify this fraction, you get 1/2. This means you have another half to cover.
So, 1 gallon plus another gallon is 2.
Answer:
2 gallons of paint.
Step-by-step explanation:
Since [tex]\frac{1}{2}[/tex] gallon of paint covered = [tex]\frac{1}{4}[/tex] of the wall.
Therefore, 1 gallon of paint covered = 1 × [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex] of the wall.
To paint 1 wall we need the paint = [tex]\frac{1}{\frac{1}{2} }[/tex] = [tex]1\times\frac{2}{1}[/tex] gallon of paints
= 2 gallons of paint.
2 gallons of paint covers the whole wall.
Find the calue of x and y using those values, explain what is wrong with the figure above
Step-by-step explanation:
When two straight lines intersect, they form 4 angles around the point. It can be seen that there are two angles in terms of x on a straight line, which sum up to 180 degrees. Therefore:
3y + y + 88 = 180 and 6x + 35 + 8x - 23 = 180.
Solving for x and y gives:
4y = 92 and 14x = 168.
y = 23 and x = 12.
Substituting the values back in the expression gives the angles:
XAW = 3(23) = 69 degrees.
WAY = 23 + 88 = 111 degrees.
ZAY = 8(12) - 23 = 73 degrees.
XAZ = 6(12) + 35 = 107 degrees.
The problem in this question is that whenever straight lines intersect, they form the vertical opposite angles. The vertical opposite angles are equal. In this question, angle XAW = angle ZAY and angle WAY = angle XAZ. However, in this question, these angles are not equal. (69 is not equal to 73 and 111 is not equal to 107). Hence, this is the problem in the question!!!
It appears that you are asking for a solution to a mathematical problem involving variables x and y and are referencing a figure which seems to be related to the problem. However, the values for x and y are not provided, and the figure in question is also missing from your message.
To solve for x and y, we need the full details of the problem including the specific mathematical equations or relationships that involve x and y. If there is a diagram or figure associated with the problem, the details about the figure such as angles, sides, shapes, or any labels are crucial in order to provide a solution.
Without this information, I cannot provide a correct solution to the problem.
To assist you better, please provide the complete problem statement with all necessary details. If there are equations that need to be solved, specify them. If there is a geometric figure involved, please describe it or provide the relevant measurements and properties that relate to x and y.
Once you provide the full context of the problem, I would be glad to help you find the value of x and y and also explain what might be wrong with the figure, if applicable.
The cost of a book was decreased from 60 to 50 by what percent the price decrased with solution
Answer:
The price decreased by 16 1/3%, or approximately 16.3%
Step-by-step explanation:
Use the formula for percent change. If the answer is negative, it is a percent decrease. if the answer is positive, it is a percent increase.
percent change = (new price - old price)/(old price) * 100%
In this case, use:
new price = 50
old price = 60
percent change = (new price - old price)/(old price) * 100%
percent change = (50 - 60)/60 * 100%
percent change = -10/60 * 100%
percent change = -1/6 * 100%
percent change = -100/6% = -50/3% = -16 1/3%
The price decreased by 16 1/3%, or approximately 16.3%
6.789 the digits 8 stand for
Answer:
8/100. Eight hundredths or we can write it as 8 * 10^-2.
Step-by-step explanation:
The first digits after the decimal point is tenths ( 7 tenths) and the second is hundredths, the third is thousandths.
If f(x) = 3x - 4, which of these is the inverse of f(x)?
A. f^-1(x) = x/3 +4
B. F^-1(x) = x/3 -4
C. f^-1(x) = x+4/3
D. F^-1(x) = x-4/3
Answer:
[tex]f^{-1}(x)=\frac{x+4}{3}[/tex]
C is the correct option.
Step-by-step explanation:
The given function is [tex]f(x)=3x-4[/tex]
Replace f(x) with y
[tex]y=3x-4[/tex]
Interchange x and y as shown below
[tex]x=3y-4[/tex]
Solve the equation for y
[tex]x+4=3y\\\\y=\frac{x+4}{3}[/tex]
Therefore, the inverse of f(x) is given by
[tex]f^{-1}(x)=\frac{x+4}{3}[/tex]
C is the correct option.
What is the value of n in the equation
1/2(n-1) - 3 = 3 - (2n + 3)?
Hey there! :)
1/2(n - 1) - 3 = 3 - (2n + 3)
Simplify.
1/2n - 1/2 - 3 = 3 - 2n - 3
Add like terms.
1/2n - 3 1/2 = -2n
Add 3 1/2 to both sides.
1/2n = -2n + 3 1/2
Then, add 2n to both sides.
1/2n + 2n = 3 1/2
Simplify!
2 1/2n = 3 1/2
Make everything into improper fractions!
5/2n = 7/2
Multiply everything by 2 to get rid of the denominators.
5/2n × 2 = 7/2 × 2
Simplify!
5n = 7
Divide both sides by 5.
n = 7/5
Hope this helped! :)
Answer:
[tex]\frac{7}{5} = n[/tex]
Step-by-step explanation:
[tex] \frac{1}{2} (n - 1) - 3 = 3 - (2n + 3) \\ [/tex]
Solve the brackets.
[tex] \frac{n}{2} - \frac{1}{2} - 3 = 3 - 2n - 3 \\ [/tex]
Make the denominator the same to solve the fractions.
[tex] \frac{n}{2} - \frac{1}{2} - \frac{3 \times 2}{1 \times 2} = 3 - 2n - 3 \\ [/tex]
Combine like terms.
[tex] \frac{n}{2} - \frac{1}{2} - \frac{6}{2} = - 2n \\ \\ \frac{n - 7}{2} = - 2n \: \: \: \: \: \: \: \: [/tex]
Use cross multiplication to solve for n.
[tex]n - 7 = - 4n \\ \\ - 7 = - 4n - n \\ \\ - 7 = - 5n \: \: \: \: \: \: \\ \\ \frac{ - 7}{ - 5} = \frac{ - 5n}{ - 5} \: \: \: \: \\ \\ \frac{7}{5} = n \: \: \: \: \: \: \: [/tex]
One angle measure in an acute isosceles triangle is 20°. What is the measure of one of the other angles?
80°
20°
140°
160°
Answer:
Option 2) 20°
Step-by-step explanation:
Step 1: Write relevant properties of triangle.
All 3 sides of a triangle are equal to 180 degrees.
In an isosceles triangle, 2 sides and 2 angles are same.
Step 2: Calculate another angles
Since it is an isosceles triangle, two sides will be same therefore, 2 angles will be same.
Angle 1 = Angle 2 = 20 degrees (because isosceles triangle)
Therefore, 20° is the measure of one of the other angles.
Option 2
!!
Answer: FIRST OPTION.
Step-by-step explanation:
It is important to remember that an Acute Isosceles triangle has two congruent sides and all its angles measure less than 90 degrees. Then, the third option and the the fourth option are not one of the other angles.
You know that the sum of the interior angles of a triangle is 180 degrees.
Then, let be "x" one the other angles, let's check the first option:
[tex]80\°+20\°+x=180\°\\x=80\°[/tex]
Since [tex]80\°<90\°[/tex], the angle provided in the first option is one of the other angles.
Let's check the second option:
[tex]20\°+20\°+x=180\°\\x=140\°[/tex]
Since [tex]140\°>90\°[/tex], the angle provided in the second option is not one of the other angles.
For every real number x,y, and z the statement (x-y)z=xz-yz is
Answer:
true.
Step-by-step explanation:
(x - y)z = xz - yz
Apply the distributive property of multiplication over addition to the left side:
(x - y)z =
= z(x - y)
= xz - yz
This is the same as the right side, so the statement is true.
plz solve
the measure of angles of a hexagon are x degree , (x-5) degrees , (x-5) degrees , (2x-5) degrees , (2x-5) degrees , (2X+20) FIND THE VALUE OF X
Answer:
6 and up
Step-by-step explanation:
this is beacuse when you add all the angels up you you would have to have a minimum of 6 to pass the negative 5
Answer:
x = 80°
Step-by-step explanation:
The sum of the interior angles of a hexagon is 720 degrees. So,
x + (x - 5) + (x - 5) + (2x - 5) + (2x - 5) + (2x + 20) = 720
Eliminating parenthesis
x + x - 5 + x - 5 + 2x - 5 + 2x - 5 + 2x + 20 = 720
Adding and subtracting
9x + 0 = 720
Isolating x
x = 720/9
x = 80
True or False? A triangle with two congruent angles can never be scalene.
O
O
A. True
B. False
is it true or false
A scalene triangle has all different side lengths and different sized angles. This means that a scalene can NOT have two congruent angles.
This means that the answer is:
True
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
it is actually false
cause you can change the angles or sides to turn it scalene
Step-by-step explanation:
The table shows the results of a student survey done by the chef at a school
cafeteria. What is the probability that one of these students is female and
likes peas?
[tex]\huge{\boxed{32\%}}[/tex]
We can find this information using the table. The number of female students that like peas is 64, and the total number of students is 200. That gives us the following fraction. [tex]\frac{64}{200}[/tex]
Now, turn this into a percentage by making the denominator 100. This is done by dividing the numerator and denominator each by 2, since the denominator is 100. [tex]\frac{64 \div 2}{200 \div 2}= \frac{32}{100}=32%[/tex]
Required probability that one of these students is female and
likes peas is 32/100 or 32%
What is probability?Probability is the chance of happening of an event.Probability is always ≤ 1How to find the probability that one of these students is female and likes peas?According to the problem,
The total number of students is 200 which is actually the total sample space.Number of students who are female and likes peas = 64∴ Required probability = 64/200 = 32/100 = 32%
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What is the product of Seven square root eight times four square root five? Simplify your answer. Twenty eight radical ten Fifty six radical two Fifty six radical ten Two hundred eighty radical four
Answer:
56√10.
Step-by-step explanation:
7√8 * 4√5
= 28 √40
= 28 √4√10
= 28 * 2√10
= 56√10.
Answer:
56[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Given
7[tex]\sqrt{8}[/tex] × 4[tex]\sqrt{5}[/tex]
= 7 × 4 × [tex]\sqrt{8(5)}[/tex]
= 28 × [tex]\sqrt{40}[/tex]
= 28 × [tex]\sqrt{4(10)}[/tex]
= 28 × [tex]\sqrt{4}[/tex] × [tex]\sqrt{10}[/tex]
= 28 × 2 × [tex]\sqrt{10}[/tex]
= 56[tex]\sqrt{10}[/tex]
What is 0.03 (with the 3 repeating)/0.03 (with both the 0 and the 3 repeating) Express your answer as a mixed number.
[tex]0.0\overline{3}=\dfrac{1}{30}\\0.\overline{03}=\dfrac{1}{33}\\\\\dfrac{0.0\overline{3}}{0.\overline{03}}=\dfrac{\dfrac{1}{30}}{\dfrac{1}{33}}=\dfrac{1}{30}\cdot33=\dfrac{11}{10}=1\dfrac{1}{10}[/tex]
Jenna bought a bike for $200. The value of the bike decreases by 5% each year. Write an equation to model the situation.
A. y = 200(0.95)x
B. y = 200(0.5)x
C. y = 195(0.95)x
D. y = 95(0.95)x
Explain how to multiply a monomial and a polynomial that is not monomial. Give examples .
Answer:
See below.
Step-by-step explanation:
To multiply a monomil by a polynomial, multiply the monomial by each term of the polynomial.
Example: Multiply 3x^2 by 4x^2 + 5x - 2
3x^2(4x^2 + 5x - 2) =
= 3x^2 * 4x^2 + 3x^2 * 5x + 3x^2 * (-2)
= 12x^4 + 15x^3 - 6x^2
To multiply a monomial and a polynomial that is not monomial, distribute the monomial term to each term of the polynomial, and then simplify the resulting expression by combining like terms.
Explanation:To multiply a monomial and a polynomial that is not monomial, distribute the monomial term to each term of the polynomial, and then simplify the resulting expression by combining like terms.
For example, let's multiply the monomial 3x^2 by the polynomial 4x^3 + 2x - 1:
Multiply 3x^2 by 4x^3, which gives 12x^5. Multiply 3x^2 by 2x, which gives 6x^3. Multiply 3x^2 by -1, which gives -3x^2. Combine these terms: 12x^5 + 6x^3 - 3x^2. Learn more about monomial and a polynomial here:https://brainly.com/question/35584608
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if A= (4,-5) and b=(7,9) what is the length of ab?
Answer:
14.3178210633
Step-by-step explanation:
distance formula, d= sq root of ((x2-x1)^2+(y2-y1)^2)
Answer:
ab = [tex]\sqrt{42}[/tex].
Step-by-step explanation:
Given : A= (4,-5) and b=(7,9).
To find : what is the length of ab.
Solution : We have given that A= (4,-5) and b=(7,9).
Distance formula : [tex]\sqrt{(x_{2}-x_{1}(y_{2} -y_{1})}[/tex].
Here, [tex]x_{1} =4[/tex]
[tex]x_{2} =7[/tex]
[tex]y_{1} =-5[/tex]
[tex]y_{2} =9[/tex].
Then [tex]\sqrt{(7-4)(9-(-5))}[/tex].
ab = [tex]\sqrt{(3)(14)}[/tex].
ab = [tex]\sqrt{42}[/tex].
Therefore, ab = [tex]\sqrt{42}[/tex].
Mr.Rector bought an 8-ounce bottle of juice. He accidentally knocked it over and spill 1/4 of the juice. How many ounces of juice does she have left to quench his thirst?
Answer:
6 oz
Step-by-step explanation:
If he spilled 1/4 of the juice, then he has 3/4 of the original volume left.
(3/4)(8 oz) = 6 oz.
He has 6 oz left to enjoy.
What is absolute value?
Answer:
Absolute value means the distance between a number and 0.
Examples:
The absolute value of -7 is 7.
The absolute value of 5 is 5.
Key Concepts:
The absolute value sign is |x|, where x is any real number.
The absolute value removes any negative sign in front of a number.
Absolute value is an important math concept to understand. To represent the absolute value of a number, we use a vertical bar on either side of the number. Absolute value means "distance from zero" on a number line. Let's try an example to understand how absolute value works.
What is the absolute value of 4 and -4?
To find the absolute value of 4, we know that 4 is 4 units from zero on a number line. Therefore, the absolute value of 4 is 4.
For the absolute value of -4, we know that -4 is also 4 units from zero on the number line. Therefore, the absolute value of -4 is also 4.
Another way that I like to think about absolute value is no matter what number you have inside the absolute value, the result will always be positive. In other words, the absolute value of any number is the positive version of that number.
The length of a field in yards is a function f(n) of the length n in feet. Write a function rule for th
situation.
$) = 30
Of(n) = 120
Answer:
[tex]f(n) = \frac{n}{3} [/tex]
Step-by-step explanation:
Recall that:
[tex]3ft = 1 \: yd[/tex]
This implies that:
[tex] 6ft = 2yds[/tex]
[tex] 9ft = 3yds[/tex]
In general:
[tex] n \: ft = \frac{n}{3} \: \: yds[/tex]
We can therefore write the function rule:
[tex]f(n) = \frac{n}{3} [/tex]
HELPPP MEEEEEE PLEASE
Step-by-step explanation:
We arrange numbers in ascending order
Range - numbers appearing (without repetition)
Median - middle value
Mean - the sum of the numbers divided by the number of items
Mode - the value that appears most often.
[tex]\bold{Q4.}\\\\22,\ 36,\ 39,\ 39,\ 40,\ 40,\ 41,\ 42,\ 45,\ 46,\ 46,\ 49\\\\\bold{Range:}\ 22,\ 36,\ 39,\ 40,\ 41,\ 42,\ 45,\ 46,\ 49\\\\\bold{Median:}\ 40,\ 41\to\dfrac{40+41}{2}=40.5\\\\\bold{Mean:}\ \dfrac{22+36+39+39+40+40+41+42+45+46+46+49}{12}=40\dfrac{5}{12}\\\\\bold{Mode:}\ 39,\ 40\ and\ 46[/tex]
[tex]\bold{Q5.}\\\\79,\ 83,\ 84,\ 86,\ 86,\ 90,\ 94\\\\\bold{Range:}\ 79,\ 83,\ 84,\ 86,\ 90,\ 94\\\\\bold{Median}:\ 86\\\\\bold{Mean:}\ \dfrac{79+83+84+86+86+90+94}{7}=86\\\\\bold{Mode:}\ 86[/tex]
The equation of the graphed line is 2x - y =-6
What is the x-intercept of the graph?
-3,-2,2,6
PLEASE ANDWER ASAP
Answer:
The x intercept = -3
Step-by-step explanation:
The x intercept is where it crosses the x axis.
Looking at the graph, it crosses at x =-3
Using the equation, we set y=0 and solve for x
2x-y =-6
2x -0 =-6
2x = -6
Divide by 2
2x/2 =-6/2
x=-3
Answer: A
Step-by-step explanation:
Edgen 2023
Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?
acute, because 62 + 102 < 122
Answer:
obtuse, because 6^2+10^2 is greather than 12^2
Step-by-step explanation:
The triangle with side lengths 6 cm, 10 cm, and 12 cm is a right triangle. This is determined by applying the Pythagorean theorem (a^2 + b^2 = c^2) to the side lengths of the triangle.
Explanation:The classification of a triangle can be determined by its side lengths. In this context, you have a triangle with side lengths 6 cm, 10 cm, and 12 cm. This is not an acute triangle, contrary to the original statement. It is, in fact, a right triangle.
To determine this, one can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as a^2 + b^2 = c^2.
If we apply the Pythagorean theorem to our triangle, we find that 6^2 + 10^2 equals 36 + 100, which is 136. Similarly, 12^2 equals 144. Since 136 is less than 144, the triangle is indeed a right triangle, not an acute triangle.
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Which part of the ear carries sound messages to the brain?
eardrum
bones of the middle ear
ear canal
auditory nerve
Answer:
auditory nerve
Step-by-step explanation:
the auditory nerve carries sound signals to the brain. The cochlea picks up sound waves and makes nerve signals.
Answer:
The auditory nerve
Step-by-step explanation:
Find the radius of the circle with equation x²+y²+8x+8y+28=0
The answer is:
Center: (-4,-4)
Radius: 2 units.
Why?To solve the problem, using the given formula of a circle, we need to find its standard equation form which is equal to:
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
Where:
"h" and "k" are the coordinates of the center of the circle and "r" is its radius.
So, we need to complete the square for both variable "x" and "y".
The given equation is:
[tex]x^{2}+y^{2}+8x+8y+28=0[/tex]
So, solving we have:
[tex]x^{2}+y^{2}+8x+8y=-28[/tex]
[tex](x^2+8x+(\frac{8}{2})^{2})+(y^2+8y+(\frac{8}{2})^{2})=-28+((\frac{8}{2})^{2})++(\frac{8}{2})^{2})\\\\(x^2+8x+16 )+(y^2+8y+16)=-28+16+16\\\\(x^2+4)+(y^2+4)=4[/tex]
[tex](x^2-(-4))+(y^2-(-4))=4[/tex]
Now, we have that:
[tex]h=-4\\k=-4\\r=\sqrt{4}=2[/tex]
So,
Center: (-4,-4)
Radius: 2 units.
Have a nice day!
Note: I have attached a picture for better understanding.
The radius of the circle is 2 units.
Explanation:To find the radius of the circle with equation x²+y²+8x+8y+28=0, we need to rearrange the equation into the standard form (x-h)²+(y-k)²=r², where (h,k) is the center of the circle and r is the radius. By completing the square, we can rewrite the equation as (x+4)²+(y+4)²=4.
Comparing this with the standard form, we can see that the center of the circle is (-4,-4) and the radius is √4 = 2. Therefore, the radius of the circle is 2 units.
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Determine whether the relations represent y as a function of x.
Answer:
Both of those are functions.
Step-by-step explanation:
[tex]y=x^2[/tex] is a parabola that opens up.
Any upward or downward parabola is a function because they pass the vertical line test.
[tex]x=\pm \sqrt{1-y}{/tex]
Square both sides:
[tex]x^2=1-y[/tex]
Subtract 1 on both sides:
[tex]x^2-1=-y[/tex]
Multiply both sides by -1:
[tex]-x^2+1=y[/tex]
So this is a another parabola and it is faced down. So this is also a function.
[tex]y=ax^2+bx+c[/tex] wit [tex]a \neq 0[/tex] willl always be a parabola.
If [tex]a>0[/tex] then it is open up.
If [tex]a<0[/tex] then it is open down.
Upwards and downward parabolas will always be functions.
[tex]x=ay^2+by+c[/tex] are also parabolas but these open to the left or right. These will not be functions because they will not pass the vertical line test.
The area of the rectangle is
square inches.
Answer:
42
Step-by-step explanation:
all I did was multiply 6 by 7 and i got 42
In a geometric progression of positive terms, the 5th term is 9 times the 3rd term and the sum of the 6th and 7th terms is 972. Find the
a) common ratio
b) sum of the first 6 terms
Answer:
a) 3
b) 364
Step-by-step explanation:
A geometric sequence in explicit form is [tex]a_n=a_1 \cdot r^{n-1}[/tex] where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio.
We are given:
[tex]a_5=9 \cdot a_3[/tex]
[tex]a_6+a_7=972[/tex].
What is a) r?
What is b) the sum of the first 6 terms?
So I'm going to use my first equation and use my explicit form to find those terms in terms of r:
[tex]a_1 \cdot r^4=9 \cdot a_1 \cdot r^{2}[/tex]
Divide both sides by [tex]a_1r^2[/tex]:
[tex]r^2=9[/tex]
[tex]r=\sqrt{9}[/tex]
[tex]r=3[/tex].
So part a is 3.
Now for part b).
We want to find [tex]a_1+a_2+a_3+a_4+a_5+a_6[/tex].
So far we have:
[tex]a_1=a_1[/tex]
[tex]a_2=3a_1[/tex]
[tex]a_3=3^2a_1[/tex]
[tex]a_4=3^3a_1[/tex]
[tex]a_5=3^4a_1[/tex]
[tex]a_6=3^5a_1[/tex].
We also haven't used:
[tex]a_6+a_7=972[/tex].
I'm going to find these terms in terms of r (r=3).
[tex]3^5a_1+3^6a_1=972[/tex]
[tex]243a_1+729a_1=972[/tex]
You have like terms to add:
[tex]972a_1=972[/tex]
Divide both sides by 972:
[tex]a_1=1[/tex]
The first term is 1 and the common ratio is 3.
The terms we wrote can be simplify using a substitution for the first term as 1:
[tex]a_1=a_1=1[/tex]
[tex]a_2=3a_1=3(1)=3[/tex]
[tex]a_3=3^2a_1=9(1)=9[/tex]
[tex]a_4=3^3a_1=27(1)=27[/tex]
[tex]a_5=3^4a_1=81(1)=81[/tex]
[tex]a_6=3^5a_1=243(1)=243[/tex].
Now we just need to find the sum of those six terms:
1+3+9+27+81+243=364.
In △ABC, m∠A=15°, a=9, and b=12. Find c to the nearest tenth.
Answer:
=20.0
Step-by-step explanation:
We can first find the angle B using the sine rule as follows:
a/Sin A=b/Sin B
9/Sin 15=12/ Sin B
Sin B= (12 Sin 15)/9
=0.345
B=Sin⁻¹ 0.345
=20.18°
We then find C by using the summation of the interior angles of a triangle.
C=180-(20.18+15)
=144.82
Finding the length of c:
a/Sin A= c/ Sin C
9/Sin 15=c/Sin 144.82
c=(9 Sin 144.82)Sin 15
=20.0
Answer:
20.0 unit ( approx )
Step-by-step explanation:
Here,
ABC is a triangle in which,
m∠A=15°, a=9, and b=12,
By the law of sine,
[tex]\frac{sin A}{a}=\frac{sin B}{b}=\frac{sin C}{c}----(1)[/tex]
[tex]\frac{sin A}{a}=\frac{sin B}{b}[/tex]
[tex]\implies sin B=\frac{b sin A}{a}[/tex]
By substituting the values,
[tex]\implies sin B=\frac{12\times sin 15^{\circ}}{9}\approx 0.3451[/tex]
[tex]\implies B \approx 20.19^{\circ}[/tex]
Now, by the property of triangle,
m∠A + m∠B+ m∠C = 180°
⇒ m∠C = 180° - 15° - 20.19° = 144.81°,
By the equation (1),
[tex]c=\frac{b sin C}{sin B}=\frac{12\times sin 144.81^{\circ}}{sin 20.19^{\circ}}=20.0370532419\approx 20.0[/tex]
Polygon LMNOP was transformed to create polygon L'M'N'O'P'. Which angle corresponds to N?
Answer:
N'
Step-by-step explanation:
L corresponds to L'
M corresponds to M'
N corresponds to N'
O corresponds to O'
P corresponds to P'
After the transformation if you copy and paste your picture over the new picture, the corresponding angles should lay on top of each other.
Polygon LMNOP was transformed to create polygon L'M'N'O'P'. The angle N corresponds to N'.
What is a polygon?
A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.
Here,
L corresponds to L'
M corresponds to M'
N corresponds to N'
O corresponds to O'
P corresponds to P'
Hence, The N corresponds to N'.
To know more about polygons refer to
https://brainly.com/question/1513726
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