Answers
x+6= women
x + (x+6)= 30
2x + 6= 30
2x= 24
x= 12
x+6= 18
8) x= first integer
x+1= second integer
x+2= third integer
x + (x+1) + (x+2)= 153
3x + 3= 153
3x= 150
x= 50
Second integer
= x+1
= x+50
= 51
9) x= first integer
x+2= second integer
x+4= third integer
x + (x+2) + (x+4)= 54
3x + 6= 54
3x= 48
x= 16
x + (x+2)= 34
16 + 16 + 2= 34
34=34
10) rate= 356 km/hr
distance= 1424 km
Distance= rate * time
D= rt
1424= 356 * t
divide both sides by 356
4 hrs= t
ANSWERS:
7) 18 (B - second choice down)
8) 51 (B - second choice down)
9) 16 (D - fourth choice down)
10) 4 (B- second choice down)
Hope this helps! :)
Related Questions
What is the measure of R to the nearest degree?
Answers
R measures 42.8 degrees, which is around average.
What are the properties of Triangle?The properties of the triangle are:
1. The sum of all the angles of a triangle (of all types) is equal to 180°.
2. The sum of the length of the two sides of a triangle is greater than the length of the third side.
3. In the same way, the difference between the two sides of a triangle is less than the length of the third side.
The sine rule states that for a triangle with sides a, b, and c opposite to angles A, B, and C respectively,
a/sinA = b/sinB = c/sinC
Using this rule, we can find the measure of angle R as follows:
a = ST = 30
b = RT = 35
c = RS
Let angle R be opposite to side b.
sinR/sinS = b/c
sinR/sin69 = 35/c
c = 35/sin69 x sinR
Now we can use the sine rule to find c:
a/sinA = b/sinB = c/sinC
30/sin69 = 35/sinR = c/sin42
c = 35/sinR x sin42
Equating the two expressions for c, we get:
35/sin69 x sinR = 35/sinR x sin42
Simplifying this equation, we get:
sinR/sin69 = sin42
sinR = sin69 x sin42
sinR = 0.672
Taking the inverse sine of both sides, we get:
R = sin^{-1}(0.672)
R ≈ 42.8 degrees
Therefore, the measure of angle R is approximately 42.8 degrees.
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Solve the system of linear equations by elimination. 3x−2y=4 3x−2y=4 6x−2y=−2
Answers
y = -5
You can get this by multiplying the first equation by -1 and then combining. That will get your y values to cancel out.
Removing which point from the coordinate plane would make the graph a function of x?
(–4, 3)
(–2, 1)
(0, 4)
(1, 1)
Answers
Sarah deposits $600 in a savings account that pays 2.5% per year. What is the minimum number of years it would take for the amount in her account to be more than $800, provided no more money is deposited in the account?
Answers
Years = {log(total) -log(Principal)} ÷ log(1 + rate)
Years = {log(800) - log(600)} ÷ log(1.025)
Years = {2.903089987 -2.7781512504} / 0.010723865392
Years = { 0.1249387366 } / 0.010723865392
Years = 11.6505319708
That's how many years it takes for the $600 to become exactly $800.00
The question specifically asks how long for the money to be MORE than $800.00?
So, if we enter 800.01 into the equation, then the answer is
Years = {log(800.01) - log(600)} ÷ log(1.025)
Years = {2.9030954156 -2.7781512504} / 0.010723865392
Years = 0.1249441652 / 0.010723865392
Years = 11.6510381875
It will take at least 12 years for Sarah's $600 deposit at a 2.5% annual interest rate to grow to more than $800, assuming the interest is compounded annually.
To determine how long it will take for Sarah's $600 deposit at a 2.5% annual interest rate to grow to over $800, we can use the formula for compound interest: [tex]A = P(1 + r/n)^{(nt)[/tex], where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per year.t is the time the money is invested for in years.Since the problem doesn't specify the compounding frequency, let's assume it's compounded annually for simplicity:
[tex]A = 600(1 + 0.025)^t[/tex]. We need A to be greater than $800.
To find the minimum number of years (t), we solve for t:
[tex]800 < 600(1 + 0.025)^t[/tex]
Solving for t gives us: t > ln(800/600) / ln(1.025).
Using a calculator, we find that t > 11.89.
Therefore, it will take at least 12 years for the amount in Sarah's account to exceed $800.
Identify the polynomial. x 3 y 3 monomial binomial trinomial
Answers
Answer:
x³y³ is monomial.
Step-by-step explanation:
Given :Polynomial x³y³ .
To find : Identify monomial binomial trinomial.
Solution : We have given that
Polynomial x³y³ .
Monomial : A polynomial with just one term.
Examples : 1) 3xy
2) 5y²x³ Both are monmial .
x³y³ is also a monomial because it has only one term.
Therefore, x³y³ is monomial.
The height of a cone is equal to the diameter of the base. What expression represents the volume of the cone, in cubic units?
Answers
[tex]V = (1/3) * (\pi) * (r ^ 2) * (h) [/tex]
Where,
r: radius of the circular base
h: height of the cone
Let's define a variable:
x: diameter of the base
We have then that the radio is:
[tex] r = x / 2 [/tex]
The height is:
[tex] h = x [/tex]
Substituting values:
[tex]V = (1/3) * (\pi) * ((x / 2) ^ 2) * (x) [/tex]
Rewriting:
[tex]V = (1/3) * (\pi) * (x ^ 2/4) * (x) V = (1/12) * (\pi) * (x ^ 3)[/tex]
Answer:
An expression that represents the volume of the cone, in cubic units is:
[tex]V = (1/12) * (\pi) * (x ^ 3)[/tex]
PLZ SOMEONE HELP ME ON THIS
Answers
I may be wrong let me know
Hope it helps
Find the volume of the composite space figure to the nearest whole number.
Answers
Answer:
The volume is 180 cube cm.
Step-by-step explanation:
By the given diagram,
The composite figure is made by the two cuboids,
First having dimensions, 2 cm × 5 cm × 6 cm,
And second having dimensions, 8 cm × 5 cm × 3 cm,
So, the volume of the given composite figure = the volume of first cuboid + the volume of second cuboid
= 2 × 5 × 6 + 8 × 5 × 3,
= 60 + 120
= 180 cube cm
The volume of the composite space figure to the nearest whole number is: 180 cube cm.
Here, we have,
from the given information, we get,
By the given diagram,
The composite figure is made by the two cuboids,
First having dimensions, 2 cm × 5 cm × 6 cm,
And second having dimensions, 8 cm × 5 cm × 3 cm,
So, the volume of the given composite figure
= the volume of first cuboid + the volume of second cuboid
= 2 × 5 × 6 + 8 × 5 × 3,
= 60 + 120
= 180 cube cm
Hence, the volume of the composite space figure to the nearest whole number is: 180 cube cm.
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3. If the volume of a cube of wood is15.625 cm3 and its mass is 10.00 grams, show the calculation for the density of the wood. @ganeshie8 @SolomonZelman,
Answers
density of wood = 0.64 gm/cm³
Explanation:
Density of a substance can be calculated as follows:
density = [tex] \frac{mass}{volume} [/tex]
We are given that:
mass of wood = 10 grams
volume of wood = 15.625 cm³
Substitute with the givens in the above equation to get the density as follows:
density = [tex] \frac{10}{15.625} [/tex] = 0.64 grams / cm³
Hope this helps :)
Answer:
The density of the wood is, 0.64 [tex]g/cm^3[/tex]
Step-by-step explanation:
Using the density formula:
[tex]\text{density} = \frac{\text{mass}}{\text{Volume}}[/tex] .....[1]
As per the statement:
If the volume of a cube of wood is 15.625 cm3 and its mass is 10.00 grams.
⇒Volume = 15.625 cubic cm and mass = 10 gram
Substitute the given values in [1] we have;
[tex]\text{density} = \frac{10}{15.625}[/tex]
Simplify:
density = 0.64 [tex]g/cm^3[/tex]
Therefore, the density of the wood is, 0.64 [tex]g/cm^3[/tex]
In your notebook, draw a right angle and then draw a bisector of the right angle. Label all parts. What are some properties of the angles formed by the bisector?
Answers
Answer:
Let's consider this right triangle described in the picture.
∠ABD = ∠CBD, since BD is a bisector.
Angles ∠ADB and ∠BDC are neighbor angles and their sum is equal to 180°.
∠BDC is an exterior angle and ∠BDC=∠ABD+∠ADB.
Similarly, ∠ADB is an exterior angle and ∠ADB=∠CBD+∠BCD
Step-by-step explanation:
WILL GIVE BRAINLIEST, 15 points-The daily number of patients visiting a dentist's office during one week are 8, 41, 35, 39, 36, and 42.
Which statement is true?
The mean, median, and mode are all appropriate measures of center.
Both the mean and median are appropriate measures of center.
The median is the only appropriate measure of center.
Both the median and mode are appropriate measures of center.
Answers
Mean and median both try to measure the central tendency in a data set.The mean is commonly used, but sometimes the median is preferred.
Mode is the element which occurs the most times in the set
therefore
the answer is the option
Both the mean and median are appropriate measures of center.
Answer: The median is the only appropriate measure of center.
Step-by-step explanation:
The statement is ''Both the median and mode are appropriate measures of center''. Actually, the three, that is, the mean, media and mode can be used to measure the central of tendency. But the MEAN has a problem, it can be Skewed by large values in the distribution/data. Assuming, the days of the week when patients visiting a dentist's office are;
Monday: 8, Tuesday: 41, Wednesday: 35, Thursday: 39, Friday: 36, and Saturday: 42.
And the mean of the distribution = 33.5. Most patients visit the dentist Tuesday to Saturday, where Saturday is the highest. The data is skewed. So, the MEDIAN will do the job perfectly.
For the mode; since we do not have; (1). two highest mode with the same value in the data provided and, (2). the highest value and the second to the highest values are not too far from each other. We can use the MODE here for measuring the central tendency.
===> CONCLUSION: (1). Assuming the data fails the two condition for mode, the most correct statement will be ''The median is the only appropriate measure of center".
===> (2). Also, for this data, the MEDIAN will be the only appropriate measure of center.
1.
(05.08 MC)
Given the equation 1 over x−1 + 2 over x =x over x−1
Part A: What values of x that would make the equation no solution? Why?
Part B: What is the solution of the equation. Show all of your steps.
Max and Maggie have to clean the house. It takes Max 10 hours to clean the house, while Maggie can complete the task in 6 hours. How long will it take for them to work together? Explain each step in solving this equation.
Answers
Part B) x=2 or x=1.
Together they could clean the house in 3.75 hours.
Explanation:
Part A is explained with the answer.
Part B)
[tex]\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}[/tex]
We will first multiply each term by (x-1) to cancel those denominators:
[tex]\frac{1}{x-1} \times \frac{x-1}{1}+\frac{2}{x} \times \frac{x-1}{1}=\frac{x}{x-1} \times \frac{x-1}{1} \\ \\ \frac{x-1}{x-1}+\frac{2(x-1)}{x}=\frac{x(x-1)}{x-1} \\ \\ 1+\frac{2(x-1)}{x}=x[/tex]
Now we multiply everything by x to cancel that denominator:
[tex]1(x)+\frac{2(x-1)(x)}{x}=x(x) \\ \\x+2(x-1)=x^2 \\ \\x+2*x-2*1=x^2 \\x+2x-2=x^2 \\3x-2=x^2[/tex]
We want all of the variables to be on the same side of the equation, so subtract 3x from both sides:
3x-2-3x=x²-3x
-2=x²-3x
To solve quadratics, we set them equal to 0. Add 2 to both sides to make this happen:
-2+2=x²-3x+2
0=x²-3x+2
To solve this by factoring, we want factors of 2 that sum to -3. -2(-1)=2 and -2+-1=-3:
0=(x-2)(x-1)
The zero product property tells us that either x-2=0 or x-1=0; therefore x=2 or x=1.
Max cleans 1/10 of the house in an hour, since it takes him 10 hours to clean the whole house. Maggie cleans 1/6 of the house in an hour, since it takes her 6 hours to clean the whole house. Our equation is then:
1/10x+1/6x=1 (one whole, since it is one house; x is the number of hours)
Find a common denominator. 60 is the first thing that 10 and 6 both evenly divide into:
6/60x+10/60x=1
16/60x = 1
Divide both sides by 16/60:
16/60x ÷ 16/60 = 1 ÷ 16/60
x = 1/1 ÷ 16/60
x = 1/1 ×60/16
x = 60/16 = 3.75.
Answer:
a
Step-by-step explanation:
What would be the next number in pattern 1/324, 1/108, 1/36, 1/12 answers are 1/3, 1/5, 1/4, 1
Answers
The next number in pattern 1/324, 1/108, 1/36, 1/12 would be 1/4
Further explanationFirstly , let us learn about types of sequence in mathematics.
Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.
[tex]\boxed{T_n = a + (n-1)d}[/tex]
[tex]\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
d = common difference between adjacent numbers
Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.
[tex]\boxed{T_n = a ~ r^{n-1}}[/tex]
[tex]\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
r = common ratio between adjacent numbers
Let us now tackle the problem!
Given:
This problem is about Geometric Sequence. Let's see why.
[tex]\frac{1}{324} , \frac{1}{108} , \frac{1}{36} , \frac{1}{12} , . . .[/tex]
T₁ = [tex]\frac{1}{324}[/tex]
T₂ = [tex]\frac{1}{108}[/tex]
T₃ = [tex]\frac{1}{36}[/tex]
T₄ = [tex]\frac{1}{12}[/tex]
[tex]\large {\boxed {\frac{T_2}{T_1} = \frac{T_3}{T_2} = \frac{T_4}{T_3} = r = 3} }[/tex]
From the above results it can be concluded that this is Geometric Sequence.
The next number will be the fifth term and can be calculated as following.
[tex]T_n = a ~ r^{n-1}[/tex]
[tex]T_5 = \frac{1}{324} \times 3^{5 - 1}[/tex]
[tex]T_5 = \frac{1}{324} \times 3^4[/tex]
[tex]T_5 = \frac{1}{324} \times 81[/tex]
[tex]\large {\boxed {T_5 = \frac{1}{4} } }[/tex]
Learn moreGeometric Series : https://brainly.com/question/4520950Arithmetic Progression : https://brainly.com/question/2966265Geometric Sequence : https://brainly.com/question/2166405Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Arithmetic and Geometric Series
Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term
The midpoint of a line segment with end points as (-10, y1) and (-6, 7) is (-8, 6). What is the value of y1?
Midpoint formula is (x1 + x2)/2 , (y1 + y2)/2 but I keep getting a wrong answer.,
Answers
M ( (x₂-x₁)/2 , (y₂-y₁)/2 )
You need to invert these to get x₁ and y₁:
x₁ =2xm - x₂
y₁ =2ym - y₂
Try with the x to prove the formulae are correct:
x₁ =2·(-8) - (-6) = -16 + 6 = -10 which is what we have!
Then, use the other formula for y:
y₁ =2 ·(6) - (7) = 12 - 7 = 5
Therefore y₁ = 5
So I tried to answer this the best that I can but I keep getting wrong answers can someone help me I will award brainliest .
Answers
[tex]2*\sqrt{3}*\dfrac{cos(x)}{sin(x)}+4*cos(x)- \dfrac{3}{sin(x)} +2*\sqrt{3}\\ =2*cos(x)*(\dfrac{\sqrt{3}}{sin(x)}+2)-\sqrt{3}(\dfrac{\sqrt{3}}{sin(x)}+2)\\ =(\dfrac{\sqrt{3}}{sin(x)}+2)*(2*cos(x)-\sqrt{3})\\\\ cos(x)=\dfrac{\sqrt{3}}{2} -\ \textgreater \ x=\dfrac{\pi}{6}\ or\ x=\dfrac{11*\pi}{6}\\ or\\ \dfrac{\sqrt{3}}{sin(x)}+2=0-\ \textgreater \ sin(x)=-\dfrac{\sqrt{3}}{2}-\ \textgreater \ x=\dfrac{5*\pi}{3}\ or\ x=\dfrac{4*\pi}{3}\\\\ [/tex]
find the range of the function f(x)=4x-1 for the domain {-1,0,1,2,3}
how do I do this?
Answers
Plug in all the values of the domain, which are x, into the equation for x. If you plug in those values you will get {-5, -1, 3, 7, 11} so the range will be (-5, 11).
So, to find the range, substitute each value of the domain in the given function f(x)=4x-1
Domain is {-1,0,1,2,3}
When x=-1, f(x)= 4(-1)-1 =-4-1 = -5
When x=0, f(x)=4(0)-1 = 0-1 =-1
When x=1, f(x) = 4(1)-1 = 4-1 = 3
When x=2, f(x) = 4(2)-1 =8-1 =7
When x=3, f(x) = 4(3) -1 =12-1 = 11
Therefore the range is {-5,-1,3,7,11}
1000p for an answer please
Answers
Also, notice that it says "the difference of a number and 6"
So your equation should have been
y - 6
And after evaluating
24 - 6
Then solve
24 - 6 = 18
18 should have been the answer
So no, the student's work is not correct, because the student wrote a division expression instead of a subtraction equation
What is the equation of the line passing through the points (2, –1) and (5, –10) in slope-intercept form?
y=-3x-5
y=-3x+5
y=3x-5
y=3x+5,
Answers
as you see the line crosses Y-axis on point 5 so the intercept is +5
nowyou can put (2,-1)as x and y to find the slope
[tex] - 1 = 2a + 5 \\ - 1 - 5 = 2a \\ - 6 = 2a \\ a = \frac{ - 6}{2} = - 3[/tex]
the slope is -3
so the correct equation will be
y=-3x+5
The equation of line passes through the points (2, -1) and (5, -10) will be;
⇒ y = - 3x + 5
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (2, -1) and (5, -10)
Now,
Since, The equation of line passes through the points (2, -1) and (5, -10)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 10 - (-1)) / (5 - 2)
m = - 9 / 3
m = - 3
Thus, The equation of line with slope - 3 is,
⇒ y - (-1)= - 3 (x - 2)
⇒ y + 1 = - 3x + 6
⇒ y = - 3x + 6 - 1
⇒ y = - 3x + 5
Therefore, The equation of line passes through the points (2, -1) and
(5, -10) will be;
⇒ y = - 3x + 5
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9x^2 - 8x - 1 = 0
What are the x intercepts?
Answers
(9x + 1(x - 1) = 0
x = -1/9 , 1
x intercepts are -1/9 and 1.
the product of two rational numbers
Answers
Answer:
'The product of two rational numbers is rational'
Step-by-step explanation:
Statement 'The product of two rational numbers'.
We know that, 'The product of two rational numbers is rational'.
We can prove it,
Let [tex]\frac{a}{b}[/tex] and [tex]\frac{p}{q}[/tex] are two rational number.
Where, a,b,p,q are integers and [tex]b,q\neq 0[/tex]
Now, Product the two rational number
[tex]\frac{a}{b}\times \frac{p}{q}=\frac{ap}{bq}[/tex]
Since, ap and bq are integers and [tex]bq\neq 0[/tex]
Thus, [tex]\frac{ap}{bq}[/tex] is an fraction with integers in the numerator and denominator making it a rational number.
Therefore, 'The product of two rational numbers is rational' is true.
Abe has a coupon for $3.50 off a pack of 24 water bottles. The regular price of this pack is $21.98. Is Abe uses his coupon what is the price per bottle.
Answers
write 4x - 2y = -8 in slope-intercept form
Answers
( 4x - 2y = -8)
--------------------
Then find the Y-intercept and X-intercept which is 4 and -2
(4x - 2y = -8)
(4x - 2y = -8)
----------------------
Since we already have the slope our equation so far is
y = 2x + M
And since we have out Y-intercept you replace 4 for m
y = 2x + 4 is your answer
How do the areas of the parallelograms compare?
The area of parallelogram ABCD is 4 square units greater than the area of parallelogram EFGH.
The area of parallelogram ABCD is 2 square units greater than the area of parallelogram EFGH.
The area of parallelogram ABCD is equal to the area of parallelogram EFGH.
The area of parallelogram ABCD is 2 square units less than the area of parallelogram EFGH.
Answers
A = b * h
Where,
b: base
h: height
We have then:
ABCD parallelogram:
A = (3) * (3)
A = 9 units ^ 2
EFGH parallelogram:
A = (3) * (3)
A = 9 units ^ 2
Answer:
The area of parallelogram ABCD is equal to the area of parallelogram EFGH.
Using your knowledge of circles, label the following on the given diagram: chord, tangent, radius, secant, point of tangency and diameter. Name a minor arc and a major arc.
Answers
A tangent is a line that only touches one point on the circle. The purple line on top of the circle is a tangent line.
A radius is a line from the center to any point on the circle. The red line is a radius.
A secant is like a chord, except it is a line and keeps going. The cyan (sky blue) line is a secant line.
A point of tangency is the point that the tangent line touches. The yellow point on the purple line is the point of tangency.
A diameter is a straight line that crosses the center and two points on the circle. You can say it’s two radii put together. Line segment BD (green) is a diameter.
Hope this helps!
In geometry, a chord, radius, diameter, tangent, secant, and the point of tangency are all parts related to a circle. A radius can also be an axis, a minor arc is the smaller arc between two points on a circle, and a major arc is the larger one. These terms help in understanding the properties and relations of lines to a circle.
In the context of circles in geometry, various terms define specific parts or aspects of a circle. Here's what each term represents:
A chord is a straight line segment whose endpoints both lie on the circle.The radius is a straight line from the center of the circle to any point on the circle. In other cases, it can form an axis which bisects a chord (as per a geometry theorem).A diameter is a chord that passes through the center of the circle, and it is also twice the length of the radius. Two radii forming a straight line constitute a diameter.A tangent is a straight line that touches the circle at just one point, this point is known as the point of tangency. A tangent is perpendicular to the radius drawn to the point of tangency.A secant is a straight line that intersects the circle at two points.A minor arc is the shortest arc connecting two endpoints on a circle, and a major arc is the longer arc connecting the same two endpoints. The length of an arc is proportional to the size of its associated angle at the center of the circle.
When drawing or labeling the parts of a circle, it's important to note these definitions. For instance, if given a diagram with a point on the circle labeled 'A' and the center labeled 'O', the segment OA would be a radius. If there's a straight line that touches the circle at point A and doesn't cross through it, that would be your tangent, and point A is the point of tangency. Any straight line through A that crosses through another point on the circle, say, point B, would be a secant, and the line OAB (if extended through O) would be a diameter. The arc's size determines if it is a minor or major arc, depending on whether it is more or less than half the circle's circumference.
PLEASE HELP ASAP
Find a solution of the linear inequality.
7>(or equal to)4x-5
(3, 4)
(1, 1)
(3, 0)
(2, 1)
Answers
The points at which the quadratic equation intersects the x-axis are referred too
Answers
The x coordinates of the points where the graph intersects the x axis would be the solutions or otherwise called zeros of the quadratic equation
A group consists of five five men and eight eight women. seven seven people are selected to attend a conference.
a. in how many ways can seven seven people be selected from this group of thirteen thirteen?
b. in how many ways can seven seven women be selected from the eight eight women?
c. find the probability that the selected group will consist of all women.
Answers
a) 116 ways to select seven people.
b) ways to select 7 women.
c) The probability is 0.004662
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
a) Number of ways can seven people be selected from this group of thirteen
C( 13, 7)
= 13! /6! 7!
= 1716
b) Number of ways seven women selected from Eight women
C(8 ,7)
= 8!/ 7! 1!
= 8
c) The probability that the selected group will consist of all women
= 8 / 1716
= 0.004662
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??? quadrilateral abcd ??? is inscribed in this circle. what is the measure of angle c? enter your answer in the box. ?? a quadrilateral inscribed in a circle. the vertices of the quadrilateral lie on the edge of the circle and are labeled as a, b, c,
d. the interior angle a is labeled as left parenthesis 2 x plus 3 right parenthesis degrees. the angle b is labeled as left parenthesis 2 x minus 4 right parenthesis degrees. the angle d is labeled as left parenthesis 3 x plus 9 right parenthesis degrees.
Answers
When, you have a quadrilateral inscribed in a circle, measure of the opposites sides are supplementary (they add to 180). Therefore, we can write and solve the following equation with angles D and B to find the value of x in the problem.
3x + 9 + 2x - 4 = 180
5x + 5 = 180
5x = 175
x = 35
Now, input x = 35 into the expression for A to find that the measure of angle A is 73.
Since A and C are supplementary:
A + C = 180
73 + C = 180
C = 107
Answer:
∠C = 107°
Step-by-step explanation:
Quadrilateral ABCD is inscribed in a circle, and a quadrilateral inscribed in a circle is known as cyclic quadrilateral.
So, ABCD is cyclic quadrilateral.
∠A = 2x + 3
∠B = 2x - 4
∠D = 3x + 9
Also. the sum of opposite angles of the cyclic quadrilateral is supplementary.
⇒ ∠B + ∠D = 180
⇒ 2x - 4 + 3x + 9 = 180
⇒ 5x = 175
⇒ x = 35
Now, ∠A = 73
Also, ∠A + ∠C = 180
⇒ ∠C = 180 - 73
⇒ ∠C = 107°
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Answers
X is negative and Y is positive so it is Quadrant 2 (or Quadrant II)
a 12-ft-long ladder is leaning against a wall and makes an 80 degree angle with the ground.how high up the wall does the ladder reach, and how far is the base of the ladder from the base of the wall? round to the nearest inch.,
Answers
Answer:
The ladder reaches 142 inches and the base of ladder is 25 inches far from the base of the wall.
Step-by-step explanation:
Let us draw a diagram for the given situation.
In the attached figure,
AB = the height of wall where the ladder reaches
AC = ladder
BC = distance of base of ladder from the base of the wall
In triangle ABC,
[tex]\sin C=\frac{AB}{AC}\\\\\sin80=\frac{AB}{12}\\\\AB=12\sin80\\\\AB=11.82[/tex]
And
[tex]\cos C=\frac{BC}{AC}\\\\\cos80=\frac{BC}{12}\\\\BC=12\cos80\\\\BC=2.08[/tex]
Now, 1 feet = 12 inches
Hence, 11.82 ft = 141.84 inches
and 2.08 feet = 24.96 inches
Therefore, in the nearest inches, we have
The ladder reaches 142 inches and the base of ladder is 25 inches far from the base of the wall.