In the triangle ABC at the right above, AB=CB, and P and Q are points on the sides CB and AB such that AC=AP=PQ=QB. Find the number of degrees in angle B.
Answers
Since QP and QB are equal the triangle PQB the angles:
[tex]\begin{gathered} \measuredangle QPB=\measuredangle QBP \\ \measuredangle QPB=x \end{gathered}[/tex]The last angle can be found by adding all the internal angles and making it equal to 180 degrees.
[tex]\begin{gathered} \measuredangle QPB+\measuredangle QBP+\measuredangle BQP=180 \\ x+x+\measuredangle BQP=180 \\ \measuredangle BQP=180-2x \end{gathered}[/tex]The angle BQP and the angle AQP are suplementary, this means that their sum is equal to 180 degrees. So we have:
[tex]\begin{gathered} \measuredangle AQP+\measuredangle BQP=180 \\ \measuredangle AQP+180-2x=180 \\ \measuredangle AQP=180-180+2x \\ \measuredangle AQP=2x \end{gathered}[/tex]Since the sides AP and PQ are equal, then the angle PAQ is equal to AQP.
[tex]\begin{gathered} \measuredangle PAQ=\measuredangle AQP \\ \measuredangle PAQ=2x \end{gathered}[/tex]To find the last angle on that triangle we can add all the internal angles and make it to 180 degrees.
[tex]\begin{gathered} \measuredangle PAQ+\measuredangle AQP+\measuredangle APQ=180 \\ 2x+2x+\measuredangle APQ=180 \\ \measuredangle APQ=180-4x \end{gathered}[/tex]The angle APC is suplementary with the sum of the angles APQ and BPQ. So we have:
[tex]\begin{gathered} \measuredangle APC+\measuredangle APQ+\measuredangle BPQ=180 \\ \measuredangle APC+180-4x+x=180 \\ \measuredangle APC=3x \end{gathered}[/tex]The sides AP and AC are equal, therefore the angles APC and ACP are also equal.
[tex]\begin{gathered} \measuredangle ACP=\measuredangle APC \\ \measuredangle ACP=3x \end{gathered}[/tex]Then we can find the last angle on that triangle.
[tex]\begin{gathered} \measuredangle CAP+\measuredangle ACP+\measuredangle APC=180 \\ \measuredangle CAP+3x+3x=180 \\ \measuredangle CAP=180-6x \end{gathered}[/tex]The angle CAB is equal to the sum of CAP and PAQ. So we have:
[tex]\begin{gathered} \measuredangle CAB=\measuredangle CAP+\measuredangle PAQ \\ \measuredangle CAB=180-6x+2x \\ \measuredangle CAB=180-4x \end{gathered}[/tex]Since the sides AB and BC are equal, then the angles ACB and CAB must also be equal. We can find the value of x with this.
[tex]\begin{gathered} \measuredangle BAC=\measuredangle ACB \\ 180-4x=3x \\ 7x=180 \\ x=\frac{180}{7} \end{gathered}[/tex]The value of x is 180/7
Related Questions
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
you have to solve the system:
1)W=L-6
2)W*L=72
so (L-6)*L=72
L^2-6L-72=0
(L-12)*(L+6)=0
so the answers for L are 12 and -6,but we only consider 12 cause there can't be -6miles. so L=12
and W=12-6, so W=6.
Answer:
Width = 6mi
Length = 12mi
Step-by-step explanation:
Let's say our length = x
Since the width is 6 miles less than the length, width = x - 6
The area of rectangle is width x length so just substitute your values
(x - 6)(x) = 72
therefore: x^2 - 6x = 72
*subtract 72 to form a quadratic equation
x^2 - 6x - 72 = 0
*solve by factorising
(x+6)(x-12) = 0
therefore x = -6 or 12
Since you can't have a negative length, x = 12
thus, our length is 12mi
To find the width, just subtract 6 which = 6mi
So: length = 12mi and width = 6mi
Determine the equation of the line that passes through the point (1/−3,−9) and is perpendicular to the line 5y+x=1.
Answers
Given the following equation of a line:
[tex]5y+x=1[/tex]We will write the equation in the slope-intercept form: y = m x + b
[tex]\begin{gathered} 5y+x=1 \\ 5y=-x+1 \\ \\ y=-\frac{1}{5}x+\frac{1}{5} \end{gathered}[/tex]Now, we will find the equation of the line that is perpendicular to the given line.
Note: if the slope of the given line = m
So, the slope of the perpendicular line = -1/m
From the given line: slope = m = -1/5
So, the slope of the perpendicular line = -1/m = 5
The required line passes through the point (-1/3, -9)
We will use the point-slope form to write the equation of the required line:
[tex]\begin{gathered} (y-k)=m*(x-h) \\ \\ y-(-9)=5*(x-(-\frac{1}{3})) \\ \\ y+9=5x+\frac{5}{3} \end{gathered}[/tex]Simplify the equation to be like the standard equation:
[tex]\begin{gathered} y+9=5x+\frac{5}{3}\to\times3 \\ 3y+27=15x+5 \\ \\ 3y-15x=-22 \end{gathered}[/tex]So, the answer will be:
3y - 15x = -22
Michaels is very busy with work and her children so she decides to subscribe to. A monthly meal plan services. The company charges a flat monthly cost of $125 per month for their classic meals. Michelle wants to try a few of the family meals so she can have her babysitter over for dinner a few nights this month . One family meal costs $9.99 if Michelle cooks dinner for her babysitter three times this month using the family package and still purchases her classic meal package how much will Michelle pay for her subscription this month
Answers
Michelle will pay $154.97 if she cooks dinner for her babysitter three times this month using the family package and still purchases her classic meal package.
What is meant by cost?A cost function is a mathematical formula that shows how production costs change at different output levels. In other words, it calculates the total cost of production based on the quantity produced. The cost function can be used to calculate the average cost, which is the amount of money it costs to produce one unit on average.
The average cost function is A(x)=C(x)x A (x) = C (x) x A (x) = C (x) x, where x>0. The average cost per unit is calculated by dividing the total cost by the number of units produced.
Given,
Monthly cost of $125 per month for their classic meals
and one family meal costs $9.99
if Michelle cooks dinner for her babysitter three times this month using the family package, the the cost of 3 family meal cost will be
3 × $9.99 = $29.97 and still purchases her classic meal package
Hence, the total pay will be $125 + $29.97 = $154.97
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The area of a triangle is 15. Two of the side lengths are 5.5 and 7.5 and the includedangle is acute. Find the measure of the included angle, to the nearest tenth of adegree.
Answers
α =46º
1) Let's start by gathering the data:
S = 15 u²
a= 5.5
b= 7.5
Sketcing out:
2) One of the formulas to find out the area of a triangle is:
[tex]S=\frac{ab\cdot\sin (\alpha)}{2}[/tex]Plugging the given data into the formula we have:
[tex]\begin{gathered} 15=\frac{5.5\cdot7.5\sin (\alpha)}{2}\text{ }\times2 \\ 30\text{ =41.25}\cdot\sin (\alpha) \\ \frac{30}{41.25}=\frac{\text{41.25}\cdot\sin (\alpha)}{41.25} \\ 0.72=\sin (\alpha) \end{gathered}[/tex]2.2) Since we want to know the measure of that angle, then let's make use of the arcsine of (0.72)
[tex]\begin{gathered} \alpha=\sin ^{-1}(0.72) \\ \alpha=46.05\approx46 \end{gathered}[/tex]3) Hence, the missing acute angle is α =46º (rounded off to nearest whole number)
6) Endpoint: (5,0), midpoint: (1, -1)
Answers
hello
we're required to find the second end point from the given values
end point = (5, 0)
mid point = (1, -1)
to solve this problem, we'll need to use thw formula for mid-point
[tex]x,y=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}[/tex]now let's identify our variables
[tex]\begin{gathered} x=1,y=-1, \\ x_1=5,y_1=0 \\ x_2=\text{ ?} \\ y_2=\text{ ?} \end{gathered}[/tex]let's substitute in our values and solve respectively
[tex]\begin{gathered} x=\frac{x_2+x_1}{2} \\ 1=\frac{x_2+5}{2} \\ \text{cross multiply both sides} \\ 1\times2=x_2+5 \\ 2=x_2+5 \\ x_2=2-5 \\ x_2=-3 \end{gathered}[/tex]now let's do the same for y
[tex]\begin{gathered} y=\frac{y_2+y_1}{2} \\ -1=\frac{y_2+0}{2} \\ \text{cross multiply both sides} \\ 2\times-1=y_2+0_{} \\ -2=y_2 \\ y_2=-2 \end{gathered}[/tex]the values of the other end point are (-3, -2)
a survey asked a group of people the size of their households. the results are shown in the frequency distribution. what is the mean of the frequency distribution?
Answers
we have the following:
[tex]m=\frac{f_1+f_2+f_3+f_4+f_5}{5}[/tex]replacing:
[tex]\begin{gathered} m=\frac{4+12+6+2+1}{5} \\ m=\frac{25}{5} \\ m=5 \end{gathered}[/tex]therefore, the mean is 5
What is this expression in simplified form?
5√63-6√28
O A. 3√7
OB. 21√7
O C. 27√7
O D. 11√7
Answers
Answer:
23467788
Step-by-step explanation:
666789909 +75445899553235653889
I'm sure the
The equation 2x = 50-3x can be solved by graphing y = 2x and y=50-3x,
Use the drop-down menu to complete the statement to explain why a graph can be
used to solve this equation. Answer
Answers
The solution of the equation is x = 10. The graph is attached below.
We are given an equation. The equation has one variable. The equation is given below.
2x = 50 - 3x
First of all, we will solve the equation directly to find the solution.
2x = 50 - 3x
5x = 50
x = 10
The above equation can be also be solved by graphing y = 2x and y = 50 - 3x. These are two linear equations. These equations represent two straight lines. The solution is found by locating the intersection point of these two straight lines on the graph. The graph of the two straight lines is attached below.
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Answer:
20 is the answer
Step-by-step explanation:
2x+1=2(x-2) solve for x
Answers
Answer:
There is no solution to this equation
Step-by-step explanation:
2x+1=2(x-2)=
2x+1=2x-4
0x = -5
Answer is no solution
this statement is false
2x+1=2(x-2)
2x+1=2x-4
cancel equal terms
1=-4
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Step-by-step explanation:
"how long" is the question.
so, we will need an answer in seconds.
the other options do not define a time duration.
to fall from top to the ground it means the object fell 1503 ft, that means that s(t) = 1503.
16t² = 1503
t² = 1503/16
t = sqrt(1503/16) = sqrt(9×167/16) = 3/4 × sqrt(167) =
= 9.692135987... seconds
it took the object 9.692135987... seconds to fall from the top to the ground.
Find the sum of the interior angles of a 22-sided polygon. 1,980° 2,160° 3,360° 3,600°
Answers
The sum of the interior angles of a 22-sided polygon is (d) 3600 degrees
How to determine the sum of the interior angles?From the question, we have the following parameters that can be used in our computation:
Shape = 22-sided polygon
Parameter to calculate = the sum of the interior angles
The sum of the interior angles is calculated using the following angle formula
The sum of the interior angles = ( n − 2 ) × 180 ∘ where is the number of sides
In this case
n = 22
Substitute the known values in the above equation, so, we have the following representation
The sum of the interior angles = (22 − 2) × 180∘
Evaluate
The sum of the interior angles = 3600∘
Hence, the angle is (d) 3600 degrees
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is two over nine a rational number
Answers
Two over nince is fraction formed by two integers which equal a repeting decimal, which means it's a rational number.
Hence, the answer is yes.Working in the health sciences, you will find that you will have to make different kinds of mathematical conversions. Start this activity by reading through the following story problems to familiarize yourself with the various conversions that you will need to perform. Use the information below to answer the questions.Submit your answer (rounded to 2 decimals) and all work.Conversion Formulas1 oz = 29.57mL1 ml = 0.20 teaspoonsQuestion 7: Dymelor 0.75 g is ordered. Scored tablets are labeled 500 mg. each. How many tablets will you give?
Answers
Since 1 g is equal to 1000 mg, multiply 0.75 g by 1000 mg / 1 g to convert the given value to mg.
[tex]0.75g\cdot\frac{1000mg}{1g}=750mg[/tex]Since one tablet is 500 mg, multiply the obtained product by 1 tablet / 500 mg.
[tex]750mg\cdot\frac{1\text{ tablet}}{500\text{ mg}}=1.5\text{ tablet}[/tex]Thus, there must be 1.5 or 1 1/2 tablet.
A book was bought for $40 and later sold at profit of 25%. What was the selling price of the book?
Answers
Answer:
The book was 50 dollars
Step-by-step explanation:
0.25% x 40 dollars = $10
10 + 40 (the original amount) = $50
Answer:
$50
Step-by-step explanation:
25% of $40 is $10 dollars. so a book sold with 25% profit is $50
if the perimeter is 28 and part of it is 5 what is the cm
Answers
The other side of the rectangle is 9 cm.
Given that:-
Perimeter of the rectangle = 28 cm
One side of the rectangle = 5 cm
We have to find the other side of the rectangle.
Let the length of the rectangle be 5 cm and,
The breadth of the rectangle be b cm.
We know that,
Perimeter of the rectangle = 2(l + b)
Hence, we can write,
2(5 + b) = 28
5 + b = 28/2
5 + b = 14
b = 14 - 5
b = 9 cm
Hence, the other side of the rectangle is 9 cm.
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Pierre's unicycle wheel has a diameter of 80 cm.
O
80 cm
a)
1
Tarks
b)
a) How far does the unicycle move if the
wheel turns once?
Give your answer in metres, correct
to 2 decimal places.
b) Pierre enters a 100 m unicycle race.
How many times must the wheel rotate
completely in order for Pierre to
travel 100 m?
Give your answer to the nearest
whole number.
+
m
1+ times
Answers
Answer:
80 cm ×2 = 160 but it is not there in the option
An inlet pipe on a swimming pool can be used to fill the pool in 34 hours. the drain pipe can be used to empty the pool in 35 hours. if the pool is 1/2 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
Answers
595 hours is time it will take to fill the swimming pool .
What are fraction ?A fraction is a mathematical symbol representing any quantity of equal parts, and it also represents a portion of a whole. When employed in conversational English, a fraction—such as one-half, eight-fifths, and three-quarters—indicates the number of components of a particular size.
Calculationinlet pipe will fill the pool in 34 hours. Every hour, it fills 1/34 of the pool
Outlet pipe will empty the pool in 35 hours. Every hour, it empties 1/35 of the pool.
In x hours we want 1/2 the pool to fill, since half is already filled.
We want (x/34) - (x/35) = 1/2
multiply by 1190 both sides, the LCD.
35x-34x=595 (1190/2)
x=595 hours
in that time 595/34-595/35=0.5
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Problem iD: PRABERUZ On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled 1 in miles, d, to the number of hours flying, t, is t=d. How long will it take the airplane to travel 800 miles? 500 Do not include units (hours) in your answer. copted for free from openupresources.org
Answers
We have a relation between the distance traveled in miles (d) and the number of hours flying (t) that is t=(1/500)*d.
Then, when d=800, we have:
[tex]\begin{gathered} t=\frac{1}{500}\cdot d \\ t=\frac{1}{500}\cdot800=\frac{800}{500}=1.6 \end{gathered}[/tex]The time is 1.6 hours.
Answer: 1.6
*Awnser this* Nikki should invest____ in the account paying 5% interest and ____ in the account paying 6.5% interest
Answers
Simple interest can be defined as the interest charged on the total amount of principal taken for a particular period of time.
Interest is only charged based on the use of funds. Calculating simple interest is fairly straightforward and is the fastest way to calculate interest.
[tex]\begin{gathered} I=P\cdot r\cdot t \\ A\to\text{Total amount} \\ P\to\text{Principal amount} \\ I\to\text{interest amount} \\ r\to\text{rate of the intererst per year in decimal} \\ t\to\text{time in years} \end{gathered}[/tex]Total amount of money inverted:
[tex]\begin{gathered} A+B_{}=250.000 \\ \\ \end{gathered}[/tex]Total interset earne
I need help with my geometry homework thank you.
Answers
Answer:
2.5
Step-by-step explanation:
point B
4K = 10
4/4 K = 10/4 K
K = 5/2 = 2.5
Raj completed his homework in 5/6 hour. His older brother took 1½ times as long as Raj did to
complete his homework.
How long did it take Raj's older brother to complete his homework?
Answers
Answer:
B
Step-by-step explanation:
Justin is taking an anti-flammatory drug and he must receive 6 milligrams for each 17 kg of weight. Justin weighs 244 pounds
Answers
Justin is taking an anti-flammatory drug and he must receive 6 milligrams for each 17 kg of weight.
Justin's weight is 244 pounds i.e., 110.677 Kg.
Theerfore, the amount of anti flammatory drug he needs is
[tex]\frac{6}{17}\times110.677\approx39.063[/tex]Therefore, Justing needs 39.063 miiligrams of anti flammatory drug.
How many different values can a 16-bit binary number store? How many digits are needed fora hexadecimal number to do the same? How about a base-5 number? Show your work.
Answers
A very simple way to know the number of possible combinations in a binary number is given by the next formula:
[tex]2^n=2^{16}=65536^{}[/tex]Now, we should remember that an hexadecimal number contain 16 different digits, from 0 to F. Therefore
[tex]\begin{gathered} 16^n=65536 \\ n\ln 16=\ln 65536 \\ n=\frac{\ln 65536}{\ln 16} \\ n=4 \\ 16^4=65536 \end{gathered}[/tex]Thus, we will need 4 hexadecimal numbers to achieve the same values as a 16-bit number.
For the base-5 number we can do a similar procedure:
[tex]\begin{gathered} 5^m=65536 \\ m\ln 5=\ln 65536 \\ m=\frac{\ln 65536}{\ln 5} \\ m=6.89\approx7 \\ 5^7^{}=78125 \end{gathered}[/tex]Therefore, we would need at least 7 numbers base-5 to achieve something similar to 16-Bit number
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Omar and Devin both leave the bookstore at the same time, but in opposite directions. If Devin travels 7 mph faster than Omar and after 3 hours they are 93 miles apart, how fast is each traveling?
Answers
Omar and Devin both leave the bookstore at the same time, but in opposite directions.
Let the speed of Omar = x
Speed of Devin = x + 7
They travel for 3 hours
Speed = Distance/Time
Distance = Speed x Time
Since, they are 93 miles apart
93 = (speed pf Omar + Speed of Devin) Time
93 = (x + x + 7)3
93 = (2x + 7)3
93 = 6x + 21
93 - 21 = 6x
6x = 72
x = 72/6
x = 12
Thus, Speed of Omar is 12 mph
Speed of Devin : x + 7
x + 7 = 12 + 7
= 19
Thus, speed of Devin is 19mph
Whats the anwser? need it asap
Answers
Answer:
B, yes because if you fold it in half then you have symmetry
Step-by-step explanation:
The quality of being made up of exactly similar parts facing each other or around an axis.
Given the function f(x)= 7lx-4l, calculate the following values:F(0)=F(2)=F(-2)=F(x+1)=F(x^2+2)=
Answers
As given by the question
There is given that the function
[tex]f(x)=7\lvert x-4\rvert[/tex]Now,
First find the value of f(0):
Then, put the value of 0 for x into the given function.
Now,
[tex]\begin{gathered} f(x)=7\lvert x-4\rvert \\ f(0)=7\lvert0-4\rvert \\ f(0)=7\lvert-4\rvert \\ f(0)=7\cdot4 \\ f(0)=28 \end{gathered}[/tex]Then,
[tex]\begin{gathered} f(x)=7\lvert x-4\rvert \\ f(2)=7\lvert2-4\rvert \\ f(2)=7\lvert-2\rvert \\ f(2)=7\cdot2 \\ f(2)=14 \end{gathered}[/tex]Then,
[tex]\begin{gathered} f(x)=7\lvert x-4\rvert \\ f(-2)=7\lvert-2-4\rvert \\ f(-2)=7\lvert-6\rvert \\ f(-2)=7\cdot6 \\ f(-2)=42 \end{gathered}[/tex]Then,
[tex]\begin{gathered} f(x)=7\lvert x-4\rvert \\ f(x)=7\lvert x+1-4\rvert \\ f(x)=7\lvert x+1-4\rvert \\ f(x)=7\lvert x-3\rvert \end{gathered}[/tex]And,
[tex]\begin{gathered} f(x)=7\lvert x-4\rvert \\ f(x^2+2)=7\lvert x^2+2-4\rvert \\ f(x^2+2)=7\lvert x^2-2\rvert \end{gathered}[/tex]how would I graph the line, 3x+4y= -4
Answers
Given the equation:
3x + 4y = -4
Let's graph the line that represents the equation above.
To grah the line, rewrite the equation in slope-intercet form:
y = mx + b
Where m is the slope and b is the y-intercept.
Rerite the equation for y:
3x + 4y = -4
Subtract 3x from both sides:
3x - 3x + 4y = -3x - 4
4y = -3x - 4
Divide all terms by 4:
[tex]\begin{gathered} \frac{4y}{4}=-\frac{3x}{4}-\frac{4}{4} \\ \\ y=-\frac{3}{4}x-1 \end{gathered}[/tex]The slope of the line is -3/4, while the y-intercept is at (0, -1).
Now, let's graph the line using 3 points.
• When x = -4:
Substitute -4 for x and solve for y
[tex]\begin{gathered} y=-\frac{3}{4}\ast(-4)-1 \\ \\ y=3-1 \\ \\ y=2 \end{gathered}[/tex]• When x = 0:
Substitute 0 for x and solve for y
[tex]\begin{gathered} y=-\frac{3}{4}\ast(0)-1 \\ \\ y=-1 \end{gathered}[/tex]• When x = 4:
Substitute 4 for x and solve for y
[tex]\begin{gathered} y=-\frac{3}{4}\ast4-1 \\ \\ y=-3-1 \\ \\ y=-4 \end{gathered}[/tex]Therefore, we have the following points:
(-4, 2), (0, -1) and (4, -4)
Plot the three points on the graph, then connect all 3 points using a straight edge.
We have the graph attached below:
7. A box contains bags of nails. Each
bag has 24 nails. There are 960 nails
in the box. How many bags are in
the box?
Answers
40 bags of 24 nails in the box
Answer:
Step-by-step explanation:
you divide 960 by 24 and you will have 40 so you will have 40 nails. :0
8) Use the graph below to answer the question. If there are 180 students 10 pointsin the girls athletics program, then how many students participated insoccer?SPORTSSOCCER15% VOLLEYBALL20%TRACK35%BASKETBALL30%O 15O 202734
Answers
Soccer = 15%
Track = 35%
Vellyball = 20%
Basketball = 30%
Total = 100%
Number of students = 180
[tex]\begin{gathered} \text{Student that participated in soccer = }\frac{15}{100}\text{ x 180} \\ =\text{ }\frac{15\text{ x 180}}{100} \\ =\text{ }\frac{2700}{100} \\ =\text{ 27} \end{gathered}[/tex]