For the construction of an inscribed circle the required construction that must be known is the angle bisector. The correct option is (A).
What is an angle bisector?The angle bisector is a line that divides an angle into two equal parts. For a circle inscribed in a triangle the line joining the center to the vertex is the angular bisector of the interior angle.
The diagram for the given case can be drawn as follows,
For the circle inscribed in the circle, all the sides are tangents.
By the property of tangents to a circle ∠ODB and ∠OFB are right angles.
Now, in ΔODB and ΔOFB the relation is obtained as,
∠ODB = ∠OFB (right angles)
OB = OB (Common sides)
And, OD = OF (radius of the circle)
⇒ ΔODB ≅ ΔOFB (by RHS criteria)
This implies that ∠ODB ≅ ∠OFB.
Thus, the line joining the centre and the vertex of triangle bisects its angles.
Hence, for the given case the required construction to be known is the angle bisector of triangle.
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Rewrite 15x^4y^3 − 45x^3y^4 using a common factor
15x^4y^3 − 45x^3y^4 Can be rewritten using a common factor as 15x^3y^3(x - 3y)
What is a common factor?common factors are defined as factors that are common to two or more numbers. In other words, a common factor is a number with which a set of two or more numbers will be divided exactly.
In the algebraic expression 15x^4y^3 − 45x^3y^4,
15x^4y^3 is a term and 45x^3y^4, is another term.
if we take each variable and constant and compare
15 is common factor between 15 and 45
x^3 is a common factor between x^4 and x^3
y^3 is a common factor between y^3 and y^4
so multiplying the common factors together we have 15x^3y^3
what is left in the first term is x and second term is 3y
so that the rewritten form becomes 15x^3y^3(x - 3y)
In conclusion the other form of 15x^4y^3 − 45x^3y^4 is 15x^3y^3(x - 3y)
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Daryl walks 10.5 miles in 3.5 hours. How many miles does he walk per hour?
Answer: 3
Step-by-step explanation: Daryl is walking 3 miles in 1 hour. When you divide 10.5 by 3.5 you get. So 3 miles in one hour. For example if you walk 12 miles in 4 hours, you divide and get 3. That three becomes the miles in one hour.
How many liters of a 10% salt solution must be mixed with 5 liters of a 40% salt solution
to give a 15% solution?
please help on all PLEASE IM BEGGING YOU I CANT FAIL PLEASE
61=7-6x
3/2a -26=-5
4=n-10/-3
system of equations: n=2/3 ,a=14,x=−9
for each thing: x= −9 | a= 14 | n= 2/3
1. x = -9
2. a = 14
3. n = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:Here are the steps to the first question:1. Rearrange Terms
61 = 7 - 6x
61 = -6x + 7
2. Subtract 7 from both sides
61 = -6x + 7
61 - 7 = -6x + 7 - 7
3. Simplify
Subtract the numbers:
61 - 7 = -6x + 7 - 7
54 = -6x + 7 - 7
Subtract the numbers:
54 = -6x + 7 - 7
54 = -6x
4. Divide both sides by the same factor
54 = -6x
[tex]\frac{54}{6}[/tex] = [tex]\frac{-6x}{-6}[/tex]
5. Simplify
Divide the numbers:
[tex]\frac{54}{6}[/tex] = [tex]\frac{-6x}{-6}[/tex]
-9 = [tex]\frac{-6x}{-6}[/tex]
Cancel terms that are in both the numerator and denominator:
-9 = [tex]\frac{-6x}{-6}[/tex]
-9 = x
Move the variable to the left:
-9 = x
x = -9
Solution to Question 1:x = -9
Here are the steps to the second question:
1. Combine multiplied terms into a single fraction
[tex]\frac{3}{2}[/tex]a - 26 = -5
[tex]\frac{3a}{2}[/tex] - 26 = -5
2. Find common denominator
[tex]\frac{3a}{2}[/tex] - 26 = -5
[tex]\frac{3a}{2}[/tex] + [tex]\frac{2(-26)}{2}[/tex] = -5
3. Combine fractions with common denominator
[tex]\frac{3a}{2}[/tex] + [tex]\frac{2(-26)}{2}[/tex] = -5
[tex]\frac{3a+2(-26)}{2}[/tex] = -5
4. Multiply the numbers
[tex]\frac{3a+2(-26)}{2}[/tex] = -5
[tex]\frac{3a - 52}{2}[/tex] = -5
5. Multiply all terms by the same value to eliminate fraction denominators
[tex]\frac{3a - 52}{2}[/tex] = -5
2 · [tex]\frac{3a - 52}{2}[/tex] = 2(-5)
6. Cancel multiplied terms that are in the denominator
2 · [tex]\frac{3a - 52}{2}[/tex] = 2(-5)
3a - 52 = 2(-5)
7. Multiply the numbers
3a - 52 = 2(-5)
3a - 52 = -10
8. Add 52 to both sides
3a - 52 = -10
3a - 52 + 52 = -10 + 52
9. Simplify
Add the numbers:
3a - 52 + 52 = -10 + 52
3a = -10 + 52
Add the numbers:
3a = -10 + 52
3a = 42
10. Divide both sides by the same factor
3a = 42
[tex]\frac{3a}{3}[/tex] = [tex]\frac{42}{3}[/tex]
11. Simplify
Cancel terms that are in both the numerator and denominator:
[tex]\frac{3a}{3}[/tex] = [tex]\frac{42}{3}[/tex]
a = [tex]\frac{42}{3}[/tex]
Divide the numbers:
a = [tex]\frac{42}{3}[/tex]
a = 14
Solution to Question 2:
a = 14
Here are the steps to the third question:
1. Divide the numbers
4 = n + [tex]\frac{-10}{-3}[/tex]
4 = n + [tex]\frac{10}{3}[/tex]
2. Subtract [tex]\frac{10}{3}[/tex] from both sides
4 = n + [tex]\frac{10}{3}[/tex]
4 - [tex]\frac{10}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]
3. Simplify
Subtract the numbers:
4 - [tex]\frac{10}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]
[tex]\frac{2}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]
Subtract the numbers:
[tex]\frac{2}{3}[/tex] = n
Move the variable to the left:
[tex]\frac{2}{3}[/tex] = n
n = [tex]\frac{2}{3}[/tex]
Solution to Question 3:n = [tex]\frac{2}{3}[/tex]
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
If i clap my hands 20 times in 12 seconds. How many times will i do it in 2minutes. Then 3 minutes.
If i clap my hands 20 times in 12 seconds. 200 times will i do it in 2 minutes.
The friend can clap his hands 28 times in 12 seconds, according to our knowledge. The first thing we need to know is how many times he can clap in a second:
What is clap ?
Gonorrhea is known by the slang term "the clap." Gonorrhea is also referred to as "the drip." Someone who has an may feel stigmatized and shamed by these words.
To do it, we must divide the number of seconds by the number of times he can clap his hands:
20/12 =1.6667
He can clap his hands 1.6667 times in 1 second:
Now we want to know how many times will he clap his hands in 2 minutes
We have to change 2 minutes into seconds:
1 (minute) = 60 (seconds in 1 minute)
2 (minutes) * 60 (seconds in 1 minute) = 120seconds
After we get the seconds he is going to clap his hands, we have to multiply the times he claps times the seconds:
1.6667 times * 120 seconds = 200
200 times in 2.25 minutes
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How much compound interest will $50,000 have earned in 10 years at
6.4% annual interest compounded quarterly?
The compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly would be $28,167.50.
What is Compound interest?Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
Compound Interest =P(1+r/n)^rt
We are given that
Principal amount = $50,000
Time = 10 year
Rate = 6.4%
Determine the compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly, we can use the formula:
Plugging in the given values, we get:
compound interest = $50,000 (1 + 0.064/4)^(4 x 10) - $50,000
= $50,000 (1.016)^40 - $50,000
= $50,000 x 2.6335 - $50,000
= $78,167.50 - $50,000
= $28,167.50
Therefore, the compound interest is $28,167.50.
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Write an equation of the line that passes through $\left(7,10\right)$ and is perpendicular to the line $y=\frac{1}{2}x-9$.
The equation of the line that passes through (7, 10) and its perpendicular to the line y = (1/2)x - 9 is y = -2x + 24
The coordinates of the line passing through the point = (7, 10)
The equation of the perpendicular line
y = (1/2)x - 9
The slope of the line = 1/2
The slope of the original line = - 1 / (1/2)
= -1 × 2
= -2
The slope intercept form is
y = mx + b
Substitute the values in the equation and find the value of b
10 = -2(7) + b
10 = -14 + b
b = 10 + 14
b = 24
Substitute the value of b and m is the equation
y = -2x + 24
Therefore, the slope of the line is y = -2x + 24
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Perpendicular lines form angles that are how many degrees at their intersection?
O a. 45 dregrees
O b. 90 degrees
O c. 135 degrees
O d. 225 degrees
Answer:
Step-by-step explanation:135 degrees
Please help me thank you
The slope of NO is 2/3 and the slope of LO is -3/2 after using the slope formula.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The parallel lines have same slope
The slope of LM = the slope of NO
The slope of LM = (-1-(-5))/(4-(-2))
The slope of LM = 4/6 = 2/3
Slope of NO = 2/3
If LMNO is rectangle:
The slope of LO = -1/(slope of LM)
The slope of LO = -1(2/3)
The slope of LO = -3/2
Thus, the slope of NO is 2/3 and the slope of LO is -3/2 after using the slope formula.
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Given vector u = ⟨−3,−2⟩ and v = ⟨1,−5⟩,determine the value of u - 2v in component form.
The component form of the linear combination of the two vectors is u - 2v = < -5, 20>
How to find the vector u - 2v?Here we have the two vectors: u = <-3, -2> and v = <1, -5> We want to determine the value of the linear combination:
u - 2v
To do that we just add the correspondent components, then we get:
u - 2v = <-3, -2> - 2*<1, -5>
= <-3, -2> - <2*1, 2*-5>
= <-3, -2> - <2, -10>
= < -3 - 2, -2 -(-10)>
= < -5, 20>
That is the component form of the linear combination.
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Evaluate f(x)=2x+5 when x=0, x=1, x=5
Answer:
f(0)=5
f(1)=7
f(5)=15
Step-by-step explanation:
f(0)=2x+5
=2(0)+5
=5
f(1)=2x+5
=2(1)+5
=2+5
=7
f(5)=2x+5
=2(5)+5
=10+5
=15
PLEASE HELP ME ASAP!!!
Answer:
$54,742.76
Step-by-step explanation:
The equation for an exponential function is [tex]f(x)=ab^x\\[/tex], where [tex]a[/tex] is the starting value, which is 40,000. This value increases by 4%, so [tex]b[/tex] is 1.04. Finally, [tex]x[/tex] is the term that the value is increasing for, which in this case is 8.
So, the equation is [tex]f(x)=40000*1.04^8[/tex]
** [tex]f(x)[/tex] can be replaced with [tex]y[/tex]
An airline finds that about 888 percent of the time, a person who makes an advance reservation does not keep the reservation. Therefore, for each of their 105105105-passenger planes, the company schedules 113113113 people with advance reservations. Based on this information, about how many of the scheduled people will not keep their reservation?.
Persons cannot be in decimals we can expect about 9 passengers will not keep their reservation.
Given,
In the question:
An airline finds that about 8 percent of the time, a person who makes an advance reservation does not keep the reservation.
Therefore, for each of their 105105105-passenger planes, the company schedules 113113113 people with advance reservations.
Now, According to the question:
Capacity of the airline per trip = 105 only
But company schedules = 113 people with advance reservations
Since 8% do not turn up
Out of 113 passengers who reserved in advance we can say
that 8% of 113 passengers will not keep their reservation
Based on this information, number of the scheduled people will not keep their reservation
= 8% x 113
= 0.08*113
=9.04
Hence, Persons cannot be in decimals we can expect about 9 passengers will not keep their reservation.
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let lines x and y be parallel, and let lines z and w be parallel. if angle a is the angle formed by lines y and z, and angle b is the angle formed by lines w and x, if the measure of angle a is 25 degrees, what is the measure of angle b?
155° is the measure of angle b .
What is an example of parallel lines?
Two lines that are equally spaced apart from one another and never cross each other are said to be parallel lines.
Both horizontal and vertical shapes are possible. In our daily lives, parallel lines can be seen in the form of zebra crossings, rows of notebooks, and the nearby railroad tracks.
from the figure , we understand that ∠1 and ∠3 together from a straight line.
thus, ∠1 + ∠3 = 180°
25° + ∠3 = 180°
∠3 = 155°
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1. A painting crew bought 55 gallons of paint for a job, The crew members used 5 gallons of paint per hour until
they used all the paint. Sketch a graph to represent the start to the end of the job, assuming all paint was
used Be sure to title your graph, label your axes, and label your intercepts. This must be graphed by hand
or by using the tools in Word. a You may not use a web-based graphing program.
The equation is 55 = 5t and the graph is attached with the answer.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a painting crew bought 55 gallons of paint for a job, The crew members used 5 gallons of paint per hour until they used all the paint.
The equation can be written as,
55 = 5t
Here, t is the number of hours.
The graph is attached with the answer below.
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There are 4 chocolate chip cookies and 3 oatmeal cookies in a cookie jar. If a child randomly takes 2 cookies, what is the probability that both are chocolate chip?
Construct a quadrilateral PQRS with PQ= 5cm, QR = 5.5cm, RS = 5.5cm, SP= 6.5cm & angle PQR = 75°.Also construct a Triangle QRM whose area is equal to quadrilateral PQRS.
The image for quadrilateral PQRS is attached below
The image for Triangle QRM is attached below
What is the construction of a quadrilateral PQRS?Generally, To construct a quadrilateral PQRS with the given dimensions, you can use a straightedge and a compass. Here is a step-by-step guide:
Start by drawing a straight line segment PQ of length 5 cm.Place the compass on point P and draw an arc with a radius of 5.5 cm.Place the compass on point Q and draw an arc with a radius of 5.5 cm. The two arcs should intersect at a point R.Place the compass on point R and draw an arc with a radius of 6.5 cm.Place the compass on point P and draw an arc with a radius of 6.5 cm. The two arcs should intersect at a point S.Connect points S and R to complete the quadrilateral PQRS.To construct a triangle QRM with an area equal to quadrilateral PQRS, you can use the same method as above. Here is a step-by-step guide:
Start by drawing a straight line segment QM of length 5 cm.Place the compass on point Q and draw an arc with a radius of 5.5 cm.Place the compass on point M and draw an arc with a radius of 5.5 cm. The two arcs should intersect at a point R.Connect points Q and R to complete the triangle QRM.To verify that the area of triangle QRM is equal to the area of quadrilateral PQRS, you can use the formula for the area of a triangle:
Area of triangle QRM = (1/2) * QM * QR * sin(angle QRM)
And the formula for the area of a quadrilateral:
Area of quadrilateral PQRS = (PQ * QR * sin(angle PQR))/2
Substituting the given values and solving for sin(angle QRM), we find that:
sin(angle QRM) = (2 * area of quadrilateral PQRS)/(QM * QR)
= (2 * (5 * 5.5 * sin(75)))/(5 * 5.5)
= sin(75)
Thus, the area of triangle QRM is equal to the area of quadrilateral PQRS, as desired.
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What is the distance from the origin to pint A graphed on the complex plane below
Answer: it's [tex]\sqrt{5}[/tex]
Step-by-step explanation:
In the diagram below, OQ = 25, PM = 9, and QN = 15. Find the length of OP.
Round your answer to the nearest tenth if necessary.
0
Answer: OP |
P
M
Q
N
Submit Answer how do I come up with the number
In the diagram, the length of OP to the nearest tenth is 5.4
How to determine the length?We are to determine the ratio of the sides of the diagram.
The ratio of the sides using the given sides is
Let the unknown side be x
The ratio of the sides is given as follows
25:34 = 15:x+15
Put into fraction we have
25/(25+9)= 15/(x+15)
Cross multiplying we have
25x+375 = 375+135
Collecting like terms
25x=510-375
Simplify further to have
25x=135
Making x the subject
x=5.4
Therefore the length OP is 5.4 units
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Emma had to finish her 366-page novel by Friday. She had already read 244 pages. Write and solve an equation to show how many pages Emma had left to read by Friday.
p − 244 = 366; p = 610 pages
p + 244 = 366; p = 122 pages
122p = 244; p = 2 pages
p over 244 equals 2; p = 488 pages
Answer: Its b my guy :)
Step-by-step explanation: 244 + 122 = 366
and the only answer with 366 is b! hope this helps!
Your grocery bill before taxe wa $265. 24. You have to pay 7. 3 ale tax. How much i your grocery bill?
If the grocery bill before tax is $265.24 and you have to pay 7.3% tax, then he has to pay $284.6 for the grocery bill
The amount of the grocery bill before tax = $265.24
The percentage of tax = 7.3%
The amount of tax = The price of the grocery bill before tax × (7.3/100)
Substitute the values in the equation
= 265.24 × (7.3/100)
= 265.24 × 0.073
= $19.36
The final bill including tax = The price of the grocery bill before tax + The amount of tax
Substitute the values in the equation
= 265.24 + 19.36
= $284.6
Therefore, the grocery bill including tax = $284.6
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A pet store sells a large dog kennel 98.50 the wholesale cost o the kennel is 63.55 what is the percent of markup round to the nearest percent.
Rounded to the nearest percent, the markup is approximately 55%.
What is the percent markup?
Markup percentage is calculated by dividing the gross profit of a unit (its sales price minus its cost to make or purchase for resale) by the cost of that unit.
To find the percent markup, you can use the following formula:
percent markup = (retail price - wholesale price) / wholesale price * 100
Plugging in the values given, we have:
percent markup = (98.50 - 63.55) / 63.55 * 100 = 34.95 / 63.55 * 100 = approximately 55%
Hence, rounded to the nearest percent, the markup is approximately 55%.
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50 POINTS IF ANSWERED PLS!!!!
Which angle is the biggest based on the sides of the triangles below? Explain your reasoning.
Answer:
angle c
Step-by-step explanation:
since the largest angle will be across from the longest side, angle c is the right answer because it is across from the longest side which measures 35 cm.
hope this helps
The ratio of two numbers is 5:6. The product of these numbers is 120. What is the smaller of these two numbers?
The smaller of the two number is 10.
What are Ratios?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
In simple words, the ratio is the number that can be used to express one quantity as a fraction of the other ones. The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things.
Given:
Ratio of two Positive number = 5:6
Let , the smaller number be 5x
then , the bigger number = 6x
According to the question,
product of these numbers = 120
Therefore,
[tex]5x * 6x = 120\\30x^{2} = 120\\x^{2} =4\\x = 2[/tex]
Smaller number = 5x = 5*2 = 10.
Hence, the smaller of the two number is 10.
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Which expression is equivalent to this polynomial?
15x - 24
A.3(5x-8)
B. 5(3x-8)
C. 3(5x-24)
D.3(5x - 5)
Answer: A 3(5x-8)
Step-by-step explanation: 3 times 5x is 15x and 3 times -8 is -24
a computer costs £2500 when new. Its value depreciates 12% compounded each year. How much does it cost after 3 years?
The computer will cost £ 33512.32
Given,
the cost of the computer = 2500
Depreciation = 12%
Cost after 3 years =?
compound interest is calculated as,
A = P(1 + r/n)nt
r = 12/100 = 0.12
So, A= P(1 + r/n)nt
A = 2500 (1+.12/1)1*3
A= 2500 (1.12)³
A= 2500 * 1.404928
A = 3512.32
So, The computer will cost £ 33512.32
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Find the measure of angle f given the information below. please help !!
The measure of Angle f from the the figure is [tex]53^{o}[/tex].
What is the relation between Angles and Parallel lines ?On a shared plane, parallel lines do not cross one another. Now, if a transversal crosses two parallel lines at two separate sites, four angles are created at each location. The characteristics of parallel lines with respect to transversals are therefore listed below.
Angles that coincide are equal.Angles that are vertically opposite or vertically angled are equal.Interior angles that alternate are equal.Exterior angles that alternate are equal.On the same side of the transversal, a pair of internal angles are additional.The pair of alternative internal angles are equal when two parallel lines are crossed by a transversal.
When a transversal cuts between two parallel lines, the interior angles on the same side of the transversal are additional.
In the problem angle
a = [tex]119^{o}[/tex]
e = [tex]66^{o}[/tex]
Now , c = e ( alternate angles, interior)
⇒ c = [tex]66^{o}[/tex]
a + b = [tex]180^{o}[/tex] ( as sum of angles on a straight line is [tex]180^{o}[/tex] )
b = [tex]180^{o}[/tex] - [tex]119^{o}[/tex] = [tex]61^{o}[/tex]
f + b+ c = [tex]180^{o}[/tex] [sum of angles of a Triangle is [tex]180^{o}[/tex] ]
f = [tex]180^{o}[/tex] - [tex]61^{o}[/tex] - [tex]66^{o}[/tex] = [tex]53^{o}[/tex].
The measure of Angle f from the the figure is [tex]53^{o}[/tex].
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help pls
P = mgh for m
Answer:
p/gh=m
Step-by-step explanation:
divide both sides by gh to isolate m
Simplify the expression:
5t+
–
9+
–
8t+
–
5
The expression 5t + (-9) + (-8t) + (-5) in the simplified form will be negative (3t + 14).
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ 5t + (-9) + (-8t) + (-5)
Simplify the expression, then the value of the expression is given as,
⇒ 5t + (-9) + (-8t) + (-5)
⇒ 5t - 9 - 8t - 5
⇒ – 3t – 14
⇒ – (3t + 14)
The expression 5t + (-9) + (-8t) + (-5) in the simplified form will be negative (3t + 14).
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Ru buy three cake for £1. 60 each. He pay with a £20 note. How much change doe he get
We know that Ru will get back £15.2 when she buys 3 cakes for £1.60 each using simple mathematical operations.
What are mathematical operations?The process of calculating a value using operands and a math operator is known as a mathematical "operation."
The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.
The rules that determine how to solve an expression with several operations are referred to as the order of operations.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).
So, we know that:
Ru buys 3 cakes for £1.60 each.
She was given £20 not.
The money she will get back is:
20 - (1.60*3)
20 - 4.8
£15.2
Therefore, we know that Ru will get back £15.2 when she buys 3 cakes for £1.60 each using simple mathematical operations.
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