In △ABC, CM is the median to AB and side BC is 12 cm long. There is a point P∈ CM and a line AP intersecting BC at point Q. Find the lengths of segments CQ and BQ , if P is the midpoint of CM
Answers
Answer:
CQ=4 cm, BQ=8 cm
Step-by-step explanation:
In given triangle ABC draw the line MD parallel to the AQ.
1. Consider triangle AMD. In this triangle PQ║MD (build) and CP=PM (P is midpoint of CM). Then by the triangle midline theorem, line PQ is midline of triangle AMD and CQ=QD.
2. Consider triangle BAQ. In this triangle AQ║MD and AM=MB. Then by the triangle midline theorem, line MD is midline of triangle BAQ and BD=QD.
Hence, CQ=QD=BD. Since BC=12 cm and
BC=BQ+QD+BD,
then
[tex]CQ=QD=BD=\dfrac{12}{3}=4\ cm.[/tex]
Note that
BQ=BD+QD=4+4=8 cm.
Final answer:
By examining the properties of median CM and midpoint P, we conclude that segment CQ is equal to QB, and both are 6 cm long in △ABC since CM bisects AB and BC is given as 12 cm.
Explanation:
The problem involves a triangle △ABC with CM being a median to side AB, and a line segment AP that intersects BC at point Q. According to the given information, P is the midpoint of CM, which implies that CP is equal to PM. Because BC is 12 cm in length, and CM is a median, we deduce that M is the midpoint of AB. This fact leads us to conclude that the triangles △CMB and △CMA are congruent by the Side-Side-Side (SSS) postulate, which means that CQ is equal to QB, and both are 6 cm long since Q lies on BC.
Related Questions
What is the solution set of the compound inequality 8< 4 - x <10
Answers
so you do
8<4-x. subtract
-4 -4
4<-x divide
-1. -1
4>x
-4>x since you divide by negative the sign flips.
4-x<10
-4. -4
-x<6
-1 -1
x>-6
8<4-x<10
-4 -4. -4 subtract 4 on all 3
4<-x<6 divide -1 to all 3
-4>x>-6 you flip sign since you divide by negative.
-
Answer:
-6 < x < -4
Step-by-step explanation:
8 < 4 - x < 10
Split this up into 2 inequalities:
4 - x > 8
-x > 8 - 4
-x > 4 Divide both sides by -1
x < -4 (Note that sign flips when dividing by a negative).
Also 4 - x < 10
-x < 6
x > -6
So the solution is -6 < x < -4
Write an equation represents the number of bracelets b Carly will have if she works t hours making bracelets in the next 2 weeks and averages one bracelet every 2 hours
Answers
or
2b × 2t ÷2 = b
PLEASE GIVE BRAINLIEST
An image point has coordinates B'(7, -4). Find the coordinates of its pre-image if the translation used was (x + 4, y + 5).
Answers
Answer:
The coordinate of pre-image is, B(3 , -9).
Step-by-step explanation:
Given an image point has coordinate B'(7, -4).
We have to find the coordinates of its pre-image:
The rule of translation on pre-image (x, y) is given by;
[tex]B(x, y) \rightarrow B'(x + 4, y + 5)[/tex]
then;
(7, -4) = (x+4, y+5)
on comparison we have;
x+4 = 7 and y + 5 = -4
First solve for x;
[tex]x + 4 = 7[/tex]
Subtract 4 from both sides we have;
x + 4 -4 =7-4
Simplify:
x = 3
To solve for y;
y+5 = -4
Subtract 5 from both sides we get;
y = -9
Therefore, the coordinate of pre-image is, B(3, -9)
Answer:
The coordinate of pre-image is, B(3 , -9).
Step-by-step explanation:
Given an image point has coordinate B'(7, -4).
We have to find the coordinates of its pre-image:
The rule of translation on pre-image (x, y) is given by;
then;
(7, -4) = (x+4, y+5)
on comparison we have;
x+4 = 7 and y + 5 = -4
First solve for x;
Subtract 4 from both sides we have;
x + 4 -4 =7-4
Simplify:
x = 3
To solve for y;
y+5 = -4
Subtract 5 from both sides we get;
y = -9
Therefore, the coordinate of pre-image is, B(3, -9)
Read more on Brainly.com - https://brainly.com/question/11847183#readmore
Step-by-step explanation:
Crystal earns $5.50 per hour mowing lawns. Write a rule to describe the amount of money m earned is a function of the number of hours h spent mowing lawns. How does Crystal earn if she works 3 hours 45 minutes? Round to the nearest cent.
Answers
Answer: Crystal earns $18.98 working 3 hours and 45 minutes.
Step-by-step explanation: Since m is the amount of money earned and we are trying to find how much money Crystal earned in h hours, the function will be set up as m = 5.50(h). If Crystal works 3.45 hours, we can plug this number into h: m = 5.50(3.45), which gives us $18.975. Rounded to the nearest cent, the answer would be $18.98 because 5 rounds 7 up.
In the diagram, AB = AC. Solve for x. Pls I need help!
Answers
x = 11
OR
x = - 5
In triangle ABC displayed in the diagram, the value of ( x ) is 11 or - 5.
STEP-BY-STEP EXPLANATION:
In triangle ABC, AB is equivalent to AC. This means that the triangle is an isosceles triangle as two sides are equivalent in length.
Since triangle ABC is an isoceles triangle, the base angles must be equivalent to each other.
( x^2 - 6x )° and 55° are both base angles of the isosceles triangle ABC.
THEREFORE:
x^2 - 6x = 55
x^2 - 6x - 55 = 0
x^2 - 11x + 5x - 55 = 0
x ( x - 11 ) + 5 ( x - 11 ) = 0
( x - 11 ) ( x + 5 ) = 0
Solution No. 1 -
x - 11 = 0
x = 11
Solution No. 2 -
x + 5 = 0
x = - 5
You read a headline that 1 out of 5 people in the world will log onto a social network Since there at 7 billion people in the world. How many people are logging in?
Answers
Answer:
1,400,000,000
Step-by-step explanation:
Since there are 7 billion people on the earth, you must divide 7,000,000,000 by 5 and you arrive at the answer of 1,400,000,000.
Hope that helps!
The result is that approximately 1.4 billion people are using social networks.
If 1 out of 5 people in the world are logging onto a social network, and the world population is 7 billion, we can calculate the number of people logging in by dividing the total population by 5.
So, the number of people logging in is:
[tex]\frac{\text{7 billion}}{5} = 1.4\text{ billion}[/tex]
So, approximately 1.4 billion people are logging into social networks, according to the headline.
The lenght of sydney's tennis racket is 2 rulers long. How many feet long is sydeney's tennis racket
Answers
Answer:
2 feet or 24 inch.
Step-by-step explanation:
Which is the best first step when solving the following system of equations?x+y=3 and 4x-y=7
I Need Answer ASAP
Answers
I think it would be x+y=3
Hope this helps
a student was 48 inches tall in 5th grade. now, the student measures 60 inches tall on 8th grade. what is the percent increase of the studet's height
Answers
The height of the student increased by 25 percent from 48 inches in 5th grade to 60 inches in 8th grade.
Explanation:The student's height increased from 48 inches to 60 inches. To find the percent increase, we use the formula:
Percent Increase = ((New Height - Original Height) / Original Height) x 100%
Substituting the given values, we get:
Percent Increase = ((60 - 48) / 48) x 100%
Percent Increase = (12 / 48) x 100%
Percent Increase = 0.25 x 100%
Percent Increase = 25%
Therefore, the height of the student increased by 25 percent from 5th grade to 8th grade.
The student's height increased by 25% from 5th grade to 8th grade.
The percent increase in the student's height from 5th grade to 8th grade is calculated as follows:
First, determine the initial height in 5th grade, which is given as 48 inches.
Next, determine the final height in 8th grade, which is given as 60 inches.
The increase in height is the final height minus the initial height:
[tex]\[ \text{Increase in height} = \text{Final height} - \text{Initial height} \] \[ \text{Increase in height} = 60 - 48 \] \[ \text{Increase in height} = 12 \text{ inches} \][/tex]
To find the percent increase, divide the increase in height by the initial height and then multiply by 100:
[tex]\[ \text{Percent increase} = \left( \frac{\text{Increase in height}}{\text{Initial height}} \right) \times 100 \] \[ \text{Percent increase} = \left( \frac{12}{48} \right) \times 100 \] \[ \text{Percent increase} = \left( \frac{1}{4} \right) \times 100 \] \[ \text{Percent increase} = 0.25 \times 100 \] \[ \text{Percent increase} = 25\% \][/tex]
The correct option is [tex]\boxed{25\%}[/tex].
The same king cobra is 4.237 meters long. Round the length to the nearest meter.
Answers
Answer:
4 is the closest meter you can round to. So your answer would be 4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
since 2<5, 4.237 ≈ 4
X/2 + 3 = -4
/=fraction
Answers
X=-7 x 2
X= -14
Given the equations `2x + 4/3 y = 1` and `y - 9/13 x = 9`, by what factor would you multiply the first equation so that combining the two equations would eliminate x? A. `-9/26` B. `9/26` C. `1/2` D. `-9/13`
Answers
Answer:
B. 9/26.
Step-by-step explanation:
You need to change the coefficient of x in the first equation to 9/13 so that adding the 2 equations would eliminate x.
So you would multiply by
= 9/13 / 2
= 9/13 * 1/2
= 9/26 (answer)
Answer:
The correct option is B) [tex]\frac{9}{26}[/tex]
Step-by-step explanation:
Consider the provided equations:
[tex]2x+\frac{4}{3}y=1[/tex] and [tex]y-\frac{9}{13}x=9[/tex]
The above equation can be written as:
[tex]2x+\frac{4}{3}y=1[/tex] and [tex]-\frac{9}{13}x+y=9[/tex]
As it is given that we need to eliminate the variable x.
Multiplying the equation [tex]2x+\frac{4}{3}y=1[/tex] with [tex]\frac{9}{26}[/tex].
Therefore,
[tex]\frac{9}{26}2x+\frac{9}{26}\times{\frac{4}{3}y}=1\times{\frac{9}{26}}[/tex]
[tex]\frac{9}{13}x+\frac{9}{26}\times{\frac{4}{3}y}=1\times{\frac{9}{26}}[/tex]
Therefore, the correct option is B) [tex]\frac{9}{26}[/tex]
I will give you literally 40 points if you answer this. In a stadium, there are 31 chairs in the first row and 37 in the second row. The number of chairs in a row continues to increase by 6 with each additional row. a) write the first 5 numbers of this sequence b)what is the explicit tilde for the number of seats in n rows c)use the rule you wrote in 1b to determine which row has 103 seats. SHOW ALL WORK
Answers
A) 1st Row = 31 seats
2nd row = 37 seats
3rd row = 37+6 = 43 seats
4th row = 43+6 = 49 seats
5th row = 49+6 = 55 seats
B) The formula for finding the number of seats in any row number is:
Number of seats in nth row = 31 + (n-1) *6
C) To find the row with 103 seats, set the equation in B to equal 103 and solve for n:
103 = 31 + (n-1)*6
Subtract 31 from each side:
72 = (n-1)*6
Divide both sides by 6:
12 = n-1
add 1 to each side:
n = 13
The 13th row has 103 seats.
What is n in the equation -5(1+6n)=5n-5?
Answers
Answer:
0 is your answer
Step-by-step explanation:
Note the equal sign, what you do to one side, you do to the other. Remember to follow PEMDAS.
First, distribute -5 to all terms within the parenthesis
-5(1 + 6n) = (-5)(1) + (-5)(6n) = -5 - 30n
-30n - 5 = 5n - 5
Isolate the variable, n. Subtract 5n and add 5 to both sides
-30n (-5n) - 5 (+5) = 5n (-5n) - 5 (+5)
-30n - 5n = -5 + 5
-35n = 0
Isolate the n, Divide -35 from both sides
(-35n)/-35 = (0)/-35
n = 0
0 is your answer
~
HELP
GIven:
QRS is an isosceles triangle
If M is midpoint of RQ, then triangle SMQ is congruent to triangle SRM
True or false
Answers
Hope this helps :)
Answer:
True
Step-by-step explanation:
Given: QRS is an isosceles triangle that is QS=SR and M is the mid point of QR.
To prove: ΔSQM≅ΔSRM
Proof: It is given that QRS is an isosceles triangle that is QS=SR and M is the mid point of QR, thus from ΔSQM and ΔSRM, we have
QS=SR (Given)
QM=MR (Mid point)
SM=MS (Reflexive)
Thus, by SSS rule of congruence,
ΔSQM≅ΔSRM
Hence the given statement is true, that is if M is teh point of RQ, then ΔSQM≅ΔSRM.
Hence proved.
What is the ratio of a to b 9/17= 3a/ a+b
3/14
6/17
13/17
50/9
Answers
Answer:
3/14
Step-by-step explanation:
We want to find the ratio of a to b, or a/b
9/17 = 3a/ (a+b)
Multiply each side by 17
17*9/17 =17* 3a/ (a+b)
9 = 51 a/ (a+b)
Multiply each side by (a+b)
9 (a+b) = 51a
Distribute the 9
9a +9b = 51a
Subtract 9a from each side
9a-9a +9b =51a-9a
9b = 42a
Divide each side by b
9b/b = 42a/b
9 = 42a/b
Divide each side by 42
9/42 = a/b
But we can simplify 9/42 because each is divisible by 3, so divide 9 and 42 by 3
3/14 = a/b
Which rules of exponents will be used to evaluate the expression. PLZ answer (MEGA NEEDS HELP :( Quick!!!!!!!!!!!!!!!!!!!!!!!! Check all that apply [( 7^5)(7^3)]-4
.quotient of powers
.product of powers
.power of a power
.power of a product
.negative exponent
.zero exponent
Answers
Answer:
Product of powers; power of a power; negative exponent
Step-by-step explanation:
A jeweler orders necklaces from a website that offers $6 shipping for any-size order. Each necklace costs $7. The jeweler wants to know the total cost of ordering n necklaces.What is the dependent (output) variable?
Answers
Answer: 6x7=n
Step-by-step explanation:
Answer:
A jeweler orders necklaces from a website that offers $6 shipping for any-size order. Each necklace costs $7. The jeweler wants to know the total cost of ordering n necklaces.
What is the independent (input) variable?
✔ n, the number of necklaces
What is the dependent (output) variable?
✔ c, the total cost (in dollars)
What is the domain?
✔ n=0, 1, 2, 3,...
Which equation expresses the order’s total cost, c, as a function of the number of necklaces, n?
✔ c(n)=7n + 6
Which expression means “the total cost, including shipping, of 5 necklaces”?
✔ c(5)
Step-by-step explanation:
For question 1-4, find the simplified form of each expression.
1. (-3)^-4 (1 point)
A. 12
B.-81
C.1/81
D.-1/81
2. (-7.4)^0 (1 point)
A.-1
B.-7.4
C.0
D.1
3. -(5)^-1 (1point)
A.-1/5
B.-5
C.5
D.1/5
4. Simplify (1 point)
-(3ab^2)^-3
Answers
Answer:
1. C
2. D
3. A
4. [tex]\frac{-1}{27a^{3}b^{6}}[/tex]
Step-by-step explanation:
To evaluate or simplify expressions with exponents, we use exponent rules.
An exponent is only a short cut for multiplication. It simplifies how we write the expression.When we multiply terms with the same bases, we add exponents.When we divide terms with the same bases, we subtract exponents.When we have a base to the exponent of 0, it is 1.A negative exponent creates a fraction.When we raise an exponent to an exponent, we multiply exponents.When we have exponents with parenthesis, we apply it to everything in the parenthesis.We will use these rules to simplify.
1. [tex](-3)^{-4} = -3*-3*-3*-3=\frac{1}{81}[/tex] Choice C.
2. [tex](-7.4)^{0}=1[/tex] Choice D.
3.[tex]-(5)^{-1}=\frac{-1}{5}[/tex] Choice A.
4. [tex]-(3ab^{2})^{-3} =-(\frac{1}{3ab^{2}*3ab^{2}*3ab^{2}})=\frac{-1}{27a^{3}b^{6}}[/tex]
Show 326 using hundreds, tens, and ones
Answers
Answer:
using hunreds 300
using tens 20
using ones 6
300+20+6= 326
Step-by-step explanation:
All you got to do is break them apart into the places.
Plzzz mark brainlest and thank me
What is the value of n in the equation 8n + 7 =31
Answers
Answer:
The answer is the third choice 3
Step-by-step explanation:
First you undo by doing the opposite 31 - 7 = 24 now we undo the 8 by undoing 24 divided by 8 is 3
Question
What is the value of n in the equation 8n + 7 =31
Answer:
3Step-by-step explanation:
8n + 7 = 31
8n = 31 - 7
8n = 24
n = 24 : 8
n = 3
--------------------
check
8 * 3 + 7 = 31
24 + 7 = 31
31 = 31
The answer is good
How can this quadrilateral be classified?
Answers
Answer:
I am pretty sure it is all but trapezoid.
Step-by-step explanation:
Answer:
B. Trapezoid
Step-by-step explanation:
We have been given image of a quadrilateral. We are asked to classify our given quadrilateral.
Let us check our given choices one by one.
A. Parallelogram.
We can see that our given quadrilateral is square as its all sides are equal and perpendicular to each other.
Since sides of square are parallel to each other and opposite sides has equal measure, therefore, it is a parallelogram.
B. Trapezoid
We know that a trapezoid has one pair of parallel sides.
Since square has two pair of parallel sides, therefore, our given quadrilateral is not a trapezoid.
C. Rhombus
We know that each square is a rhombus, therefore, our given quadrilateral is a rhombus as well.
D. Square.
Our given quadrilateral is square as its all sides are equal and perpendicular to each other. Therefore, option D is correct as well.
5.5 ÷ .25 plz show work
Answers
Answer:
22
Step-by-step explanation
that is how many times .25 goes into 5.5
Question
5.5 ÷ .25 and plz show work
Answer:
22
Step-by-step explanation:
5.5 : 0.25 =
55 : 2.5 =
550 : 25 =
22
Suppose Department X is 8,000 square feet, Department Y is 5,000 square feet, and Department Z is 6,000 square feet. What's the percent of overhead expense applied to Department Z?
Answers
Answer:
31.6%
Step-by-step explanation:
it is given that
Area of Department X = 8,000 square feet
Area of Department Y = 5,000 square feet
Area of Department Z = 6,000 square feet
now the total area = [tex]8000+5000+6000[/tex]
=[tex]19,000[/tex] square feet
Percentage of area covered by Department Z = [tex]\frac{area of Department Z}{total area }100[/tex]%
=[tex]\frac{6000}{19000} 100[/tex] %
=[tex]31.6[/tex] %
percentage of overhead expenses applied to Department Z = percentage of area covered by Department Z
hence we have,
percentage of overhead expenses applied to Department Z = 31.6%
A department store sells logo shirts at an original price of $20. Every month that a shirt doesn’t sell, the store reduces the selling price by 25%. The store employees get a 50% markdown off the current price. Macy works at the store and sees the shirts going into the second markdown month. She decides that since 25% + 25% + 50% = 100%, the shirts must be free to employees. What is Macy’s error?
Answers
Answer: The pre-tax price of the shirt for Macy will be $5.63
Step-by-step explanation:
Given:
Original price = 20
reduces selling price by 25% every month it's not sold.
First markdown month:
20 * (100%-25%) = 20 * 75% = 15
Second markdown month
15 * 75% = 11.25
Macy, employee gets a 50% discount off the current price.
11.25 * 50% = 5.625
11.25 - 5.625 = 5.625 or 5.63
hope it helps! :)
Answer:
teacher's response
Step-by-step explanation:
Macy was calculating the employee price off the original amount each time instead of off the new selling price each month. Macy cannot add up all the discounts; she must apply them one by one.
find the angle of elevation of the sun if a building 100 feet tall casts a shadow 150 feet long.
Answers
The angle of elevation of the sun can be determined using trigonometry by finding the inverse tangent of the ratio of the building height to the shadow length, which is approximately 33.69 degrees.
To find this, we can use trigonometry, specifically the tangent function, which is the ratio of the opposite side over the adjacent side in a right-angled triangle. Here, the building height represents the opposite side, and the shadow length represents the adjacent side.
Using the formula tangent = opposite/adjacent, we have:
tangent(\(\theta\)) = 100 / 150tangent(\(\theta\)) = 2/3Now, we need to find the angle whose tangent is 2/3. By using a calculator or a trigonometry table, we find:
\(\theta\) = tan-1(2/3) \(\approx\) 33.69 degreesTherefore, the angle of elevation of the sun is approximately 33.69 degrees.
Algebra 2 math problem
please help I am stuck on this.
Answers
Answer:
x=5
Step-by-step explanation:
[tex]\sqrt{3x+2} - \sqrt{2x+7} \\\\PLUG IN 5\\\\\sqrt{3*5+2} - \sqrt{2*5+7} = 0[/tex]
What is the sum of 5(−3.4k−7) (3k+ 21) =
Answers
Answer:
welp i got -891k - 357 but that seems really big
Step-by-step explanation:
i distributed the 5 to the -3.4k and the -7 and got -17k-35. then i foiled that out with the 3k+21 and got -51k -357 - 105k -735k. then i combined like terms and got -891k -357
hope this helps rip sorry
Solve equation for a
Answers
[tex]\dfrac{3ax-n}{5}=-4\qquad\text{multiply both sides by 5}\\\\3ax-n=-20\qquad\text{add n to both sides}\\\\3ax=n-20\qquad\text{divide both sides by 3a}\neq0\\\\\boxed{x=\dfrac{n-20}{3a}}[/tex]
Two large single-topping pizzas cost $25.00. What is the constant of proportionality (k)?
Answers
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{\underline{c}cost directly proportional to \underline{p}izzas}}{c=kp} \\\\\\ \textit{we know that } \begin{cases} p=2\\ c=25 \end{cases}\implies 25=k(2)\implies \cfrac{25}{2}=k\implies 12\frac{1}{2}=k[/tex]