If m is the midpoint of pq, what is the relationship between pm and pq

Answers

Answer 1

m is the mid point of pq
then pm= 1/2 pq

Answer 2

Midpoint, as the word suggests, means the point which lies in the middle of something. If m is the midpoint of PQ then PM will be half of PQ.

What does a midpoint mean?

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point that lies in the mid of the given line segment.

Given that m is the midpoint of PQ. Therefore, it will divide PQ into two equal parts. Therefore, we can write,

PQ = PM + MQ

But since PM = MQ,

PQ = PM + PM

PQ = 2 PM

PM = PQ/2

Hence, if m is the midpoint of PQ then the relationship between PM and PQ will be half of PQ.

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Related Questions

Add the following military times: 0645 + 0745

Answers

14:30 is the answer.
(Aka 2:30 PM)

How do I do these only need to do 1 I just need to see how to do it!

Answers

Lets do the first one(7). Fist change 10x -2y = 3,which is in standard form to point slope form so you can see the slope.

10x - 2y = 3

-2y = -10x + 3

-2y/-2 = -10x / -2 + 3/-2

y = 5x - 3/2

The slope is the m in y = mx + b so our slope is 5x, well it wants you to find the equation of a line that passes through (0,1) that is parallel to the equation this (Parallel) mean has the same slope.The slope is 5. Now that we know the slope is 5 we can find the equation by using the point slope form of an equation of a line.

point slope form = y – y1 = m(x – x1)

Remember m = slope = 5. Now plugin our x and y cord from the point (0,1) and our slope of 5

y - y1 = m(x - x1)

y - 1 = 5(x - 0)

y - 1 = 5x - 0

y - 1+1 = 5x + 1

y= 5x + 1

So the point (0,1) passes through y = 5x + 1

Number 8 is already in slope intercept form so you don't have to do anything to find the slope. You can see that the slope is 7 so just plug your point into y - y1 = m(x - x1) and then put it into slope intercept form.

Point = (5,8)

Slope = 7

y - y1 = m(x - x1)

y - 8 = 7(x - 5)

y = 7x - 27

So for number 8 the point (5,8) passes through y = 7x - 27

(9) For nine they want an equation that is perpendicular, which means to flip the slope. For instance, if you have a slope of 2/5 the perpendicular slope would be 5/2. For 9 we see that the slope is 2/5 so its perpendicular slope would be 5/2. Now just plug your point into the point slope form equation.

Point = (-4, 6)

Slope = 2/5

perpendicular slope = 5/2

y - 6 = 5/2(x - (-4))

y = 5/2 x + 16

So point (-4, 6) passes through y = 5/2 x + 16

(10) Point (4,1) passes through y = 7/5 x - 23/5

first off, let's keep in mind something, two lines that are parallel to each other, have the same slope, and two lines that are perpendicular to each other, have negative reciprocal slopes.

7)

so is parallel to 10x-2y=3... now, let's solve that for "y", to put it in slope-intercept form

[tex]\bf 10x-2y=3\implies 10x-3=2y\implies \cfrac{10x-3}{2}=y \\\\\\ \stackrel{\textit{slope-intercept~form}}{\cfrac{5}{2}x-\cfrac{3}{2}}=y\impliedby \textit{slope is }\frac{5}{2}[/tex]

so then, we're looking for a line whose slope is 5/2 and passes (0,1)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 0}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{5}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=\cfrac{5}{2}(x-0)\implies y-1=\cfrac{5}{2}x \\\\\\ \boxed{y=\cfrac{5}{2}x+1}[/tex]

8)

now, is parallel to [tex]\bf y=\stackrel{slope}{7}x-6[/tex] , now, that's already in slope-intercept form, so the slope we can see is just 7, so then.

we are looking for a line whose slope is 7 passes (5,8)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 5}}\quad ,&{{ 8}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 7 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-8=7(x-5)\implies y-8=7x-35 \\\\\\ y=7x-35+8\implies \boxed{y=7x-27}[/tex]

9)

well, this function is also already in slope-intercept form, so we can tell the slope is 2/5.

now, the line we're looking for, is perpendicular to it, so it has a negative reciprocal slope, let's check

[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{2}{5}\\\\ slope=\cfrac{2}{{{ 5}}}\qquad negative\implies -\cfrac{2}{{{ 5}}}\qquad reciprocal\implies - \cfrac{{{ 5}}}{2}[/tex]

so, we're looking for a line whose slope is -5/2 and passes (-4,6)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -4}}\quad ,&{{ 6}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -\cfrac{5}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-6=-\cfrac{5}{2}[x-(-4)] \\\\\\ y-6=-\cfrac{5}{2}(x+4)\implies y-6=-\cfrac{5}{2}x-10\implies \boxed{y=-\cfrac{5}{2}-4}[/tex]

10)

let's solve for "y" first

[tex]\bf 5x-7y=44\implies 5x-44=7y\implies \cfrac{5x-44}{7}=y \\\\\\ \stackrel{slope}{\cfrac{5}{7}}x-\cfrac{44}{7}=y[/tex]

now, let's find the negative reciprocal of that

[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{5}{7}\\\\ slope=\cfrac{5}{{{ 7}}}\qquad negative\implies -\cfrac{5}{{{ 7}}}\qquad reciprocal\implies - \cfrac{{{ 7}}}{5}[/tex]

so, we're looking for a line whose slope is -7/5 and passes (4,1)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 4}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -\cfrac{7}{5} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=-\cfrac{7}{5}(x-4)\implies y-1=-\cfrac{7}{5}x+\cfrac{28}{5} \\\\\\ y=-\cfrac{7}{5}x+\cfrac{28}{5}+1\implies \boxed{y=-\cfrac{7}{5}x+\cfrac{33}{5}}[/tex]

Question 1 (3 points) study the Proof Given.

List the reasons for Items 2,3, & 4.

Right the number and then the answer.
Question 2 (3 points
)Study the Proof: Give the reasons for the missing reason. List the number and then state the reason.

Answers

Question 1
2. Definition of midpoint
3. Given
4. Transitive Property

Question 2
1. Given
2. Addition Property of Equality
3. Segment Postulate Property.

Four times the difference of a number and seven is 32

Answers

as a formula, you're saying 4*(n-7)=32

This solves to n-7 = 8, so n=15

An exhibit at Tabu World Square in Japan includes a scale model of the Empire State Building. The model was built using a scale of 1 m : 25 m. The height of the actual Empire State Building is 443.2 meters. What is the height of the model? Round your answer to the nearest thousanths place.

Answers

The scale is 1 m : 25 m.
The actual height = 443.2 m

Therefore the scaled height is 443.2/25 = 17.7280 m

Answer: 17.728 m (nearest thousandth)

How do you solve this ?

Answers

The length is w+8 and the width is w.
Perimeter= 2(w+l)

256= 2(w+8+w)
256= 2(2w+8)
256= 4w+16
240= 4w
60= w

Final answer: Width= 60 ft, Length= 68 ft

width = w

length = w+8

perimieter = 256 feet

formla for perimeter is p=2L+2w

so you have: 256 =2(w+8) +2w =

256 = 2w+16 +2w

256= 4w+16

240=4w

w=240/4 = 60

width is 60 feet

length = 60+8 = 68 feet

What is the area of a circle with a radius of 14 feet? use 22/7 for π?

Answers

So the formula is pi*r^2 and if you plug that in it is 22/7* 14^2 and you get 616

If you only have a 1/3 measuring cup and a recipe calls for 8 2/3 cups of flour, how many 1/3 cups would you need to use?

Answers

(8+2/3) cups divided by 1/3 = 26 cups

8*3=24=24/3
24/3+2/3= 26/3
you are going to need 26 1/3 cups

How to draw a grid of area of 12 square centimeters and a perimeter of 16 centimeters?

Answers

Alright, so if w is the width and l is the length, we have 2w+2l=16 (for the perimeter) and w*l=12. For 2w+2l=16 , we can subtract 2l from both sides to get 2w=16-2l, and then divide both sides by 2 to get w=8-l. Substituting that into w*l=12, we get (8-l)*l=12 and -l^2+8l=12. Subtracting 12 from both sides, we get -l^2+8l-12=0. Using the quadratic formula, we get
l=(-8+-sqrt(64-(4*-1*12))/-2=(-8+-sqrt(16))/-2= (-8+-4)/2=either 2 or 6. Plugging them into 8-l=w, we get that w is either 2 or 6 too, meaning that you just have to draw the grid with one side being the length of 2 and the other with the length of 6

Y = -27x + 577, where x represents the number of weeks and y represents the amount of money left in her account. After how many weeks will Alma have $145 left in her account?

Answers

To solve this problem, plugin 145 where the y is located and then solve for x
y = -27x +577
145 = -27x +577
145 -577 = -27x
-432 = -27x
-432/-27 = -27x/-27
16 = x
x = 16
After 16 weeks she will have $145 dollars in her account.

Find f(x) and g(x) so the function can be expressed as y=f (g (x)).
y=2/x^2 +3

Answers

Since f(g(x)) essentially means that we plug f(x) into what g(x) already is (e.g. if g(x) is x^2 and f(x) is x+1, then f(g(x)) is x^2+1). If g(x) is 2/x^2 (the first part of y) and f(x) is x+3, in f(g(x)) g(x) essentially replaces x to be (2/x^2)+3

Can someone help me with these maths questions? I totally don't get them.

Do the following coordinates lie on the following graphs?

1) y=2x+4 (7,20)
2) y=4x-14 (-1,-18)
3) y=5x-1 (0.5,2.5)
4) y=-2x+6 (0.8,5.4)
[tex] 5) y=\frac{1}{2}x+2 (0.7,1.6) [/tex]

Answers

1. 2(7) +4 = 18, does not = 20, does not lie on graph

2. 4(-1) -14 = -18, equals -18, does lie on the graph

3. 5(.5)-1 = 1.5, does not = 2.5, does not lie on the graph

4. -2(0.8)+6 = 4.4, does not = 5.4 does not lie on graph

5. 1/2(0.7) +2 = 2.35, does not = 1.6, does not lie on graph

Express the volume v of the box as a function of the length x of the sidfe of the square cut from each corner

Answers

i dont know what the word sidfe

Mason deposited $763.21 in a savings account that earns 1.7% simple interest. What is Mason's account balance after nine years?

Answers

The formula is
A=p (1+rt)
A future value?
P present value 763.21
R interest rate 0.017
T time 9 years

A=763.21×(1+0.017×9)
A=879.98

Hope it helps!

Solve the following problem for the roots by completing the square

3x^2 -12x = 9

Answers

3(x^2+3) is the answer you are looking for. :)

3x^2 - 12x = 9
Divide both sides by 3
x^2 - 4x = 3
To make a square with "x^2 - 4x", you need to have a "+ 4" after it so it can be simplified as (x-2)^2. So add 4 to both sides.
x^2 - 4x + 4 = 7
(x-2)^2 = 7
x - 2 = (square root) of 7
x = 2 (+/-) (square root) of 7.
x = {-0.65, 4.65}

The solutions are -0.65 and 4.65.

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Two thirds of a number is no more than -10

Answers

Let x be the number in the problem. When it states that x is "no more than -10", it means than it is less than or equal to -10. So, we have

[tex] \frac{2}{3} [/tex]x≤-10

In order to cancel out the [tex] \frac{2}{3} [/tex] on the left and isolate x, we multiply both sides by [tex] \frac{3}{2} [/tex] (since [tex] \frac{3}{2}[/tex]·[tex] \frac{2}{3} [/tex]=1). Thus, we have

x≤-10·[tex] \frac{3}{2} [/tex]=-15

Therefore, x≤-15

The perimeter of a rectangle is 44 inches, and its area is 105 square inches. find the length and width of the rectangle.

Answers

Perimeter = (Length + Width)x2
Area = LengthxWidth

P=(L+W)x2
P/2=L+W
L=P/2 - W

Area=(P/2 - W)(W)
A=WP/2-W^2
105=W(44)/2 - W^2
105=22W - W^2
W^2-22W+105=0
(W-7)(W-15)=0
Width= 7 or 15

A=LxW
105=Lx7
105/7=L
L=15

Length is 15 inches, Width is 7 inches.

Graph the image of the given triangle after the transformation with the rule (x, y)→(y, x) .

Answers

See the attached figure. The original triangle is shown in red (triangle ABC). The line of reflection is the blue dashed line. This is the equation y = x. Reflecting triangle ABC over the line y = x results in the purple triangle A'B'C'.

Note how the x and y values swap places.
We have...
point A = (5,1) turn into point A' = (1,5)
point B = (8,1) turn into point B' = (1,8)
point C = (8,6) turn into point B' = (6,8)
The swap occurs because the rule (x,y) --> (y,x) tells this to happen.

The purple triangle is the final answer.

Long Division for a quadratic polynomial and binomial, please show your work!
Quadratic polynomial: x^2-x-6=f(x)
Binomial: (x-3)

Answers

answer is given above

[tex]$x^2 - x - 6$[/tex] can be expressed as the product of [tex]$(x - 3)$ and $(x - 2)$[/tex]. The long division image is given below.

Long division for polynomials is similar to long division for numbers. We'll divide the quadratic polynomial [tex]$f(x) = x^2 - x - 6$[/tex] by the binomial [tex]$(x - 3)$[/tex].

Here's a step-by-step breakdown of the process:

1. Start by dividing the highest-degree term of the dividend (in this case, [tex]$x^2$[/tex]) by the highest-degree term of the divisor (in this case, [tex]$x$)[/tex]. This gives us [tex]$x$[/tex].

2. Multiply the divisor [tex]$(x - 3)$[/tex] by the result from step 1, which is [tex]$x$,[/tex] and write the result below the dividend, aligning like terms. So, [tex]$x \cdot (x - 3) = x^2 - 3x$[/tex].

3. Subtract the result from step [tex]2 ($x^2 - 3x$)[/tex] from the dividend ([tex]$x^2 - x - 6$[/tex]). This gives us [tex]$x^2 - x - 6 - (x^2 - 3x)$[/tex], which simplifies to [tex]$-x + 3x - 6$,[/tex] resulting in [tex]$2x - 6$[/tex].

4. Now, we repeat the process with the new expression [tex]$2x - 6$[/tex]. We divide the highest-degree term ([tex]$2x$[/tex]) by the highest-degree term of the divisor [tex]($x$),[/tex] which gives us [tex]$2$.[/tex]

5. Multiply the divisor [tex]$(x - 3)$[/tex] by the result from step 4, which is [tex]$2$[/tex], and write the result below the previous result: [tex]$2 \cdot (x - 3) = 2x - 6$[/tex].

6. Subtract the result from step [tex]5 ($2x - 6$)[/tex] from the previous expression [tex]($2x - 6$)[/tex], which results in [tex]$0$[/tex].

Since we have a remainder of [tex]$0$,[/tex] this means that [tex]$x^2 - x - 6$[/tex] is evenly divisible by [tex]$(x - 3)$[/tex], and the quotient is [tex]$x - 2$.[/tex] The final result is:

[tex]\[ \frac{x^2 - x - 6}{x - 3} = x - 2 \][/tex]

This tells us that [tex]$x^2 - x - 6$[/tex] can be expressed as the product of [tex]$(x - 3)$ and $(x - 2)$[/tex].

40 students are going on a field trip to the aquarium. Every student needs to be in a group, and all groups must have the same number of students. If there is 1 group, there will be students in the group. If there are groups, there will be 20 students in each group. If there are 4 groups, there will be students in each group.

Answers

10 is the answer because 40/1 = 40, 40/2= 20 and 40/= 10

If there is 1 group there will be 40 students in the group. There will be 20 students in each group if there are 2 groups. If there are 4 groups, there will be 10 students in each group.

What is Division?

Division is one of the four basic operations of mathematics.

On performing the operation division, a number is divided into some number of equal parts.

The number which is being divided is called the dividend, the number which divides the dividend is called divisor and the number got when division is performed is called the quotient and the remaining number which has not divided is called the remainder.

Total number of students = 40

If there is 1 group, number of students in the group = 40/1 = 40

If there are 20 students in each group, then the number of groups = 40/20 = 2.

If there are 4 groups, then number of students in each group = 40/4 = 10.

Hence there will be 40 students in the group if there is 1 group. There are 2 groups if there will be 20 students in each group. There will be 10 students in each group if there are 4 groups.

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16 pound turkey cost $14.24 what is the price per pound

Answers

$.89 per pound is the answer

The answer would be $0.89,
$14.24 divided by 16

NEED HELP BADLY PLEASEEEE WILL GIVE BRAINLY

List the next three terms in the following sequence:
1, 2, 4, 8, 16, 32,...

a. 48, 80, 128
b. 64, 96, 160
c. 64, 128, 256
d. 46, 92, 184

Answers

Its C because it multiplies by 2

The first number multiplied by two is 2. Two multiplied by two is four. Four multiplied by two is eight. Eight multiplied by two is 16....and so on. So in this case, the answer would be C because 32*2=64, 64*2=128, 128*2=256.

Is 0 prime odd or even prime or composite?

Answers

0 is a unique case. It is neither prime nor composite, and is neither odd nor even. Zero is an absence of value case which is not made from other numbers...and didn't appear in numbering systems until the past couple of thousand years...it's a weird concept!

Answer:

0 is nor prime or composite

Step-by-step explanation:

The definition of a prime number is a positive integer that has exactly two positive divisors. Therefore, the simplest reason why 0 is not prime is that 0 is not a positive integer, and the axiom says that all whole numbers greater than 1 are either prime or composite.

Do you know the answer to this question

Answers

Answer: [C]: " f(x) = log₃ (x − 3) " .
_______________________________________________________

The sum of the first and third of three consecutive even integers is 128. find the three even integers.

Answers

62, 64, and 66. 62+66=128

Final answer:

The three even integers are 62, 64, and 66.

Explanation:

The sum of the first and third of three consecutive even integers is 128. To find the three even integers, we start by letting the first integer be x. Because the integers are consecutive even numbers, the second integer will be x + 2 and the third will be x + 4. The sum of the first and third integers gives us the equation:

x + (x + 4) = 128

Solving this equation:

Combine like terms: 2x + 4 = 128.

Subtract 4 from both sides: 2x = 124.

Divide both sides by 2: x = 62.

So, the first even integer is 62. Consequently, the second is 62 + 2 = 64, and the third is 62 + 4 = 66. Therefore, the three consecutive even integers are 62, 64, and 66.

Explain why the following statement are equivalent 4(x+y)=4x+4y

Answers

They are equivalent because they are showing the Distributive Property....The Distributive Property shows that you can Distribute one number into another one, and still get the same answer.....So, you would have to do 4x+4y!!! I hope this helps!!!

The equation 4(x+y)=4x+4y represents the same value after solving.

What is Distributive Property?

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

Given:

We have 4(x+y)=4x+4y.

We have the Distributive Property

a x ( b+ c )= a x b + a x c

let x= 2 and y = 5

So, 4 (x+ y) = 4 (2+ 5)= 4(7) = 28

and, 4x+ 4y= 4(2)+ 4(5) = 8+ 20 = 28

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A kennel owner needs 4 1/2 feet of wall space for each crate. How many crates can she fit along a 27 foot wall?

Answers

6 /////////////////////////////////////

What is the 100th term in the following arithmetic number pattern: 2,7,12

Answers

So the change in between terms is 5 so you would put 5x, then for the first term, which is 2, 5*1(x)(because it's first term) then the difference between 5-2(because it's the 2nd term) So you would plug 100 in for x so 5(100)-3=497. Hope this helped!

what property is illustrated by this problem 2(3 + 4) = 2x 3 +2 x 4

Answers

Distributive Property

Amber has 4/5-pound bag of colored sand. She uses 1/2 of the bag for the project. How much sand does she use for the project?

Answers

3/10
4/5 - 1/2= 8/10-5/10

Answer:

[tex]\frac{2}{5}[/tex]-pound of sand

Step-by-step explanation:

We have been given that Amber has [tex]\frac{4}{5}[/tex]-pound bag of colored sand. She uses 1/2 of the bag for the project.

We need to find 1/2 'of' the 4/5 as:

[tex]\frac{4}{5}\times \frac{1}{2}[/tex]

[tex]\frac{4\times1}{5\times2}[/tex]

[tex]\frac{2\times1}{5\times1}[/tex]

[tex]\frac{2}{5}[/tex]

Therefore, Amber used [tex]\frac{2}{5}[/tex]-pound of sand for the project.

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