The x coordinates are 3 and -5. They add to 3+(-5) = -2
Cut this in half to get -2/2 = -1
The x coordinate of the midpoint is x = -1
-------------------
The y coordinates are 2 and 5. They add to 2+5 = 7.
Then we cut this in half to get 7/2 = 3.5
The y coordinate of the midpoint is y = 3.5
-------------------
Overall, the midpoint is (-1, 3.5)
Answer: (-1, 3.5) which is the same as (-1, 7/2)John went on a bike ride to the store 4 miles away. If it took John 3 1/0 of an hour to get there and 12 of an hour to get back, what was his average rate of speed (miles per hour) for the entire trip?
Answer:
His average rate of speed for the entire trip is 10 miles/hour.
Step-by-step explanation:
We are given that John went on a bike ride to the store 4 miles away. If it took John 3/10 of an hour to get there and 1/2 of an hour to get back.
And we have to find his average rate of speed (miles per hour) for the entire trip.
As we know that the Distance-Speed-Time formula is given by;
[tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]
Here, the distance for the entire trip = 8 miles (4 miles for reaching store and 4 miles for returning back)
The time taken for the entire trip = [tex](\frac{3}{10} )[/tex] of an hour to reach the store and [tex](\frac{1}{2})[/tex] an hour to get back.
So, the average rate of speed for the entire trip = [tex]\frac{\text{Total Distance}}{\text{Total Time}}[/tex]
= [tex]\frac{8}{\frac{3}{10}+\frac{1}{2} }[/tex]
= [tex]\frac{8}{\frac{8}{10} }[/tex] = 10 miles per hour
Hence, his average rate of speed for the entire trip is 10 miles/hour.
−4 − 6 + 2 + 5 + 8 − 3 (8 − 6 − 3) − (−6 − 2 − 5) (9 − 4)(−6 − 3) pls help me
Answer:
-577
Step-by-step explanation:
−4 − 6 + 2 + 5 + 8 − 3 (8 − 6 − 3) − (−6 − 2 − 5) (9 − 4)(−6 − 3)
complete the table for the given rule.
Answer:
x y
10 → 6
4 → 0
8 → 4
Step-by-step explanation:
Using the given rule, plug in any known values:
[tex]y=x-4\\\\6=x-4[/tex]
Solve for x. Add 4 to both sides of the equation to isolate the variable:
[tex]6+4=x-4+4\\\\x=10[/tex]
Repeat:
[tex]y=x-4\\\\0=x-4\\\\0+4=x-4+4\\\\x=4[/tex]
[tex]y=x-4\\\\4=x-4\\\\4+4=x-4+4\\\\x=8[/tex]
:Done
Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of $ 65 $65dollar sign, 65 along with an hourly rate of $ 28 $28dollar sign, 28. The plumber only charges for a whole number of hours. Anand would like to spend no more than $ 250 $250dollar sign, 250, and he wonders how many hours of work he can afford. Let H HH represent the whole number of hours that the plumber works. 1) Which inequality describes this scenario? Choose 1 answer:
Answer:
Step-by-step explanation:
Basic Charge = $ 65
Rate per hour = $ 28
Number of hours = H
Rate for H hours = 28 *H = 28H
Equation:
65 + 28H ≤ 250
Anan consideration requires:
A plumber that charges an initial fee of = $65An hourly rate of = $28Anan doesn't want to spend more than = $250Requirements of the plumber
charges at a whole number of hour rate = HThus, to determine the number of how many hours Anan can afford for his total amount of $250, we have the following:
The initial fee + hourly rate ≤ 250
(why we use a less than or equal to sign is because Anan is not willing to spend more than $250)∴
$65 + $28 H ≤ 250
Therefore, we can conclude that the perfect inequality that describes Anan Scenario is: $65 + $28 H ≤ 250
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The graph of a line passes through the two points (-2, 1) and (2, 1). What is the equation of the line written in general form? y - 1 = 0 x - y + 1 = 0 x + y - 1= 0 Please explain your answer! Thanks!
Answer:
Step-by-step explanation:
Slope = 0
The line is parallel to x-axis
Equation: y = 1
y -1 = 0
Answer:
y - 1 = 0
Step-by-step explanation:
As we move from the first point to the second, x increases by 4 (this is the 'run') but y does not change (that is, the 'rise' is zero). Thus, the slope of the line is 0, and the equation of the line is y = 1, or (equivalently) y - 1 = 0.
For the given congruence, list the six poirs of congruent parts.
Answer:
ummm
Step-by-step explanation:
look it up
I'm helping you look it up right now
il comment when I find ... ok?
If the Discriminant is 73 how many roots are there
The solution is 2 roots
The number of roots the equation will have if the value of the discriminant is 73 will be 2 roots
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the quadratic equation be A
where A = ax² + bx + c=0
Let the discriminant of the equation be D
Now , the value of D = 73
To calculate the number of roots a quadratic equation A
We need to compute the discriminant (b² - 4ac).
If the discriminant is less than 0, then the quadratic has no real roots.
If the discriminant is equal to zero then the quadratic has equal roots.
If the discriminant is more than zero then it has 2 distinct roots.
So , the value of D > 0
Therefore , the equation has 2 roots
Hence , the number of roots of the quadratic equation is 2 roots
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What is the solution of StartRoot x squared + 49 EndRoot = x + 5?
Answer:
2.4
Step-by-step explanation:
√(x² +49) = x + 5(√(x² +49) )²= (x + 5)² ⇒ square of both sidesx² + 49 = x² + 10x + 25 ⇒ simplifying, x² get cancelled10x = 49 -2510x = 24x= 24/10x= 2.4Answer is 2.4
Answer:
12/5
Step-by-step explanation:
my dudes could you help me cause im really bad at math heres the problem choose all the values that make the inequality true. 28-7x ≤ -4(-7x - 7) the options : -10 -5 0 5 10
Answer:
0, 5, 10
Step-by-step explanation:
You can solve the inequality to determine what values to select.
28 -7x ≤ -4(-7x -7) . . . . . . given
28 -7x ≤ 28x +28 . . . . . . eliminate parentheses*
-7x ≤ 28x . . . . . . . . . . . . . subtract 28 from both sides
0 ≤ 35x . . . . . . . . . . . . . . add 7x to both sides
0 ≤ x . . . . . . . . . . . . . . . . . divide by 35
So, all values that are 0 or greater will make the inequality true:
0, 5, 10
_____
* Parentheses are eliminated using the distributive property. The factor outside parentheses multiplies each of the terms inside. Pay attention to signs.
-4(-7x -7) = (-4)(-7x) +(-4)(-7) = 28x +28
Which expression is equal to
to (-10 – 2i) + (3 + i)?
0 -7 ti
o – 13 –
07-
-7-
Answer:
- 7 - i
Step-by-step explanation:
Given
(- 10 - 2i) + (3 + i) ← remove parenthesis
= - 10 - 2i + 3 + i ← collect like terms
= - 7 - i
La siguiente figura representa una torre de transmisión de energía eléctrica: ¿Mediante cual razón trigonométrica se puede determinar la altura de la torre? dejar procedimiento o justificación. A. sen α = BC/c B. sen α = BC/b C. sen α = c/b D. sen α = b/c
Answer:
B. sen α = BC/b
Step-by-step explanation:
Las identidades trigonométricas se utilizan para resolver problemas de ángulos rectos.
En un ángulo recto, el lado al que se hace referencia como opuesto es el lado opuesto al ángulo, el lado al que se hace referencia como adyacente es el lado siguiente al ángulo (entre el ángulo y el ángulo recto) mientras que la hipotenusa es el lado más largo (opuesto al ángulo recto)
De identidades trigonométricas:
[tex]sen\ \alpha=\frac{lado\ opuesto}{hipotenusa} \\\\lado\ opuesto=BC=a\\\\hipotenusa=b\\\\sen\ \alpha=\frac{lado\ opuesto}{hipotenusa} =\frac{BC}{b} \\\\sen\ \alpha =\frac{BC}{b}[/tex]
A ladder is placed with its foot 5m from the bottom of a wall 12m high. The top of the ladder just
reaches the top of the wall. Find the length of the ladder 5
(3 Points)
14m
13m
169m
15m
Answer:
13 m
Step-by-step explanation:
The ladder forms a right triangle with the wall that has legs of 5 and 12. We need to solve for the length of the ladder, which in this case, is the hypotenuse of the right triangle. You could use the Pythagorean Theorem but there's an easier way to do this. We can use the 5 - 12 - 13 Pythagorean triple so we know that the length of the ladder is 13 m.
A coin is flipped 20 times. The results are 12 heads and 8 tails. Determine the theoretical probability of getting heads.
The theoretical probability of getting heads is; 12%
Theoretical Probability
We are given;
Number of times coin is flipped = 20 times
Number of heads gotten = 12 heads
Number of tails gotten = 8
Assuming the coin is fair, then;
p = 0.5 and q = 0.5
Using binomial probability formula we have;
P(getting heads) = ²⁰C₁₂ * 0.5¹² * 0.5⁽²⁰ ⁻ ¹²⁾
P(getting heads) = 125970 * 0.00000095367431640625
P(getting heads) = 0.12 or 12%
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PLEASE HELP !!! Find the measure of y A. 43 B. 90 C. 53 D. 47
===============================================
Explanation:
Notice how inscribed angles x and y subtend (or cut off) the same minor arc measure. This means that x = y. So if we find x, we found y also.
The vertical line is a diameter of the circle. The blue angle marked in the diagram below is a right angle due to Thales Theorem, which is a special case of the inscribed angle theorem. Thales Theorem says that any inscribed angle in a semicircle is 90 degrees.
Therefore the triangle marked in red (same diagram) is a right triangle, allowing us to say
x+47+90 = 180
x+137 = 180
x = 180-137
x = 43
So y = 43 as well.
If x= 4y + 3 and y = -2x - 3, what is the value of xy?
Given that :-
x = 4y +3 y = -2x -3To Find :-
Value of x.ySolution :-
→ x = 4y + 3 equation 1st
→ y = -2x -3 equation 2nd .
Now putting the value of x from first equation to second equation.
→ y = -2(4y +3 ) -3
→ y = -8y - 6 - 3
→ y + 8y = -9
→ 9y = -9
→ y = -1
Now putting the value of y in equation first .
→ x = 4(-1) + 3
→ x = -4 + 3
→ x = -1
Now multiply and X and y.
→ x.y = -1(-1)
→ x.y = 1 .
[tex]\huge {\bold {\star {\fcolorbox {black} {yellow} {Answer}}}} [/tex]
Given, x = 4y + 3 ⠀⠀⠀⠀⠀⠀ iy = -2x - 3⠀⠀⠀⠀⠀⠀⠀⠀iiTo find;The value of xy [tex]{\boxed{\red{\underline{\sf{Solution:}}}}}[/tex]Putting the value of x in ii, we get ;
➝ y = - 2(4y+3) - 3
➝ y = - 8y - 6 - 3
➝ y = - 8y - 9
➝ y + 8y = - 9
➝ 9y = - 9
∴ y = - 1
Putting the value of y in i, we get ;
➝ x = 4y + 3
➝ x = 4(-1) + 3
➝ x = - 4 + 3
∴ x = - 1
Now,➛ xy = (- 1)(-1)
⛬ xy = 1
pleaee solve this problem!!
Answer:
RHS=tanA/2
Step-by-step explanation:
LHS=1+sinA-cosA/1+sinA+cosA
=(1-cosA)+sinA/(1+cos A)+sinA
=2sin^2A/2+2sinA/2*cosA/2
_____________________
2cos^2A/2+22sinA/2*cosA/2
=2sinA/2(sinA/2+cosA/2)
___________________
2cosA/2(sinA/2+cosA/2)
sinA/2
=_____
cosA/2
= tanA/2 proved.
Answer: see proof below
Step-by-step explanation:
Use the following Double Angle Identities:
sin 2A = 2cos A · sin A
cos 2A = 2 cos²A - 1
Use the following Quotient Identity: tan A = (sin A)/(cos A)
Use the following Pythagorean Identity:
cos²A + sin²A = 1 --> sin²A = 1 - cos²A
Proof LHS → RHS
Given: [tex]\dfrac{1+sin\theta - cos \theta}{1+sin \theta +cos \theta}[/tex]
Let Ф = 2A: [tex]\dfrac{1+sin2A - cos 2A}{1+sin2A +cos2A}[/tex]
Un-factor: [tex]\dfrac{\bigg(\dfrac{1- cos^2\ 2A}{1+cos\ 2A}\bigg)+sin\ 2A }{1+sin\ 2A +cos\ 2A}[/tex]
Pythagorean Identity: [tex]\dfrac{\bigg(\dfrac{sin^2\ 2A}{1+cos\ 2A}\bigg)+sin\ 2A }{1+cos\ 2A +sin\ 2A}[/tex]
Simplify: [tex]\dfrac{sin\ 2A}{1+cos\ 2A}[/tex]
Double Angle Identity: [tex]\dfrac{2sin\ A\cdot cos\ A}{1+(2cos^2 A-1)}[/tex]
Simplify: [tex]\dfrac{2sin\ A\cdot cos\ A}{2cos^2\ A}[/tex]
[tex]=\dfrac{2sin\ A\cdot cos\ A}{2cos^2\ A}[/tex]
[tex]=\dfrac{sin\ A}{cos\ A}[/tex]
Quotient Identity: tan A
[tex]\text{Substitute} A = \dfrac{\theta}{2}}:\qquad tan\dfrac{\theta}{2}[/tex]
[tex]tan\dfrac{\theta}{2} = tan\dfrac{\theta}{2}\quad \checkmark[/tex]
Given: <2 and <4 are vertical angles.
Prove: <2 ~= <4
Statements Reasons
Assemble the proof by dragging tiles to
the Statements and Reasons columns
Statement 1: [tex]\angle 2[/tex] and [tex]\angle 4[/tex] are vertical angles
Reason 1: Given
We basically just restate the given information word for word. This is true of any two column proof.
-------------------------------------
Statement 2: [tex]m \angle 2 + m \angle 3 = 180[/tex]
Reason 2: [tex]\angle 2[/tex] and [tex]\angle 3[/tex] are a linear pair
The term "linear pair" means the angles are adjacent and supplementary (they form a straight line), so this is why the two angles add to 180.
--------------------------------------
Statement 3: [tex]m \angle 3 + m \angle 4 = 180[/tex]
Reason 3: [tex]\angle 3[/tex] and [tex]\angle 4[/tex] are a linear pair
--------------------------------------
Statement 4: [tex]m \angle 2 + m \angle 3 = m \angle 3 + m \angle 4[/tex]
Reason 4: Substitution
Each of the equations formed in statements 2 and 3 above have 180 on the right side, so the left hand sides must be the same
--------------------------------------
Statement 5: [tex]m \angle 2 = m \angle 4[/tex]
Reason 5: Subtraction property of equality
We subtracted the quantity [tex]m \angle 3[/tex] from both sides (they go away)
--------------------------------------
Statement 6: [tex]\angle 2 \cong \angle 4[/tex]
Reason 6: Definition of congruence
If two items are congruent, then they have the same measure. In other words, they are the same.
The proof of [tex]\angle 2 \ and \ \angle4[/tex] are vertical angles is explained below.
Given, [tex]\angle 2 \ and \ \angle4[/tex] are vertical angles as shown in fig.
We know that, Vertical angles are formed when two straight lines intersect at a point.Vertical angles are two angles which are vertically opposite and have the same measure. So, the two angles are to be congruent.
We have to prove that angle 2 and angle 4 congruent.
Given [tex]\angle 2 \ and\ \angle 3[/tex] makes linear pair so,
[tex]\angle 2+\angle 3= 180[/tex]
[tex]\angle 3 =180-\angle 2[/tex]..........(1)
Again [tex]\angle 3 \ and \ \angle 4[/tex] makes linear pair so,
[tex]\angle 3+\angle 4= 180[/tex]
[tex]\angle 3 =180-\angle 4[/tex].......(2)
From (1) and (2) we get,
[tex]180-\angle 2=180-\angle 4[/tex]
Subtracting 180 from both the sides we get,
[tex]-\angle 2=-\angle 4[/tex]
Or, [tex]\angle 2=\angle 4[/tex]
Hence angle 2 and angle 4 are congruent.
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Which of the following is true of the data represented by the box plot
Answer:
The data is skewed to the bottom and contains an outlier.
Step-by-step explanation:
1. Test for outlier
An outlier is a point that is more than 1.5IQR below Q1 or above Q3.
IQR = Q3 - Q1 = 74 - 51 = 23
1.5 IQR = 1.5 × 23 = 34.5
51 - 15 = 36 > 1.5IQR
The point at 15 is an outlier.
2. Test for normal distribution
The median is not in the middle of the box.
Rather, it cuts the box into two unequal parts, so the data does not have a normal distribution.
3. Test for skewness
The longer part is to the left of the median, so the data is skewed left.
The midpoint M and one endpoint of JK are given. Find the coordinates of the other endpoint. J(7,2) and M(1,-2)
Step-by-step explanation:
Xj + Xk/2 = Xm
7 + Xk/2 = 1
to get rid of the bracket, multiply all two sides by the denominator.
2(7 + Xk/2) = 1(2)
7 + Xk = 2
Xk = 2 - 7
Xk = -5
Yj + Yk/2 = Ym
2 + Yk/2 = -2
to get rid of the bracket, multiply all two sides by the denominator.
2(2 + Yk/2) = -2(2)
2 + Yk = -4
Yk = -4 - 2
Yk = -6
Therefore the coordinates of point K is (-5,-6)
Write a word phrase for the expression: 13p + 12 12 more than the product of 13 and a number p The sum of p and 12 12 more than the quotient of 13 and a number p
Answer:
Add 12 to the product of 13 and a number p.
Step-by-step explanation:
Given expression: 13p + 12
In the expression, 13 is multiplied by a number p, and 12 is added to the result. Therefore, a simple word phrase for the given expression would be: Add 12 to the product of 13 and a number p.
i.e 13 × p = 13p
Then add 12,
= 13p + 12
4. (x+ 2)(2x2 + 9x+8)
A.
2x3 + 13x2 + 26x+ 16
B.
16x3 + 728 + 46x - 16
C.
2x3 + 17x2 + 22x+ 16
D.
2x3 + 13x2 - 26x+ 16
Answer:
2x3+9x2+8x+4x2+18x+16
2x3+13x2+26x+16
MOD Pizza purchased a new brick-fired oven for $14,500. If they make a profit of $3 for every pizza they sell, how many pizzas must be in order to make their money back on the purchase of the oven?
Answer:
4,834
Step-by-step explanation:
$14,500/($3 / pizza) = 4833.3 pizzas
MOD Pizza must sell 4,834 pizzas to cover the cost of the oven.
the length of a rectangle is 4 units more then its breadth.its perimeter is 28 units. what is the length
Hi there! :)
Answer:
[tex]\huge\boxed{L = 9 \text { units}}[/tex]
Given:
Perimeter = 28
Let the breadth = x. The length is 4 units greater, so we can represent this as (x + 4).
Set up an expression. Remember that the formula for the perimeter of a rectangle is:
P = 2(l) + 2(w)
Substitute:
28 = 2(x) + 2(x+ 4)
Distribute:
28 = 2x + 2x + 8
Combine like terms and simplify:
28 = 4x + 8
20 = 4x
x = 5.
The length of the breadth is 5 units. Substitute in 5 to solve for the length:
(5) + 4 = 9 units.
The length of the rectangle is 9 units.
5/6 divided by -5/6. Please don’t say -1 put the answer as a fraction
Answer:
1/-30
Step-by-step explanation:
5/6/-5/6
= 5/6 x 6/-5
= 5/30 x 6/-30
= 30/-900
= 1/-30
the ratio of the weights of two men is 1/2:1/3 if weight of the first person is 22 1/2kg then find the weight of the second person
Answer:
15 kg
Step-by-step explanation:
We can multiply the given ratio units by 6 to make them be integers:
(1/2) : (1/3) = 3 : 2
Then we can see that the second man has 2/3 the weight of the first man.
(2/3)(22.5 kg) = 15 kg
The second person weighs 15 kg.
Could someone please help me!!!?? First answer gets brainliest.
Answer:
5A: All you got to do is put in the number of videos (v) and figure the equation out. For example, 40 x 20 + 3v = $803v.
I really hope this helps you!
solve the system by adding or subtracting
-3x-3y=9
3x+8y=6
Answer:
x = -6 y = 3
Step-by-step explanation:
Adding the two equations and you get, -3x-3y + 3x+8y= 6+9
=> 5y = 15
=> y = 3
Plug y in each equation
-3x -3(3) = 9
-3x -9 = 9
-3x = 18
x = -6
3x + 8(3) = 6
3x +24 = 6
3x = -18
x = -6
Find the smallest positive integer x which is greater than 1 and relatively prime to 120 (recall that relatively prime means that the GCD of x and 120 is 1)
Answer: 7
Explanation:
List out the factors of 120 until we hit a gap
1,2,3,4,5,6,8
Note that 7 is not shown above. We can see that 120/7 = 17.14 approximately meaning that 7 doesn't go evenly into 120. So this is why 7 isn't a factor. Something like 3 is a factor because 120/3 = 40 is a whole number result.
Also, 7 is prime. The only factors of 7 are 1 and itself. This means that 7 and 120 do not have any common factors other than 1. The GCF of 7 and 120 is 1, leading to the two numbers being relatively prime
Side note: The term "coprime" is sometimes used in place of "relatively prime"
Find the midpoint of the segment with the given endpoints.
(10,5) and (-2, -10)
Answer:
The answer is
[tex] (4, - \frac{ 5}{2} )[/tex]Step-by-step explanation:
The midpoint M of two given points is given by
[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )[/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(10,5) and (-2, -10)
The midpoint of points is
[tex]M = (\frac{10 - 2}{2} , \frac{5 - 10}{2} ) \\ = ( \frac{8}{2} , - \frac{5}{2} )[/tex]We have the final answer as
[tex]M = (4, - \frac{ 5}{2} )[/tex]Hope this helps you
84 POINTS!!!!!!!! The hands on a clock represents rays. At 6:00, they forn opposite rays. What undefined term do the hands of the clock represents at 6:00?
A. Point
B.Line
C. Plane
D. Space
Answer:
B
Step-by-step explanation:
The clock at six o clock form a line:
12
|
9 | 3
|
6