Answer:
a = - 1
Step-by-step explanation:
Given the points are equidistant from A then AP = AQ
Calculate the distance using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A(0, a) and (x₂, y₂ ) = P(3, - 3)
AP = [tex]\sqrt{3-0)^2+(-3-a)^2}[/tex] = [tex]\sqrt{3^2+(-3-a)^2}[/tex] = [tex]\sqrt{9+(-3-a)^2}[/tex]
Repeat with (x₁, y₁ ) = A(0, a) and (x₂, y₂ ) = Q(- 2, 2)
AQ = [tex]\sqrt{(-2-0)^2+(2-a)^2}[/tex] = [tex]\sqrt{(-2)^2+(2-a)^2}[/tex] = [tex]\sqrt{4+(2-a)^2}[/tex]
Equating AP and AQ
[tex]\sqrt{9+(-3-a)^2}[/tex] = [tex]\sqrt{4+(2-a)^2}[/tex] ( square both sides )
9 + (- 3 - a)² = 4 + (2 - a )² ← expand parenthesis on both sides
9 + 9 + 6a + a² = 4 + 4 - 4a + a² ( subtract a² - 4a from both sides )
18 + 10a = 8 ( subtract 18 from both sides )
10a = - 10 ( divide both sides by 10 )
a = - 1
The value of a is -1 if A(0,a) is equidistant from P(3,-3) and Q(-2,2) the answer is a = -1.
What is an ordered double?It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
It is given that:
A(0,a) is equidistant from P(3,-3) and Q(-2,2).
It is required to find the value of a:
Using the distance formula:
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
AP = AQ
[tex]\rm \sqrt{(3-0)^2+(-3-a)^2} = \sqrt{(-2-0)^2+(2-a)^2}[/tex]
After simplification:
9 + (3 + a)² = 4 + (2 - a)²
9 + 9 + 6a + a² = 4 + 4 - 4a + a²
18 + 10a = 8
10a = - 10
a = - 1
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division.
Thus, the value of a is -1 if A(0,a) is equidistant from P(3,-3) and Q(-2,2) the answer is a = -1
Learn more about the order double here:
brainly.com/question/10757890
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A restaurant chef made 1 1/4 pints of mushroom soup. Each bowl of soup holds 5/8 of a pint.
How many bowls of soup will the chef be able to fill?
Answer:
2 bowls of soup
Step-by-step explanation:
1. Make 1 1/4 an improper fraction
1 1/4 = 5/4
2. Then divide 5/4 by 5/8 (KCF - Keep the 5/4 - Change the division sign to multiplication - 'Flip' 5/8 to 8/5)
5/4 x 8/5 = 40/20
3. Simplify the fraction (divide the numerator and denominator by 20)
40/20 = 2
4. Final answer:
2 (bowls of soup)
Please help me find the answer
Answer:
[tex]k = \frac{2P}{x^2}[/tex]
Step-by-step explanation:
[tex]P= \frac{1}{2} kx^2\\\\P=\frac{kx^2}{2}\\\\ 2P =kx^2\\\\\frac{2P}{x^2}= \frac{kx^2}{x^2} \\\\k= \frac{2P}{x^2}[/tex]
3 + (5 + 7) = (3 + 5) + 7
Answer:
true
Step-by-step explanation:
3 + (5 + 7) = (3 + 5) + 7
3 + (12) = (8) + 7
15 = 15
I don't get this at all can you pls help me?
Answer: -13.85
Step-by-step explanation:
Simplify.
4.6−7.28−11.17
=−13.85
Answer:
[tex]\huge \boxed{\mathrm{-13.85}}[/tex]
Step-by-step explanation:
[tex]4.6+(-7.28)-11.17[/tex]
Removing brackets.
[tex]\Rightarrow 4.6-7.28-11.17[/tex]
Combining.
[tex]\Rightarrow -2.68-11.17[/tex]
[tex]\Rightarrow -13.85[/tex]
Select all the ways the rectangle could have been rotated to get from Frame 1 to Frame 2. 40 degrees clockwise 40 degrees counterclockwise 90 degrees clockwise 90 degrees counterclockwise 140 degrees clockwise 140 degrees counterclockwise Lesson 3
Answer:
40 degrees clockwise
140 degrees counterclockwise
Step-by-step explanation:
The rectangle is rotated in Figure B. The angle of rotation is 40 degrees. If we rotate a rectangle at an angle of 40 degrees clockwise then wit will be at the position as shown in figure B. The 90 degrees angle is perpendicular angle. Rectangle will not reach the desired position. If we rotate the rectangle at 140 degrees counterclockwise this will be the figure B representation. The rotation to 90 degree counterclockwise is either not suitable for the desired rectangle position.
Is ......... a rational number ?
Answer:
The third one.
Step-by-step explanation:
Find the equation of the line below.
Answer:
y = 2x
Step-by-step explanation:
The equation of a line is y = mx + b
We can plug in values for x and y,:
x = 1, y = 2
2 = m + b <- equation 1
x = 4 y = 8
8 = 4m + b <- equation 2
We can multiply equation 1 by 4, getting 8 = 4m + 4b.
We can them subtract equation 1 by equation 2, getting 3b = 0.
Therefore, b = 0.
We can use the equation 2 = m + b and find m:
Since b = 0, m = 2.
The equation is then y = 2x.
Which property is not a characteristic of a parallelogram?
O A. Opposite sides are congruent.
B. All angles are congruent.
O C. Opposite sides are parallel.
D. Opposite angles are congruent.
Answer:
B
Step-by-step explanation:
need this answer quick due soon help
Answer:
2/9
Step-by-step explanation:
Let 0.2222..... be x
10x = 2.2222222......
=> 10x - x = 2.22222..... - 0.22222....
=> 9x = 2
=> x = 2/9
Growth and decay question
Answer:
Decay
Step-by-step explanation:
Staring at 3000 every y = half of the previous one.
A store sells three varieties of cheese cheddar, Gouda, and Swiss. Each variety of cheese is available in two different styles shredded or sliced. How many possible outcomes for the variety and style of cheese are there?
Answer:
6 possible outcomes
Step-by-step explanation:
To solve this problem, we have to make use of the Fundamental Counting Principle formula.
The formula counting principle states that when we are given two or more distinct events, in order to get the total number of possible outcomes, we multiply such events together.
In the above question, we are given two events.
Event 1
3 varieties of cheese: Cheddar, Gouda, and Swiss.
Event 2
2 styles of cheese: Shredded and Sliced
The possible outcomes for the variety and style of cheese = Event 1 × Event 2
= 3 × 2
6 possible outcomes.
These 6 Possible outcomes are listed below:
1) Cheddar cheese , Shredded
2) Cheddar cheese , Sliced
3) Gouda cheese , Shredded
4) Gouda cheese , Sliced
5) Swiss cheese , Shredded
6) Swiss cheese , Sliced
Lee measured a restaurant and made a scale drawing. The scale he used was
2 millimeters : 1 meter. The restaurant's kitchen is 27 meters long in real life. How long is the kitchen in the drawing?
Answer:1 meter
Step-by-step explanation:
because in drawing it cant be as big as it is in real life
a+3ab+67a-2ab-1 and for 5 stars
Answer:
68a+ab−1
Step-by-step explanation:
cancel out
Answer:
Step-by-step explanation:a+67a=68a
3ab+2ab=5ab
so 69a+5ab-1
economic factors in decision making fall under
Answer:
external factors...
Step-by-step explanation:
...
consider the following expression
-10x^2 + 5x +3
2x^2 + 4
select the true statements
the numerator has 3 terms
the denominator includes a coefficient of 4
the denominator includes a coefficient of 2
the numerator has 2 terms
the numerator includes a coefficient of 3
Answer:
Statements 1 and 3 are correct
Step-by-step explanation:
you are installing a support wire for an electrical pole. the pole is 25 feet and the ground connection is 10 feet from the base of the pole. the wire is sold per whole feet. how many feet of support why should you purchase
ans=26.92
use trigonometric ratios
a²= b²+c²
a²=25²+10²
a²=625+100
now take square root on both sides
a
[tex] \sqrt{a { }^{2} } = \sqrt{725} [/tex]
a=26.92
a=27 (2decimal place)
5 divided by 2/5
5 divided by 2/5
Answer:
Hey there!
5 divided by 2/5 is equal to 25/2, or 12.5
Hope this helps :)
Answer:
[tex] \boxed{ \bold{ \huge {\boxed{ \sf{ \frac{25}{2} }}}}}[/tex]
Step-by-step explanation:
[tex] \sf{5 \div \frac{2}{5} }[/tex]
When any number of fraction is divided by a fraction , we multiply the dividend by reciprocal of the divisor.
We can obtain the reciprocal of any fraction by interchanging the position of numerator and denominator.
⇒[tex] \sf{5 \times \frac{5}{2} }[/tex]
To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator.
⇒[tex] \sf{ \frac{5 \times 5}{2} }[/tex]
Multiply the numbers : 5 and 5
⇒[tex] \sf{ \frac{25}{2} }[/tex]
Hope I helped!
Best regards! :D
What is the solution to the equation 3x – 8 = -2?
O A. -3 1/3
O B. 3 1/3
C. 2
D. -2
Answer:
option (c) 2
Step-by-step explanation:
We have the linear equation :-
→ 3x - 8 = -2
add 8 both sides
→ 3x - 8 + 8 = -2 + 8
→ 3x = 6
→ x = 6 ÷ 3
→ x = 2
Which square root is between 4 and 5?
O 10
O 014
0 24
V32
Answer:
C. 25
Step-by-step explanation:
4*4=16
5*5=25
24 is found in the middle of 16 and 25.
Hope this helps ;) ❤❤❤
Help a girl out pls! Lmkkk!
As a decimal number
8×1+1× 1/ 10 +6× 1 /100 +7× 1/ 1000 =
Answer:
the answer is 8.167
Step-by-step explanation:
Solve the system of linear equations in two variables by elimination or substitution.
2x + 4y = 4
2x - y=1
Answer:
x = 0.8 y = 0.6
Step-by-step explanation:
Solve one of the equations for a single variable, I chose the 2nd equation and solved for the variable y and I got y = 2x -1.
Next plug in the value for y into the 1st equation, I got :
2x + 4 ( 2x - 1) = 4
Next solve for x by first distributing the 4 to the (2x-1), this becomes (8x -4) then add like terms and move the -4 to the other side of the equation by addition. I got 10x =8 then I divided 8/10 to solve for x and I got 0.8.
Now plug the value 0.8 in for x in the 2nd equation : 2*(0.8) - y = 1
Then solve for y by subtracting 2*(0.8) or 1.6 from 1 and I got -0.6, lastly divide by -1 to solve for y.
Simplify.
40w4
8w6
Only simplify don’t actually solve and if u give me the right answer first I’ll give u the crown
is this a expression or inqualities 15x < x + 8
Answer:
Inequality
Step-by-step explanation:
An expression would not have a greater than or less than sign and this has one so it is an inequality
Answer:
inequalities
Step-by-step explanation: it deals with inequalities
The are of a rectangle is 50m^2 , the length is 100m . Calculate the width
w = 0.5 m
Step-by-step explanation:A = l × w
50m² = 100m × w
w = 50m²/100m
w = 0.5 m
Answer:
The answer is 0.5 m i.e Width = 0.5 m
Step-by-step explanation:
Given,
Area (A) = [tex]50m^{2}[/tex]
length (l) =100 m
width ( b ) = ?
Now,
A = l * b
or, 50 = 100 * b
or, [tex]\frac{50}{100}[/tex]= b
or, b = 0.5 m
what is the standard deviation for 54, 36, 30, 28, 27
Answer:
11.18
Step-by-step explanation:
Step 1: average : (54+36+30+28+27) / 5 = 35
Step 2: variance:
sum of the squares of (each number - average value) divided by (n-1)
[ (54-35)^2 + (36-35)^2 + (30-35)^2 + (28-35)^2 + (27-35)^2 ] / (5-1) = 125
Step 3: standard deviation = √(variance) = √125 = 5√5 (about 11.18)
the presence of a segment bisected will result in what type of segments?
A: noncoplanar segments
B. parallel segments
C. congruent segments
D. perpendicular segments
first person to get it right will get brainliest
Answer:
Option C → Congruent segments
Step-by-step explanation:
The meaning of segment bisector is a segment which divides another segment into two equal parts.It is not necessary that the segement which is bisecting the another segment are perpendicular with one another.
So, when a segment is bisected the two segments are equal.
Equal means the two segments are congruent.
Most appropriate statement
Answer:
Congruent.
Step-by-step explanation:
Bisecting will give 2 segments of equal length.
is the square root of 5 between 2 and 3
Answer: Yes, it’s 2.23607
Taking the square root of a number is the *blank * Of squaring a number
Answer:
Opposite
Step-by-step explanation:
They are complete opposites:
When you take the square root of a number, you are taking the number to the 1/2 power. For example, the square root of 9 is 3.
When you square a number, you multiply it by itself. For example, 3 squared is 9.
So, these are opposites because when doing these operations to the same number, the products will be "opposites" of each other, like the examples above.
HELP ME PLEASE!!!! :))