Answers
Step-by-step explanation:
you have both points : (1, 1) and (5, 5).
so, we don't need to do any triangle calculations to get the height of the main triangle.
all we need to do is calculate the distance between these 2 points.
2 points in a coordinate grid create a right-angled triangle.
the direct distance is the Hypotenuse (the side opposite of the 90° angle). and the legs are the x- and the y-coordinate differences (one up or down the other left or right).
and we can use Pythagoras
c² = a² + b²
c being the Hypotenuse a and b being the legs.
so, how long are these legs here ?
the x-difference is 5 - 1 = 4.
also the y-difference is 5 - 1 = 4
so,
distance² = 4² + 4² = 16 + 16 = 32
distance = sqrt(32) = sqrt(16×2) = 4×sqrt(2) =
= 5.656854249...
the distance of P to the line RQ is 5.656854249...
Related Questions
What is the slope of the line below? If necessary, enter your answer as afraction in lowest terms, using the slash (/) as the fraction bar. Do not enteryour answer as a decimal number or an equation.
Answers
To find the slope of a line use two points (x,y) in the next formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In the given line you have the points: (-4, -9) and (-2, -3)
[tex]m=\frac{-3-(-9)}{-2-(-4)}=\frac{-3+9}{-2+4}=\frac{6}{2}=3[/tex]Then, the slope of the given line is 314.select the correct answerwhat is the sum of [tex]9.72 \times {10}^{8 \: and} 1.93 \times {10}^{7} [/tex]Answer options[tex]9.913 \times {10}^{7} [/tex][tex]9.913 \times 10 {}^{8} [/tex][tex]1.165 \times {10}^{8} [/tex][tex]1.165 \times {10}^{9} [/tex]
Answers
9.72 x 10⁸ + 1.93 x 10⁷
= 972 000000 + 193 00000
=991 300 000
= 9.913 x 10⁸
42. If a pipe can drain a tank in t hours, what part of the tank does foes it drain in 3 hours? A. 3t B. t/3C. t + 3D. 3/t
Answers
Let us assume that the volume of a full tank is 1
If the tank can drain the full tank in t hours, it means that
1 = t
Let x represent the volume of the tank that would be drained in 3 hours. It means that
x = 3
We would solve both equations for x
1 = t
x = 3
By crossmultiplying,
xt = 3
x = 3/t
Thus, the correct option is D
please when I send u this math explain it for me I'm only 12 and stuff is kinda hard to comprehend
Answers
First, we have to get rid of the parenthesis, to do that, we just multiply signs to get
[tex]-14-42[/tex]Now, we sum these numbers since they have the same signs
[tex]-14-42=-56[/tex]Therefore, the answer to (a) is -56.
The second operation is [tex]34+(-24)[/tex]We get rid of the parenthesis
[tex]34-24[/tex]Then, we subtract these numbers since they have different signs
[tex]34-24=10[/tex]Therefore, the answer to (b) is 10.
The third operation is[tex]-7+10[/tex]We just subtract these numbers since they have different signs
[tex]-7+10=3[/tex]Therefore, the answer to (c) is 3.
The fourth operation is[tex]-50+45[/tex]We just subtract
[tex]-50+45=-5[/tex]Therefore, the answer to (d) is -5.
The last operation is[tex]8+88[/tex]We just sum
[tex]8+88=96[/tex]Therefore, the answer to (e) is 96.
Help please I’ll give 10 points
Answers
Choose the right symbol for the following
What are Symbols?
Many operations in mathematics are carried out using mathematical symbols. Mathematical quantities are easy to refer to thanks to the symbols. It's interesting to consider how entirely dependent mathematics is on numbers and symbols. In addition to referring to various amounts, math symbols also show how two quantities relate to one another. The primary purpose of all mathematical symbols is to carry out mathematical operations under distinct conceptions.
1) 0.02 > 0.002
2) 0.05 < 0.5
3) 0.74 < 0.84
4) 0.74 > 0.084
5) 1.2 < 1.25
6) 5.130 = 5.13
7) 3.201 > 3.099
8) 0.159 < 1.590
9) 8.269 > 8.268
10) 4.60 > 4.060
11) 302.026 > 300.226
12) 0.237 > 0.223
13) 3.033 < 3.303
14) 9.074 < 9.47
15) 6.129 < 6.19
16) 567.45 > 564.75
17) 78.967 > 78.957
18) 5.346 < 5.4
19) 12.112 < 12.121
20) 26.2 = 26.200
21) 100.32 > 100.232
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What is the mean for the data shown in the dot plot?
Answers
We will determine the mean as follows:
[tex]x=\frac{1(4)+4(5)+3(6)+2(7)+1(10)}{11}\Rightarrow x=6[/tex]So, the mean will be 6.
the vertices of ABC and the endpoints of DE have coordinates that are integers. Determine the coordinates of point F so That ABC≈DEFOPTIONS:(-7, 1)(-5, 3)(-7, -8)(-2, -8)
Answers
We want figure EDF≈ABC.
We can see that if we rotate figure ABC we will obtain the following:
If we rotate it we can see that the segment AB is exactly as the segment ED.
We can now find the answer if we look how far is the point C, we see it is three unities up from B and 5 unities to its left. Then F must be 3 unities up from E and 5 unities to its left.
Since E is located :
at y = -2 if we go up 3 unities
-2 + 3 = 1
at x = -2 if we go at its left 5 unities then
-2 - 5 = -7
Then, F must be at x = -7 and y = 1.
Answer: (-7, 1)In the circle below, if arc AB is congruent to arc CD, chord AB = 3x - 6 and chord CD = x + 12, find x.
Answers
Solution
We will equate the two values
[tex]\begin{gathered} 3x-6=x+12 \\ \\ 3x-x=12+6 \\ \\ 2x=18 \\ \\ x=9 \end{gathered}[/tex]The answer is
follow the order of operations and evaluate the exponential expression (5+1)^2-(9-5)^2x3
Answers
what is 2^-3 as a fraction
Answers
Answer:
Solution below.
Step-by-step explanation:
The question tests on the concept of indices.
We know the following indices rule:
[tex] {x}^{ - y} \\ = \frac{1}{ {x}^{y} } [/tex]
Which means by inversing the power, we will multiply the power by -1.
So in the case of this question, we can:
[tex] {2}^{ - 3} = \frac{1}{ {2}^{3} } \\ = \frac{1}{8} [/tex]
Sharel spent the day at the mall. First, she bought five phones for $35each. Later, she found two five dollar bills. Write the total change to
Answers
if Sharel bought 5 phenes for 35 each, se spent 5 times 35 = $175
And when she found two $5 bills, it is like she received 2 times 5 = $10
Normally, expenses are negative numbers and earning are positive numbers, in this case
-$175 + $10 = - $165
Sothe answer is -165
it takes a rat 65 seconds to run from its food source to its home. If the rat has to run 28 meters which is going faster: the rat, or a child on a bike moving at 2 m/s?
Answers
Given data:
The given distance covered by rat is d= 28 m.
The given time is t= 65 seconds.
The speed of the child is s'=2 m/s.
The expression for the speed is,
[tex]\begin{gathered} s=\frac{28}{65}\text{ m/s} \\ =0.43\text{ m/s} \end{gathered}[/tex]As the speed of the child is greater than speed of the rat, so child is going faste.
r
Which ordered pair is a solution to the equation? y=7x-3 O only (14) O neither only (-1,-) both (1, 4) and (-1,-4)
Answers
The givenn equation can be written as
[tex]\begin{gathered} 7x-y=3 \\ On\text{ substituting (1,4) in the left hand side of the equation we get:-} \\ 7-4=3 \\ \text{which is equal to RHS} \end{gathered}[/tex][tex]\begin{gathered} \text{Now substitute (-1,-4) in LHS of the equation} \\ -7+4=-3 \\ \text{which is not equal to RHS.} \end{gathered}[/tex]Hence only (1,4) satisfies the given equation.
So the correct option is the first one (1,4).
.. Find the values indicated. For g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)} g(-3) = g(-9) = g(-7)=
Answers
Given:
g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)}
So,
To find g(-3), we need to find the term that contains -3 in the location of x of the order pair
So, g(-3) = 3
And by the same manner, we will find the others
So,
g(-9) = 12
g(-7) = 9
Question 6 of 10
Assume that two chords in a given circle are the same distance from the
center of the circle. Which of the following must also be true?
O
A. They must be perpendicular.
B. They must be parallel.
C. They must be diameters.
D. They must be congruent.
SUBMIT
Answers
The true statement is the same distance from the center of the circle is they must be perpendicular.
We have given that,
Two chords in a given circle are the same distance from the center of the circle.
What prerequisites must be met for the chords to be in harmony?The two chords must be equally spaced apart from the circle's center if they are congruent.
A is disregarded because it's possible that the chord won't travel through the circle's center.
Because the chords are not required to be parallel, B is rejected.
Because the chords do not have to be perpendicular, C is rejected.
A chord is any line segment that joins two points on the circle's circumference. While a circle's radius connects the center to the circle's point. As a result, we can conclude that radius is not a chord based on the definitions of both terms.
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A glassblower makes vases. To prevent them from breaking,each vase's thickness should be 6 millimeters and candeviate by no more than 1 millimeter.Write an inequality to represent this situation, where t is thethickness in millimeters, and solve for the maximumthickness.
Answers
Since each vase should be 6 millimeters and can only deviate by no more than 1 millimeter, the inequality for the thickness would be:
[tex]6\ge t\leq7[/tex]And the maximum thickness would be 7 millimeters.
x+y=22x+7y=9can u help me solve this equation
Answers
Keeping Od, this is the solution:
x + y = 2
2x + 7y = 9
___________
Step 1: Let's isolate x in equation 1, as follows:
x + y = 2
x = 2 - y
__________________
Step 2: Let's substitute x and solve for y in equation 2, this way:
2x + 7y = 9
2 (2 - y) + 7y = 9
4 - 2y + 7y = 9
4 + 5y = 9
Subtracting 4 at both sides:
4 + 5y - 4 = 9 - 4
5y = 5
Dividing by 5 at both sides:
5y/5 = 5/5
y = 1
_______________________
Step 3: Let's substitute y and solve for x in the first equation, as follows:
x + y = 2
x + 1 = 2
Subtracting 1 at both sides:
x + 1 - 1 = 2 - 1
x = 1
_____________________
Step 4: Let's write the solution as an ordered pair, this way:
(1, 1)
Last month, Ebony had 110 dollars in achecking account. The current balance is146 dollars. What is the percent change inthe account balance from last month to thismonth? Round your answer to the nearest whole percent.
Answers
Problem
Last month, Ebony had 110 dollars in a
checking account. The current balance is
146 dollars. What is the percent change in
the account balance from last month to this
month? Round your answer to the nearest whole percent.
Solutiion
For this case we can use the following formula:
[tex]\text{Change}=\frac{\text{Actual}-\text{Before}}{\text{Before}}\cdot100[/tex]And replacing we got:
[tex]\text{Change}=\frac{146-110}{110}\cdot100=32.72[/tex]And then the answer wounded to the nearest percent would be:
33%
Show that the points (3, 6), (0, -2), (-7, -5) and (-4, 3) are thevertices of a parallelogram.
Answers
Let
A(3,6) B(0,-2) C(-7,-5) D(-4,3)
Remember that
A parallelogram has opposite sides congruent and parallel
so
step 1
Find out the length of the side AB
using the formula to calculate the distance between two points
[tex]\begin{gathered} AB=\sqrt{(-2-6)^2+(0-3)^2} \\ AB=\sqrt{73} \end{gathered}[/tex]Find out the slope of the side AB
[tex]m_{AB}=\frac{-2-6}{0-3}=\frac{8}{3}[/tex]step 2
Find out the length of the side BC
[tex]\begin{gathered} BC=\sqrt{(-5+2)^2+(-7-0)} \\ BC=\sqrt{58} \end{gathered}[/tex]Find out the slope of the side BC
[tex]m_{BC}=\frac{-5+2}{-7-0}=\frac{3}{7}[/tex]step 3
Find out the length of the side CD
[tex]\begin{gathered} CD=\sqrt{(3+5)^2+(-4+7)^2} \\ CD=\sqrt{73} \end{gathered}[/tex]Find out the slope of the side CD
[tex]m_{CD}=\frac{3+5}{-4+7}=\frac{8}{3}[/tex]step 4
Find out the length of the side AD
[tex]\begin{gathered} AD=\sqrt{(3-6)^2+(-4-3)^2} \\ AD=\sqrt{58} \end{gathered}[/tex]Find out the slope of the side AD
[tex]m_{AD}=\frac{3-6}{-4-3}=\frac{3}{7}[/tex]step 5
Compare the length of the sides
we have that
AB=CD
BC=AD
that means ----> opposite sides are congruent
Compare their slopes
mAB=mCD
mBC=mAD
that means ----> opposite sides are parallel
therefore
The given figure is a parallelogramI'll send you the pic a
Answers
Let's complete the four equations, as follows:
1. 5 * x = 15
Solving for x:
5x = 15
Dividing by 5 at both sides:
5x/5 = 15/5
x = 3
3 is the value to fill in the box
2. 4 * x = 32
Solving for x:
4x = 32
Dividing by 4 at both sides:
4x/4 = 32/4
x = 8
8 is the value to fill in the box
3. 6 * x = 9
Solving for x:
6x = 9
Dividing by 6 at both sides:
6x/6 = 9/6
x = 1.5
1.5 is the value to fill in the box
4. 12 * x = 3
Solving for x:
12x = 3
Dividing by 12 at both sides:
12x/12 = 3/12
x = 3/12
Simplifying:
x = 1/4
1/4 or 0.25 is the value to fill in the box
&A(n)is formed when two rays have a common endpoint.Oline segmentangle
Answers
When two rays are with a common endpoint, an angle is formed and the common endpoint is called the vertex of the angle
Trini bought some jeans that she had been saving up for. She purchased them for $88 but has wornthem 4 times already. So far, what is the cost of wear for the jeans?
Answers
In order to find the cost of wear for the jeans, we just need to divide the cost of the jeans by the number of times Trini worn it.
So we have:
[tex]\frac{88}{4}=22[/tex]Therefore the cost of wear so far is $22.
Tiffany deposited two checks into her bank account this month.One check was for $50, and the second check was for $22.Her balance at the end of the month was $306, and she made no withdrawals.Which expression shows Tiffany's balance at the beginning of the month?
Answers
Tiffany's balance at the beginning of the month = $229
Explanations:First Deposit = $50
Second Deposit = $22
End of the month balance = $306
Balance at the beginning of the month = End of the month balance - (First Deposit + Second deposit)
Balance at the beginning of the month = 306 - (50 + 22)
Balance at the beginning of the month = 306 - 77
Balance at the beginning of the month = $229
Which of the following are solutions to the inequality below? Select all that apply.
Answers
Step-by-step explanation:
1.12+8×10<66
12+80<66
92<66
2.12+8×3<66
12+24<66
36<66
3.12+8×8<66
12+64<66
76<66
4.12+8×4<66
12+32<66
44<66
therfore the answer is 2 and 4
If a number with two places to the right of the decimal place is added to a number with three places to the right of thedecimal place then the answer should be reported as having how many numbers to the right of the decimal place
Answers
Let the number with two places to the right of the decimal place be represented as 20.45 and the number with three places to the right of the decimal place be 20.456
Required:
When we add the two numbers, how many numbers to the right of the decimal place is it going to have?
We can know this by adding the two fictitious numbers:
[tex]20.45\text{ + 20.456 = 40.906}[/tex]Here we can see that
Use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization. (If the first expression is not a factor of the second, enter DNE.)x − 2, 3x4 − 6x3 − 8x + 16(x − 2)=
Answers
Find out the division
3x^4-6x^3-8x+16 : (x-2)
3x^3-8
-3x^4+6x^3
-----------------------
-8x+16
8x-16
------------
0
The remainder is zero
that means
The expression (x-2) is a factor of the polynomial
so
3x^4-6x^3-8x+16=(x-2)(3x^3-8)
If a = (3.2) and b=(-5. 3), what is a +b?
Answers
Given the value of a and b
[tex]\begin{gathered} a=3.2 \\ b=-5.3 \end{gathered}[/tex]To get a+b
[tex]a+b=3.2-5.3[/tex]Thus
[tex]a+b=-2.1[/tex]Thus, a + b = -2.1
whats the simplest term of 9m-2(3m-1)
Answers
Answer:
[tex]3m+2[/tex]
Step-by-step explanation:
I'm assuming you mean: [tex]9m-2(3m-1)[/tex] and not: [tex](9m-2)(3m-1)[/tex]
So you simply need to know the Distributive Property, which allows you to expand out values being multiplied within parenthesis without adding the values first as such: [tex]A(B+C)=AB+AC[/tex]
Applying this to distribute the -2, we get: [tex]9m-6m+2[/tex]
Adding like terms we get: [tex]3m+2[/tex]
Find the areas of the figure. Area of Parallelogram, Trapezoid and Composite figure. Round to the nearest hundredth where necessary.
Answers
Let
A₁ be the area of the parallelogram
A₂ be the area of the trapezoid
Solving for the area of the parallelogram
Given the following dimensions
b = 23 cm
h = 14 cm
The area is solved using
[tex]\begin{gathered} A_1=bh \\ A_1=(23\text{ cm})(14\text{ cm}) \\ A_1=322\text{ cm}^2 \end{gathered}[/tex]The area of the parallelogram therefore is 322 square centimeters.
Solving for the area of the trapezoid.
Given the following dimensions
b₁ = 15 cm
b₂ = 34 cm
h = 19 cm
The area is solved using
[tex]\begin{gathered} A_2=\frac{b_1+b_2}{2}\cdot h \\ A_2=\frac{15\text{ cm}+34\text{ cm}}{2}(19\text{ cm}) \\ A_2=\frac{49\text{ cm}}{2}(19\text{ cm\rparen} \\ A_2=(24.5\text{ cm})(19\text{ cm}) \\ A_2=465.5\text{ cm}^2 \end{gathered}[/tex]The area of the trapezoid is 465.5 square centimeters.
Solving for the area of the composite figure.
Get the sum of the two areas to get the area of the composite figure, we have
[tex]\begin{gathered} A_{\text{total}}=A_1+A_2 \\ A_{\text{total}}=322\text{ cm}^2+465.5\text{ cm}^2 \\ A_{\text{total}}=787.5\text{ cm}^2 \end{gathered}[/tex]Therefore, the area of the composite figure is 787.5 square centimeters.
Use the quadratic formula to solve the problems. Then state whether the roots are real number roots or complex number roots.
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
Solving the quadratic equation using the quadratic formula, we have that:
From the solution above, we can see that the roots are complex.
[tex]\begin{gathered} \text{The roots of the equation are:} \\ x\text{ = }\frac{-5}{4}\text{ + i }\frac{\sqrt[]{31}}{4}, \\ x\text{ =}\frac{-5}{4}-i\frac{\sqrt[]{31}}{4} \end{gathered}[/tex]