Find the distance between the
following points using the
Pythagorean theorem: (5, 10)
and (10, 12)
Answer:
[tex]\displaystyle d = \sqrt{29}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]Step-by-step explanation:
*Note:
The distance formula is derived from the Pythagorean Theorem.
Step 1: Define
Identify
Point (5, 10)
Point (10, 12)
Step 2: Find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(10 - 5)^2 + (12 -10)^2}[/tex][√Radical] (Parenthesis) Subtract: [tex]\displaystyle d = \sqrt{5^2 + 2^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{25 + 4}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{29}[/tex]The length of a rectangle is 3 times the width. The perimeter of the rectangle is 64 cm. Show the equation that would be used to find the dimensions of the rectangle.
Answer:
64 = 2(3x + x)
Step-by-step explanation:
Perimeter of the rectangle = 64 cm
Width of the rectangle = x
Length of the rectangle = 3x
Perimeter of a rectangle = 2(length + width)
The equation is
64 = 2(3x + x)
64 = 6x + 2x
64 = 8x
x = 64/8
x = 8 cm
Width of the rectangle = x = 8 cm
Length of the rectangle = 3x
= 3(8 cm)
= 24 cm
Give the order of symmetry from the fig 3
a)2
b)3
c)6
d)4
C=-(251x3+281)+3X251-(1-281)
Answer:
-1
Step-by-step explanation:
=-251x3+281 +251x3-1+281
=-1
Question 6 of 25
In APQR, m P= 60°, m_ Q = 30°, and m2 R = 90°. Which of the following
statements about APQR are true?
Check all that apply.
Answer:
A, E, F
Step-by-step explanation:
From the angles given, we can infer that ΔPQR is a 30-60-90 special triangle. In a 30-60-90 triangle, the leg opposite the 30 degree angle is 1/2 the hypotenuse and the leg opposite the 60 degree angle is √3 times the one opposite the 30. Using this, we can say:
PR = 1/2 PQ which is just 2 PR = PQ(E)
PR √3 = QR (A)
We can substitute in PR from the first equation to the second to get:
√3/2 PQ = QR(F)
Find the value of both variables.
[tex] \cos(45) = \frac{5 \sqrt{2} }{x} \\ \frac{1}{ \sqrt{2} } = \frac{5 \sqrt{2} }{x} \\ x = 10 \\ \\ \tan(45) = \frac{y}{5 \sqrt{2} } \\ 1 = \frac{y}{5 \sqrt{2} } \\ y = 5 \sqrt{2} [/tex]
I hope I helped you ^_^
6.7.35
Question Help
As(t)
800-
A toy rocket is launched from the top of a building 360
feet tall at an initial velocity of 112 feet/second. The
height of the rocket t seconds after launch is given by
the equation s(t)= - 16t2 + 112t+ 360. When does the
rocket reach its greatest height? What is the greatest
height?
600-
400-
200-
0-
0 1
8 9 10
The rocket reaches its greatest height at
feet after
second(s)
Answer:
Step-by-step explanation:
This is most easily solved with calculus, believe it or not. It is way more direct and to the point, with a whole lot less math!
The position function is given. The velocity function is the first derivative of the position, so if we find the velocity function and set it equal to 0, we can solve for the amount of time it takes for the rocket to reach its max height. Remember from physics that at the top of a parabolic path, the velocity is 0.
If:
[tex]s(t)=-16t^2+112t+360[/tex], then the velocity function, the first derivative is:
v(t) = -32t + 112 and solve for t:
-112 = -32t so
t = 3.5 seconds. Now we know how long it takes to get to the max height, we just need to find out what the max height is.
Go back to the position function and sub in 3.5 for t to tell us that position of the rocket at 3.5 seconds, which translates to the max height:
[tex]s(3.5)=-16(3.5)^2+112(3.5)+360[/tex] and
s(3.5) = 206 feet. I imagine that your answer, if you had to choose one from the list, would be 200 feet, rounded a lot.
aint the answer for this 10 just let me if im wrong
Answer:
Yup
Step-by-step explanation:
Solve the equation for x: (4x+38) + (2x-18)=180
Answer:
80/3
Step-by-step explanation:
try mathw4y it helps alot.
Answer:
x = 80/3
Step-by-step explanation:
(4x+38) + (2x-18)=180
Combine like terms
6x +20 = 180
Subtract 20 from each side
6x+20 -20 = 180-20
6x = 160
Divide by 6
6x/6 = 160/6
x = 80/3
Find the slope
of the line passing through the points (3, 4)
and
(8, -3).
Answer:
-7/5
Step-by-step explanation:
I think let me know
Answer:
7/-5 or -7/5
Step-by-step explanation:
This shall be quite an easy problem, I shall be doubting that this is high school, however, I am happy to aid :)
We shall begin by labeling the points given to us to prepare for inputting the values in the slope formula
(3,4). (8,-3)
x1,y1 x2,y2
Slope Formula:
y1 - y2
x1 - x2
Inputting the values:
4 - (-3)
3 - 8
Solve:
7
-5
The slope of the line passing through the points (3,4) and (8,-3) shall be 7/-5 or -7/5 negatives shall go both ways of fractions
A machine with velocity ratio of 5 is used to raise a load with an effort of 500N . If the machine is 80% efficient , determine the magnitude of the load.
Answer:
Solutions given:
Velocity ratio V.R =5
effort =500N
efficiency =80%
magnitude of load=?
mechanical advantage [M.A ]
we have
efficiency =M.A/V.R*100%
80=M.A./5*100
80/100*5=M.A
M.A.=4
again
we have
M.A =load/effort
4=load/500
load=500*4
load=2000N
the magnitude of the load is 2000N.Instructions: Point T is the centroid. Find TE if XE= 21.
Answer:
TE = 7
Step-by-step explanation:
The centroid divides a median in this ratios 1/3 and 2/3. In particular
XT = 2/3 XE
XT = 2/3 * 21
XT = 14
TE = 7
similar right triangles, i need help with this please
Answer:
Step-by-step explanation:
the answer is a)
Choose the graph that correctly corresponds to the equation y = −4
Answer:
e
Step-by-step explanation:
the graph should look something like this
The measure of two complementary angles are 2x degree and 3x degree, then value of x is
Answer:
2x+3x=90
or ,5x=90
or,x=90/5
X=18
Answer:
90/5=18 degrees
Step-by-step explanation:
Please help me solve this
Answer:
The 2nd one is 3x+1
The 3rd answer is x+3
Step-by-step explanation:
Given g(x)=4x-1 and f(x)=x-2
Subtracting both
4x-1-(x-2)=4x-1-x+2=x(4-1)+(2-1)=3x+1
The next one is 3x+1-(2x-2)=3x+1-2x+2=x+3
Finish the following table for the given function with x as the independent variable
Answer:
hi?
Step-by-step explanation:
The width of a rectangle is twice as long as the length. if the length is increased by 50% and the width is decreased by 20%, the perimeter becomes 248. find the width and length of the original rectangle.
Answer:
Step-by-step explanation:
The percents here make this more tricky than it originally seems to be. We'll make a table and see where it takes us:
original new
length
width
And we'll fill it in according to our rules given. Starting with the original, we are told that the width is twice as long as the length. We don't know the length, so we'll call that L, and if the width is twice that, the width is 2L:
original new
length L
width 2L
Now here's the tricky part. What I'm going to do is fill in the "new" column with the expressions and then we'll simplify them in the next step.
The length is increased by 50%. So we have 100% of the original length and we are adding another 50% to that:
original new
length L 100%L + 50%L
width 2L
The width is decreased by 20%, so we have 100% of 2L and we are subtracting 20% of 2L from that:
original new
length L 100%L + 50%L
width 2L 100%(2L) - 20%(2L)
And now we'll simplify that "new" column:
original new
length L 150%L = 1.5L
width 2L 80%(2L) = 160%L = 1.6L
Now we're ready for the perimeter part. The formula for the perimeter of a rectangle is P = 2L + 2w, so filling in from our "new" column, since 248 is the perimeter given for AFTER the rectangle's length and width are manipulated:
248 = 2(1.5L) + 2(1.6L) and
248 = 3L + 3.2L and
248 = 6.2L so
L = 40 and that means that w = 80 (because in the "original" column, the width is twice the length)
What is the area of this polygon
Answer:
51
Step-by-step explanation:
1. Approach
One is given the polygon, (ABCDE); the problem asks one to find the area of this polygon. The most logical step to take is to divide this polygon into easier parts, find the area of each part, and then add up the area to find the total area of the figure.
One way to divide this figure up is to draw the line (AC). This will create the triangle (ABC) and rectangle (ACDE).
2. Find the area of (ABC)
The formula to find the area of a triangle is the following:
[tex]A=\frac{b*h}{2}[/tex]
Where (b) is the base of the triangle, and (h) is the height. The base of the triangle (ABC) is (AC), which has a measure of (6) units. The height of the triangle is the distance from the base of the triangle to the vertex opposite the base. This measurement is (3) units. Substitute these values into the formula and solve for the area:
[tex]A=\frac{b*h}{2}[/tex]
Substitute,
[tex]A=\frac{6*3}{2}\\\\A=\frac{18}{2}\\\\A=9[/tex]
3. Find the area of (ACDE)
The formula to find the area of a rectangle is as follows:
[tex]A=b*h[/tex]
The base of the rectangle is the segment (AE), with a measure of (7) units. The height of the rectangle is the segment (AC) with a measurement of (6) units. Substitute these values into the formula and solve for the area:
[tex]A=7*6\\\\A=42[/tex]
4. Find the area of the total figure
To find the area of the total figure, add up the area of the triangle, and the area of the rectangle:
[tex]9+42= 51[/tex]
1. 80 = -10b
2. 6 = 2n
3. -16r = 32
1.
2.
3.
Answer:
1. - 8
2. 3
3. - 2
Step-by-step explanation:
1.
80 = - 10b
- 10b = 80
b = 80 / - 10
b = - 8
2.
6 = 2n
2n = 6
n = 6 / 2
n = 3
3.
- 16r = 32
r = 32 / - 16
r = - 2
Express 3.023 in P form where p and q are integers and q= 0 D
Given:
The number is 3.023.
To find:
The given number in the form of [tex]\dfrac{p}{q}[/tex], where [tex]q\neq 0[/tex].
Solution:
The given number is 3.023. It can be written as:
[tex]3.023=3.023\times \dfrac{1000}{1000}[/tex]
[tex]3.023=\dfrac{3023}{1000}[/tex]
It cannot be simplified further because 3023 and 1000 have no common factors.
Therefore, the given number 3.023 can be written as [tex]\dfrac{3023}{1000}[/tex].
Jack rides his bike 4 miles in 1/3 of an hour. What is jack unit rate in miles per hour?
Answer:
12 miles
Step-by-step explanation:
1/3 of an hour = 20 minutes = 4 miles
1 minute = 4/20 miles
60 minutes = 4/20 x 60 miles
= 4 x 3 miles
= 12 miles
60 minutes = 1 hour
=> 1 hour = 12 miles
Jacks unit rate is 12 miles/hr
Answer:
12
Step-by-step explanation:
There are two ways of doing this problem. I think the easiest way is to use a decimal in the denominator and round
4/0.333333333 = 12.000000001
The answer is obviously meant to be 12.
The other way is more sophisticated, but more accurate.
4/1 // 1/3 This is a 4 tier fraction. The rule is to invert the denominator (turn the bottom fraction upside down) and multiply.
4/1 * 3/1 = 12
The first method is easier to understand. The second is more accurate and more useful for physics.
Can someone please help me with this I’m struggling
Answer:
Equation: [tex]70=(x+3)x[/tex]
x = -10 or x = 7
x = 7 (width can't be negative)
x + 3 = 10
Step-by-step explanation:
Represent the width of the rectangle by x. "The length of a rectangle EXCEEDS the width by 3" means the length is 3 LONGER than the width, so the length is represented by the expression x + 3.
Area = (length)(width)
70 = (x + 3)x
Multiply out the right side.
[tex]70=x^2+3x\\x^2+3x-70=0[/tex]
Factor the left side.
[tex](x+10)(x-7)=0[/tex]
Each binomial could equal 0, so
[tex]x+10=0 \text{ or }x-7=0\\x=-10\text{ or }x=7[/tex]
The negative solution does not make sense as the width of a rectangle.
x = 7, making the length, x + 3 = 10
Answer:
Pls mark this as brainiest
Step-by-step explanation:
Area of the rectangle = length x breadth
consider 'x' to be width
therefore length = x+3
area = (x+3)*x
Area = 70 square
x = 7
x+3 = 7+3
= 10
verification
7 x 10
= 70
[tex]\text{Solve for 'x':}\\\\3(x+1)=12+4(x-1)[/tex]
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]x = -5[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'...}}\\\\3(x+1)=12+4(x-1)\\----------\\\rightarrow 3x + 3 = 12 + 4x - 4\\\\\rightarrow 3x + 3 = 12 -4+4x\\\\\rightarrow 3x + 3 = 8 + 4x\\\\\rightarrow 3x + 3 = 4x + 8\\\\\rightarrow3x + 3 -3 = 4x + 8 - 3\\\\\rightarrow 3x = 4x + 5\\\\\rightarrow 3x - 4x = 4x - 4x + 5\\\\\rightarrow -x = 5\\\\\rightarrow \frac{-x=5}{-1}\\\\\rightarrow \boxed{x = -5}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
x=-5Step-by-step explanation:
3(x+1)=12+4(x-1)
3(x+1)=8+4x
3x+3=8+4x
3x+3−4x=8
-x+3=8
-x=8-3
-x=5
-x(-1)=5(-1)
-x(-1)=-5
x=-5
What is the solution to this system of equations?
2x+y = 6
- - x - y = 2
0
0
(1, -1)
(0,8)
infinitely many solutions
no solution
Answer:
Step-by-step explanation:
{ 2/3 x+y=6
+
{ -2/3x-y=2
= 0=6
Hence,no solution.
Dan invests £18790 into his bank account. He receives 5.9% per year simple interest. How
much will Dan have after 2 years? Give your answer to the nearest penny where appropriate.
Answer: £21007.22
Step-by-step explanation:
First, find the interest amount using the formula SI = (P × R × T) / 100.
SI = interest amount P = principle amount = £18790R = interest rate(in percentage) = 5.9T = time(in years) = 2SI = (P × R × T) / 100 = (18790 × 5.9 × 2)/100 = 221722/100 = £2217.22
The total amount = principle amount + interest amount
= £18790 + £2217.22 = £21007.22
A diver begins at 140 feet below sea level. She descends at a steady rate of 7 feet per minute for 4.5 minutes. Then, she ascends 112.2 feet. What is her current depth?
Negative 549.3 feet
Negative 59.3 feet
59.3 feet
549.3 feet
Answer:
Step-by-step explanation:
starting point: 140 feet below sea level.=-140
she then decends= 7(4.5)=31.5
-140-31.5=-171.5
finally she ascends 112.2 feet
-171.5+112.2=-59.3 feet or 59.3 feet below sea level
Answer:
It's B
Step-by-step explanation:
ASAP HELP!! PLEASEEEE!!
Answer:
Step-by-step explanation:
5.1, please this is just a guess from using my head to calculate
(8) The average daily temperatures in July of some cities in Texas are shown in the table. Which
of the following fiets the cities from greatest temperature to least temperatura
City
Average Daily
Temperature
Austin
84.52F
Dallas
85.9°F
San Antonio
85 F
Fort Worth
85.31°F
a. Dallas, Fort Worth, San Antonio, Austin
b. Austin, Dallas, San Antonio, Fort Worth
c. Austin, San Antonio, Fort Worth, Dallas
d. Dallas, San Antonio, Fort Worth, Austin
Answer:
A.
Step-by-step explanation:
85.9 > 85.31 > 85 > 84.52
Dallas, Fort Worth, San Antonio, Austin
Second time posting this. Please help!! :)
Answer:
Step-by-step explanation:
[tex]\frac{480+24(x-40)}{x}[/tex]
The numerator of the rational expression the money he earned for 'x' hours
The rate at which William is paid for each hour in excess of 40 hours 24.
x = 50 hours = (40 + 10 ) hours
The amount paid for excess 10 hours = 24 *10 = 240
Total amount earned for the week = 480 + 240 = 720
