In order to prove that there are only four of these triangles, we need to first restate the formula for the perimeter of a triangle which is given as: P = a + b + c. Hence, we must identify all the triangles that have two or more equal sides, and each side is a whole number.
What is the proof?
Step 1 - First, we state all the possible combination three whole numbers which when added together result in fifteen.
The numbers are given as:
1 1 132 2 113 3 94 4 75 5 56 6 37 7 1Step 2 - Eliminate options where a side is more than the sum of the other two sides
Hence,
are eliminated. The remaining triangles are four in number.
QED.
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find xif S is between R and T, RS=2x+3, ST=4x, and RT=63
Answer:
x = 10
Step-by-step explanation:
If S is between R and T, then RS + ST will be equal to RT.
See image.
Use this idea to write an equation.
2x + 3 + 4x = 63
Combine like terms, Subtract 3, Divide by 6, to solve for x. See image.
quadrilateral PQRS is transformed to create quadrilateral P’Q’R’S
Answer:
D
Step-by-step explanation:
Reflection over the X-axis
All point passes, (x,-y)
Answer:
D.
Step-by-step explanation:
Reflection over the x-axis because the quadrilateral reflected.
Frank bought 6 pens and 3 highlighters in the school store and paid $21 for the whole purchase. His friend , Andy paid $19 for 2 pens and 4 highlighters. If all pens cost the same and all highlighter cost the same, what is the price of one pen?
The price of one pen will be $1.5 and one highlighter is $4.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
Frank bought 6 pens and 3 highlighters in the school store and paid $21 for the whole purchase.His friend, Andy paid $19 for 2 pens and 4 highlighters.The cost of the pen and the highlighter will be calculated by forming the two expressions from the given data in the question the expressions are as follows:-
6p + 3h = 21
2p + 4 h = 19
Solving the above linear equations by elimination method:-
( 6p + 3h = 21 ) x 2
( 2p + 4 h = 19 ) x 6
The new equations are:-
12p + 6h = 42
12p + 24h = 114
Substracting the below equation from the above equation we will get:-
6h - 24h = -72
-18 h = -72
h = $4
Put the value of h in any of the above equations:-
2p + 4 h = 19
2p + 4 ( 4 ) = 19
2p + 16 = 19
p = 3 / 2
P = $1.5
Therefore the price of one pen will be $1.5 and one highlighter is $4.
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Use the standard deviation values of the two samples to find the standard deviation of the sample mean differences.
The standard deviation of the sample mean differences is; 0.6898
How to find the standard deviation of the mean differences?
From online research, the sample size of the session regarding the number of people who will purchase the red box is; N₁ = 45
From online research, the sample size of the session regarding the number of people who will purchase the blue box is; N₂ = 60
Formula for standard deviation of the sample mean differences is;
σm₁ - σm₂ = √[(σ₁²/n₁) + (σ₂²/n₂)]
Thus;
σm₁ - σm₂ = √[(3.868²/45) + (2.933²/60)]
σm₁ - σm₂ = 0.6898
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how would you solve for the missing value in a proportion?
Answer:
a/b = c/d
a*d = b*c
Ex:
a/2 = 2/4
4a = 4
a = 1
1/2 = 2/4
10 POINTS, please explain your answer ik so confused about how to get surface areas ty lol
Step-by-step explanation:
since there is triangle , you use the formula
1/2 × b × h
as you can see the base is 6 and the height is 4, so
1/2 × b × h
= 1/2 × 6 × 4
=12
12 × 2 = 24 , you times by 2 because there is 2 triangle
There is also rectangle in the diagram, so you use the formula , length × breadth , the length is 8 and the breadth is 5, so
length x breath
= 5 × 8
=35
35 × 2 = 70 , times by 2 because you can see 2 rectangles with the same length and breadth
length x breath
= 8 × 6
= 48
this one is different because the length is 8 and the breadth is 6.
SA = 48 + 35 + 24
= 107 cm ²
Sorry for my bad eng ,its not my first language.
Katrina lives directly east of the park. The football field is directly south of the park. The
library sits on the line formed between Katrina's home and the football field at the exact point
where an altitude to the right triangle formed by her home, the park, and the football field
could be drawn. The library is 4 miles from her home. The football field is 18 miles from the
The distance between library and park is 6√2 miles and the distance between park and field is 6√11 miles.
What is Similar Triangle?Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.
Here, mark the park as A, Home as B, Library as C and field as D.
Now, CD = 18 miles
BC = 4 miles
we have to find AC (distance between library and park)
BD = BC + CD = 18 + 4 = 22 miles
Using property of similar triangles,
AD² = BD X CD
AD² = 22 X 18
AD = √22 X √18
AD = 6√11 miles
By Pythagoras theorem,
AD² = AC² + CD²
396 = AC² + 324
AC² = 396 - 324
AC² = 72
AC = √72
AC = 6√2 miles
Thus, the distance between library and park is 6√2 miles and the distance between park and field is 6√11 miles.
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Use the equation of y = 1.5x +5 to predict the amount of milk needed for a 17-pound goat and a 55-pound goat
The amount of milk needed for a 17-pound goat and a 55-pound goat are 55 and 87.5 cubic units, respectively
How to determine the amount of milk?The equation is given as:
y =1.5x + 5
For a 17-pound goat, we have:
x = 17
This gives
y =1.5 * 17 + 5
y = 30.5
For a 55-pound goat, we have:
x = 55
This gives
y = 1.5 * 55 + 5
y = 87.5
Hence, the amount of milk needed for a 17-pound goat and a 55-pound goat are 55 and 87.5 cubic units, respectively
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PLEASE HELP ASAP MARKING BRAINLEIST + 50 POINTS
Answer:
scale factor = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{V'W'}{VW}[/tex] = [tex]\frac{1}{5}[/tex]
Abby is making a necklace that is 16 1/2 inches long. She is placing a colorful bead every 3/8 inch. How many beads will she need to make the necklace?
Answer:
44
Step-by-step explanation:
16.5 / 3/8 = 44
she will need 44 beads to complete that necklace
PLEASE HELP simplify (-2)(-3)^2-2(2-5)
Answer: -12
Step-by-step explanation: When solving this problem, PEMDAS is a key component. What is PEMDAS?
PEMDAS stands for the following:
P- Parentheses
E- Exponents
M-Multiplication
D- Division
A-Addition
S-Subtraction
This is also known as order of operations. Following this order, we can easily simplify the problem.
P-Parentheses
(-2)(-3)^2-2(2-5)
Our parentheses is (2-5). We can simply this to -3. Our problem now is
(-2)(-3)^2-2(-3)
E-Exponents
We have one set of exponents in this. It is -3^2. This simplifies to 9. Our problem now is
(-2)(9)-2(-3)
M- Multiplication
We can simply to.
-18+6
These simplifies into
-12
Answer:
-12
Step-by-step explanation:
-2*9-2(2-5) : Raise -3 to the power of 2
-18-2(2-5) : Multiply -2 by 9
-18-2*-3 : Subtract 5 from 2
-18+6 : Multiply -2 by -3
-12 : Add -18 and 6
Otto used 5.5 cups of whole wheat flour and X cups of white flour in the recipe what is the equation that can be used to find the value of y the total amount of flour that Otto  used in the recipe and what are the constraints  on the values of X and y
The solution to the equation is y = 5.5 + x , for any real number x greater than or equal to zero and y any real number greater than or equal to 5.5.
Analysis:
since number of items cannot be negative x and y are real number numbers since y or x can be a decimal so we do not use integers alone.
so y = 5.5 + x , for any real number x greater than or equal to zero and y any real number greater than or equal to 5.5.
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Answer: C
Step-by-step explanation:
If EFGH is a parallelogram, what is the value of x?
F
(4x-2)
34
G
E
H
A. 34
OB. 30.5
OC. 36
D. 82
OE. 37
OF. 9
Based on the property of the consecutive angles of a parallelogram, the value of x is calculated as: E. 37.
What are the Properties of the Angles of a Parallelogram?In a parallelogram, the angles that are opposite to each other are congruent while consecutive angles are supplementary.
Angles F and G are consecutive angles and are therefore supplementary (have a sum of 180 degrees.)
Angle F + angle G = 180
4x - 2 + 34 = 180
4x + 32 = 180
4x = 180 - 32
4x = 148
x = 148/4
x = 37
Value of x is: E. 37.
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What is the area of the following circle? Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal. d=10
the applicants for a soccer coaching position were asked how many years of coaching experience they had. here are the resuts 1,2,2,2,2,4,4,5,5,6,8,8,8,10
Answer:
Mean: 4.7
Mode: 2
Median: 4.5
Step-by-step explanation:
2. At the beginning of a trip, the odometer on a car reads 30,680 and the
car has a full tank of gas. At the end of the trip, the odometer reads
30,970. It takes 20 gallons of gas to refill the tank.
a. What is the average rate of change of the number of miles with respect
to the number of gallons?
3. The total number of words M(t) that a person can memorize in time t, in
minutes, is shown in the following table
t
8 16 24 32 36
M(t) 10 20 25 25 25
a. Find the average rate of change of M as t changes from 8 to 16.
b. Find the average rate of change of M as t changes from 16 to 24.
c. Find the average rate of change of M as t changes from 24 to 32.
The average rate of change of the number of miles with respect to the number of gallons is 14.5 miles per gallon
How to determine the average rate of change?The given parameters can be represented as:
M(0) = 30680
M(20) = 30970
The average rate of change is calculated as:
M'(t) = (M(20) - M(0))/(20 - 0)
This gives
M'(t) = (30970 - 30680)/(20 - 0)
M'(t) = 14.5
Hence, the average rate of change of the number of miles with respect to the number of gallons is 14.5 miles per gallon
The average rate of change of M as t changes from 8 to 16.
This is calculated using
M'(t) = (M(16) - M(8))/(16 - 8)
M'(t) = (20 - 10)/(16 - 8)
M'(t) = 1.25
The average rate of change of M as t changes from 16 to 24.
This is calculated using
M'(t) = (M(24) - M(16))/(24 - 16)
M'(t) = (25 - 20)/(24 - 16)
M'(t) = 0.625
The average rate of change of M as t changes from 24 to 32.
This is calculated using
M'(t) = (M(32) - M(24))/(32 - 24)
M'(t) = (25 - 25)/(32 - 24)
M'(t) = 0
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Point M(5, 2) is the midpoint of segment XY. Point X has coordinates
(-4, 6). Find the coordinates of point Y
Please help!
Answer:
(14, -2)
Step-by-step explanation:
The coordinates of the midpoint is equal to the mean of the coordinates of the endpoints.
=============================================================
Solving :
⇒ 5 = -4 + x / 2
⇒ x - 4 = 10
⇒ x = 14
⇒ 2 = 6 + y / 2
⇒ y + 6 = 4
⇒ y = -2
===========================================================
Coordinates of Point Y :
⇒ Y = (x, y)
⇒ Y = (14, -2)
Answer:
Y (14, - 2 )
Step-by-step explanation:
using the midpoint formula for (x₁, y₁ ) and (x₂, y₂ ) , then
midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1+y_{2} } }{2}[/tex] )
equating the x- coordinates and the y- coordinates
let coordinates of Y = (x, y )
[tex]\frac{x-4}{2}[/tex] = 5 ( multiply both sides by 2 )
x - 4 = 10 ( add 4 to both sides )
x = 14
and
[tex]\frac{y+6}{2}[/tex] = 2 ( multiply both sides by 2 )
y + 6 = 4 ( subtract 6 from both sides )
y = - 2
coordinates of Y = (14, - 2 )
Evaluate using the given value: y+9-x; use x=1, and y=3
[tex]y+9-x =[/tex]
[tex]x=1 \\ y=3[/tex]
[tex]3 +9 -1=11[/tex]
Answer:
y+9-x = 3+9-1 which would end up equaling: 11
9-1=8+3=11
please help because I don’t know!!
Answer:
Step-by-step explanation:
Comment
There was a flat fee of 10 dollars
Each 1/4 hour brought in 3,75
The total charge was 55 dollars.
Equation
Charge = 10 + 4*3.75*x as an hourly rate,
Solution
55 = 10 + 4*3.75x Combine
55 = 10 + 15x Subtract 10 from both sides
55-10= 10-10 + 15x
45 = 15x Divide by 15
45/15 = 15x/15
x = 3 hours
Answer 3 hours
Answers need to be fractions, if they are not whole numbers. No decimals
y=−4x−10
Slope of lines parallel to line
Slope of lines perpendicular to line
5x+5y=0
-8x+y=36
I need help with this.
Answer:
x= -4, y = 4.
Step-by-step explanation:
first, divide the first equation by its G.C.D (5), to obtain its simplest form.
5x/5 + 5y/5 = 0/5 to obtain x + y = 0.
Then, find the value of y by rearranging the second equation.
y = 36 + 8x. (Rem; when 8x moves to the other side of the equation, it changes the sign)
Now substitute the value of y (36 + 8x) in the first equation which is x + y = 0.
x + 36+8x = 0
Put like terms together.
36 + 9x = 0
move 9x to the other side and change its sign.
36 = -9x
divide both sides by 9,
x = -4.
Lastly, find the value of y by replacing the value of x in either equation.
-8(-4) + y = 36
32 + y = 36
rearrange to obtain
y = 36 - 32
y = 4.
9(w – 4) – 7w = 5(3w – 2)
Answer:
-2 =w
Step-by-step explanation:
9(w – 4) – 7w = 5(3w – 2)
The first step is to distribute
9w -36 - 7w = 15w -10
Combine like terms
2w -36 = 15w -10
Subtract 2w from each side
2w -36 -2w = 15w-10-2w
-36 = 13w -10
Add 10 to each side
-36+10 =13w-10+1-
-26 = 13w
Divide by 13
-26/13 =13w/13
-2 =w
Segment Given: BA= BC and DA= EC
Proofs
Prove: BD BE
Statements
BA BC 3 DA FC. Given
BDE BE
A
Reasons
Answer:
Step-by-step explanation:
[tex]1) \overline{BA} \cong \overline{BC}, \overline{DA} \cong \overline{EC} \text{ (given)}\\2) \overline{BD} \cong \overline{BE}[/tex] (congruent segments subtracted from congruent segments form congruent segments)
30 x 17 - ( 10 divided by 2 ) + 3 =
Answer:
508?
Step-by-step explanation:
what is this factor? simplify?...etc
Find the following measure for this figure.
Volume=
36 square units
24 square units
12 square units
these box plots show daily low temperatures for a sample of days in two different towns which statment is the most appropriate comparison of the centers
The correct statement about the center of both box plots is: the median for Town A, 30° is greater median for Town B, 25°
What is the correct statement?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile.
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what is the volume of a sphere with an 8 cm radius
Answer:
Approx. 2140.16 cubic centimeters
Step-by-step explanation:
[tex]Volume=\frac{4}{3}\pi r^{3} \\V=\frac{4}{3}(3.14)(8)^{3} \\V=4.18(8)^{3} \\V=4.18(512) \\V=2140.16[/tex]
Classify the following triangle. Check all that apply.
Answer:
The answer to the question is F
Step-by-step explanation:
Why it is an Scalene Triangle ,it because all the sides and angle are not equal
if the area of a square is 32ft how long is the diagonal?
Answer: 8
Step-by-step explanation:
To find the diagonal, we need to use two formulas:
Area of a square: [tex]A = s^{2}[/tex] (Area = side * side)
Pythagorean Theorem: [tex]a^{2} +b^{2} =c^{2}[/tex]
Since every side of a square is the same:
[tex]a^2 = b^2\\a = b = \sqrt{32} \\a^{2} = 32\\b^2 = 32[/tex]
Our equation:
[tex]32 + 32 = c^2\\64 = c^2\\8 = c[/tex]
The picture below visually explains the problem
Hope this helps!
Timmy has forty-five cents in his pocket. How many different ways can he have forty-five cents in change using only quarters, dimes, and nickels?
Answer:
Hi,
number of ways: 8
Step-by-step explanation:
[tex]\begin{array}{|c|c|c|}Quater&dime&nickel\\------&---&---\\0&0&9\\0&1&7\\0&2&5\\0&3&3\\0&4&1\\1&0&4\\1&1&2\\1&2&0\\------&---&---\\\end{array}[/tex]