explain why the sum of two angles of any triangle always equals the exterior angle of the third.
Answer:
they are congruent
Step-by-step explanation:
b because a same size
see attached question please please help!!
Based on the size of the pool that Mr. DelGrande wants to build, the ratio of the Olympic pool to the smaller pool is 2.5:1 and the area of an Olympic pool is 1,250 m².
What is the ratio of the length of an Olympic pool to Mr. DelGrande's pool?The ratio of the pools is:
Olympic pool length : Mr. DelGrande pool
50 : 20
Simplest terms give:
50 / 20 : 20 / 20
2.5 : 1
What is the area of a regulation Olympic Pool?Given the area of Mr. DelGrande's pool, the area of an Olympic pool is:
= Ratio ² x Area of Mr. DelGrande pool
= 2.5² x 200
= 1,250 m²
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Marcus states that the polynomial expression 3x3 – 4x2y y3 2 is in standard form. ariel states that it should be y3 – 4x2y 3x3 2. explain which student is correct and why.
The correct student is Marcus because the power of the polynomial decreases till 0
How to determine the correct student?The polynomial expressions are given as:
Marcus: 3x³ - 4x²y + y³ + 2
Ariel: y³ - 4x²y + 3x³ + 2
The standard form of a polynomial with the variable x is:
P(x) = ax³ + bx² + cx + d
This means that the power of the polynomial decreases till it gets to 0
Using the above form as a guide, the correct student is Marcus.
Marcus is correct because the power of the polynomial decreases till it gets to 0
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For what values of x is x2-36=5x true? -9 and -4 -4 and 9 4 and -9 9 and 4.
Answer: -4 and 9
Step-by-step explanation:
You travel 10 miles north and then 3 miles west.
How many miles are you from your starting location?
Round your answer to the nearest tenth.
Which is the graph of the inequality?
3y−9x≥9
Number graph ranging from negative ten to ten on the x and y axes. A dotted line passes through (zero, negative two) and (five, negative three). The area above the line is shaded gray.
Number graph ranging from negative ten to ten on the x and y axes. A solid line passes through (negative one, zero) and (zero, three). The area to the left of the line is shaded gray.
Number graph ranging from negative twenty to twenty in increments of two on the x and y axes. A solid line passes through (zero, negative fourteen) and (two, zero). The area to the right of the line is shaded gray.
Number graph ranging from negative twenty to twenty in increments of two on the x and y axes. A dotted line with a positive slope is drawn in the fourth quadrant of the graph. The area above the line is shaded gray.
A solid line passes through (-1, 0) and (0, 3). The area to the left of the line is shaded gray.
How to get the graph of the inequality?
Here we have the inequality:
3y - 9x ≥ 9
First, we should isolate y on one side of the inequality.
3y ≥ 9x + 9
y ≥ 3x + 3
Then, the graph will be a solid line of the form:
y = 3x + 3
Where the line is solid because the points on the line are solutions, and we need to shade all the region above the line.
Also, notice that for the line:
y = 3x + 3
if x = -1 we have:
y = 3*(-1) + 3 = 0
if x = 0 we have:
y = 3*0 + 3 = 3
Then the line passes through (0, 3) and (-1, 0). So the correct option is the second one.
"Number graph ranging from negative ten to ten on the x and y axes. A solid line passes through (negative one, zero) and (zero, three). The area to the left of the line is shaded gray."
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Evaluate the expression when x = 4 and y = 5.
3x2 + 4y0 • x –1
Answer:
60
Step-by-step explanation:
The evaluated expression of 3x² + 4y⁰(x - 1) when x = 4 and y = 5 is 60.
What is Substitution?
Substitution simply means to put in place another. Therefore, let's substitute the value of x and y in the mathematical expression.
3x² + 4y⁰(x - 1)
Therefore,
y⁰ = 1
3x² + 4y⁰(x - 1)
3x² + 4y⁰(x - 1)
3x² + 4(x - 1)
3x² + 4x - 4
Therefore, when x = 4 and y = 5
3(4)² + 4(4) - 4
48 + 16 - 4 = 60
HOPE THIS HELPED!
Answer:
B
Step-by-step explanation:
A 15-foot ladder rest against a wall, The base of the ladder is 8 feet from the wall.
How far is the top of the ladder from the ground, Enter your answer as a decimal to the nearest tenth.
Can someone help I’ve been stuck on this question for almost a hour (please help).
Answer:
12.7
Step-by-step explanation:
Its a pythagerous question question
so if the ladder is 8 feet from the wall the base is 8
and the ladder is 15 foot and is the hypotemuse
so 15^2-8^2=161^2
The root of 161 = 12.69 rounded to 2 dp
so 12.7
The distance far the top of the ladder from the ground is 12.7 feet
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
We are given that;
Length= 15foot
Base= 8feet
Now,
In this case, the ladder is the hypotenuse, and the base and the height are the legs. So, we can write:
15^2 = 8^2 + h^2
where h is the height of the ladder from the ground. Solving for h, we get:
h^2 = 15^2 - 8^2
h^2 = 225 - 64
h^2 = 161
h = sqrt(161)
h = 12.688
Therefore, by Pythagoras theorem the answer will be 12.7 feet.
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Hugo lives in the northwest corner of Greene County, Lena lives 29 miles away in the southeast corner, and the office where they work is directly between them. On Monday, Hugo took the bus into work, taking a direct route at 32 miles per hour. Lena left at the same time, taking her car along a direct route at a speed of 36 miles per hour. The two coworkers arrive at the office at the same time. How long did the commute take? If necessary, round your answer to the nearest minute.
Using the relation between velocity, distance and time, it is found that the commute took 48 minutes.
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
[tex]v = \frac{d}{t}[/tex]
For Lena, we have that d = 29, v = 36, hence the time in hours is given by:
[tex]t = \frac{d}{v} = \frac{29}{36} = 0.8056[/tex]
In minutes, the time is given by:
tM = 0.8056 x 60 = 48.
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Round 7.09 to the nearest tenth
Answer:
7.1
Step-by-step explanation:
To round 7.09 to the nearest tenth, you must use the hundredths' place value of 7.09, which is 9 and equal or more than 5. Therefore, the tenths value of 7.09 increases by 1 to 7.1.
Round this number to the nearest one.
87.2
Answer:
i guess 87
Step-by-step explanation:
87.2
nearest must be 87
if 87.5
nearest is 88
See
The rule is If the number aside(right) to the number where to be rounded is less than 5 then it remains same else increases one
2<5So
it will yield as 87
This is a substitution problem
Julianna has thirty two pieces of candy in a candy jar. Julianna only has two kinds of candy,
jolly rangers and twix. For every four twix bars, she has two pieces of jolly rangers. How many
pieces of each candy are in the candy jar?
a. The number of twix bars is 21
b. The number of jolly rangers is 11.
Julianna has thirty two pieces of candy and has four twix bars for every two jolly rangers, we need to find the ratio of candy bars.
What is the ratio of candy bars?Let
x = number of twix bars and y = number of jolly rangers.Since for every four twix bars, she has two pieces of jolly rangers, the ratio of candy bars is
x:y = 4:2 = 2:1
a. Number of twix barsThe number of twix bars is 21
The number of twix bars x = ratio of twix bars/total ratio × total number of candy bars
So, x = 2/(1 + 2) × 32
= 2/3 × 32
= 64/3
= 21.33
≅ 21
So, the number of twix bars is 21
b. Number of jolly rangersThe number of jolly rangers is 11.
The number of jolly rangers y = ratio of jolly rangers/total ratio × total number of candy bars
So, y = 1/(1 + 2) × 32
= 1/3 × 32
= 32/3
= 10.66
≅ 11
So, the number of jolly rangers is 11.
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Match each equation with the number that makes it true.
the first equation is 15
the second equation is 3
the third equation is 17
the fourth equation is 7
the fifth equation is 6
the sixth equation is 50
the seventh equation is 2
the eighth equation is 5
the ninth equation is 11
the tenth equation is 31
Please can i have brainliest I did all answers correct I hope this helps you
Line segment AB has vertices A(-3, 4) and B(1, -2). A dilation centered at the orgin is applied to AB. The image has vertices A(-1, 4/3) and B(1/3, -2/3). What is tjr scale factor of the dilation?
1. 1/6
2. 1/3
3. 3
4. 6
Answer:
option 2
Step-by-step explanation:
consider the coordinates A (- 3, 4 ) and A' (- 1, [tex]\frac{4}{3}[/tex] )
since the dilatation is centred at the origin, then corresponding coordinates are multiples/ divisors of each other, then image to original gives scale factor.
scale factor = [tex]\frac{A'}{A}[/tex] = [tex]\frac{-1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] and [tex]\frac{\frac{4}{3} }{4}[/tex] = [tex]\frac{1}{3}[/tex]
similarly B (1, - 2 ) and B' ([tex]\frac{1}{3}[/tex], - [tex]\frac{2}{3}[/tex] )
[tex]\frac{\frac{1}{3} }{1}[/tex] = [tex]\frac{1}{3}[/tex] and [tex]\frac{-\frac{2}{3} }{-2}[/tex] = [tex]\frac{1}{3}[/tex]
Apply the means-extremes property to the ratios of the corresponding sides to determine if the polygons are similar. has sides of length 2 cm, 3 cm, and 3.5 cm. has sides of length 4 cm, 6 cm, and 7 cm.
The ratio of the sides of the triangles ΔABC and ΔDEF are constant that is 1/2. Then the triangles ΔABC and ΔDEF are similar triangles.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The triangles are given below.
The ratio of the sides of the triangles ΔABC and ΔDEF will be
AB / DE = BC / EF = CA / FD
2 / 4 = 3 / 6 = 3.5 / 7
1 / 2 = 1 / 2 = 1 / 2
The ratio of the sides of the triangles ΔABC and ΔDEF are constant that is 1/2. Then the triangles ΔABC and ΔDEF are similar triangles.
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The table below represents a breakdown of food costs for Eddie, a traveling
salesman. How much did he spend in total for food on Tuesday?
Mon.
Tue.
Wed.
Thurs.
Fri.
Breakfast $7.88
$12.02
$9.64
$6.98
$13.30
Lunch
$13.41
$11.79
$14.55
$16.09
$10.76
Dinner
$18.80
$22.13
$20.79
$24.82
$16.74
OA. $40.09
OB. $42.56
OC. $41.23
OD. $45.94
SURMIT
The total amount of money that was spent on lunch on Tuesday is $45.94.
What is the total amount spent on food?
The total amount that was spent on food on Tuesday can be determined by adding the amount spent on breakfast, lunch and dinner. Addition is the mathematical operation that is used to determine the sum of two or more numbers.
Total amount spent = 22.13 + 12.02 + 11.79 = $45.94
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You start at (8, 0). You move right 2 units. Where do you end?
Answer:
(10,0)
Step-by-step explanation:
Moving right 2 units will increase the x value by 2 since you are going further 'down the corridor'. Hope this helps.
Please help!! <333
Hurry
Answer:
159.25cm²
Step-by-step explanation:
A=lw
A=12×10cm
The rectangle’s area is 120cm²
First, substitute the given information into the equation for the area of a circle.
A=πr²
A=(3.14)(5²)
A=3.14×25
A=78.5
Next, because the figure is only half of a circle, divide this in two.
78.5/2= 39.25cm²
Asc=39.25cm²
Add the two areas together.
A=Ar+Asc
120cm²+39.25cm²
The area of the combined figure is 159.25cm²
Two spinners are used in a game. Each spinner has four equal sections: red, green, white, and blue.
Create an organized list showing all the possible outcomes after both spinners are spun. Use R to represent red, G to represent green, W to represent white, and B to represent blue. Explain how to find the total number of outcomes from the list.
The total number of outcomes is 16 if the two spinners are used in a game. Each spinner has four equal sections: red, green, white, and blue.
What are permutation and combination?A permutation can be defined as the number of ways a set can be arranged, order matters, but in combination, the order does not matter.
Total number of outcomes on the first spinners = 4 (red, green, white, blue)
Total number of outcomes on the second spinners = 4 (red, green, white, blue)
Total number of outcomes = 4×4 = 16
Total outcomes:
RR RG RW RB
GR GG GW GB
WR WG WW WB
BR BG BW BB
Thus, the total number of outcomes is 16 if the two spinners are used in a game. Each spinner has four equal sections: red, green, white, and blue.
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Im Not Sure of this. Can I get some help?
Answer: The amount of grain it can hold can also be called it's volume. 423.9
The formula for volume is PI × Raduis² × Height
And for the radius we divide the diameter by 2.
Answer:
Option A.
V = π × r(9)² × 15 ≈ 3,817.04
Which rounds closest to
3,815.10 inches
Which explicit function defines this arithmetic sequence?
-351, -343, -335, -327, -319
A.
f(n) = 8n − 351
B.
f(n) = -8n − 351
C.
f(n) = 8n − 359
D.
f(n) = -8n + 359
Answer:
C. f(n) = 8n − 359
Step-by-step explanation:
The given arithmetic sequence has first term -351, and common difference (-343 -(-351)) = 8. The common difference will be the multiplier of n in the explicit function.
__
You can identify the appropriate explicit function by finding the one that correctly describes the sequence. Evaluating each for n=1 is sufficient. (You will note that choices B and D have the wrong sign on the multiplier of n.)
A f(1) = 8 -351 = -343
B f(1) = -8 -351 = -359
C f(1) = 8 -359 = -351 . . . . correctly gives the first term
D f(1) = -8 +359 = 351
The sequence is defined by the explicit function ...
f(n) = 8n -359
Answer:A:f(n)=8n-359
Step-by-step explanation:
what is 40% of 526,367.50
Answer:
[tex]210547[/tex]
Hope this helps. :)
Answer:
210547
Step-by-step explanation:
Multiply 526, 367.50 by 40 percent than the answer you get from that subtract from 526,367.50 then you get 210547.
Hope this Helps!
:D
THIS IS EASY BUT PLEASE HELP ME IM BIT SLOW
Answer:
A: Isosceles (two sides the same)
B: Equilateral (all sides the same)
C: Scalene (all sides different)
Step-by-step explanation:
The egg delivery truck arrives to savers supermarket with 250 dozen eggs. how many total eggs are in that truck.
Answer:
3000
Step-by-step explanation:
12x250=3000
solve the system using substitution. show all work
Help me with this question please
An associate in a scatter plot tells us the relation between the two variables. The points that are true about the given scatter plot are C and F.
What is an associate?An associate in a scatter plot tells us the relation between the two variables. There are 4 types of associates:
Positive associate: If the value of one variable is increasing the value of another increase as well, but the relation is not linear.
Negative associate: If the value of one variable is decreasing with the value of another increasing as well, but the relation is not linear.
Linear Associate: If the value of one is dependent on the other such that they follow a function of line, and all the data points are on that function line.
Non-linear Associate: If the data points of the plot are scattered and random, such that there is no relationship between the points.
The points that are true about the given scatter plot are:
C.) There appears to be a positive association.
F.) A cluster appears to be at the bottom left corner.
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pls help, full explanation pls
Step-by-step explanation:
Apply exponent rule: (a. b)^n= a^n b^n
=3²(x¹⁰)²(y⁴)²
3²=9
=9(x¹⁰)²(y⁴)²
break =9(x¹⁰)²(y⁴)² into two
simplify (X¹⁰)² = (x²⁰)
simplify (y⁴)²=(y⁸)
=9(x²⁰)(y⁸)
Jacob opens a savings account for a vacation with $200.50. Jacob wants to have at least $856.90 in the account in 4 weeks. What is the minimum amount Jacob should save per week to meet his goal? Enter your answer in the box.
Answer:
x = 164.10
Step-by-step explanation:
translated question says :
200.50 + 4x = 856.90
4x=656.40
x = 164.10
Help please
5x-2y=-10
Answer:
[tex]5x - 2y = - 10 \\ 5x = - 10 + 2y \\ x = \frac{ - 10 + 2y}{5} \\ \\ [/tex]
when y=0,-5,5,-10,10
then x=-2,-4,0,-6,2
5. A sum of money is divided among Ethan, Jun Wei
and Raj in the ratio 5:6:9. After Ethan gives $50
Find the amount of money Ethan has after giving
to his mother, the ratio becomes 3:4:6.
$50 to his mother.
(Step by step explain pls)
Answer:
$450
Step-by-step explanation:
Let E be the amount of money Ethan starts with, J be the amount Jun Wei starts with, and R be the amount Raj starts with. Let M be the total amount of money to start with.
To start:
[tex]E:J:R = 5:6:9[/tex]
This means Ethan has 5/20 of M, the money to start with. This reduces to 1/4 of M.
Afterwards:
[tex](E-50):J:R = 3:4:6[/tex]
This means Ethan has 3/13 of the remaining money (which is M-50!) after giving up 50. So
E = (M/4), or 4E = M
and
[tex](E - 50) = 3/13 * (M - 50)[/tex]
We know 4E = M, so we can substitute that in:
[tex](E - 50) = 3/13 * (4E - 50)E - 50 = (12/13)E - 150/13E - 650/13 = (12/13)E - 150/13(1/13)E = 500/13E = 500[/tex]
That's how much money Ethan had to start with. But we're asked how much he has AFTER giving $50 away, so that's $450.