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Explanation:
Consider a triangle with side lengths a,b,c such that a < b < c
a = 3 and b = 19 are the two known sides
Let c be the missing side length
The missing side has the property that...
b-a < c < b+a
19-3 < c < 19+3
16 < c < 22
Meaning that if c is a whole number then it can take on any of these values {17, 18, 19, 20, 21}
So c = 21 is the largest possible third side, where only whole number sides are considered.
We can't have a third side of 22 because the two other sides add to a+b = 3+19 = 22 and a triangle wouldn't form (instead only a straight line would). I recommend cutting out strings of paper trying this out yourself.
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Side note: The inequality b-a < c < b+a is a variation of the triangle inequality theorem.
A salt mixture hss 7 parts water and 1 part salt. Suppose another part of salt is added. What is the new ratio of salt to water?
A) 7 to 1
B) 1 to 7
C) 2 to 7
D) 2 to 8
Answer:a
Step-by-step explanation:
Answer:
C) 2 to 7
Step-by-step explanation:
1 part salt:7 parts water
Add 1 part salt
2 part salt: 7 Parts water
UPS charges $7 for the first pound, and $0.20 for each
additional pound. FedEx charges $5 for the first pound and
$0.30 for each additional pound. How many pounds, p, will it
take for UPS and FedEx to cost the same?
george is going to rent a car for 10 hours to use for travel. he will figure his cost by using the chart below. what is his cost for 10 hours?
Answer:
Where's the chart?
Step-by-step explanation:
What value of p makes the equation true?
-3p+1/8=-1/4
Answer:
p= 1/8 or p= 0.125
Step-by-step explanation:
If f(x) = 2x2 − 30, find f(4).
a. 35
b. −14
c. 2
d. 17
Answer:
2
Step-by-step explanation:
i took the test
Question 30
A person standing 44 feet from a street light casts a shadow as shown. What is the height h of the street light? Assume the triangles
are similar.
Please help!!!
Answer:
a. 26 ft
Step-by-step explanation:
When triangles are similar their sides are proportional
4/8 = h/(44+8)
1/2(52) = h
h = 26
∆ABC is translated 2 units down and 1 unit to the left. Then it is rotated 90° clockwise about the origin to form ∆A′B′C′. The coordinates of vertex A′ of ∆A′B′C′ are . The coordinates of vertex B′ of ∆A′B′C′ are . The coordinates of vertex C′ of ∆A′B′C′ are .
Answer:
A'(-2, 1), B'(1, 0), C'(-1, 0)
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, dilation and translation.
If a point X(x, y) is translated a units right and b units down, the new location is X'(x + a, y + b) whereas if a point X(x, y) is translated a units left and b units up, the new location is X'(x - a, y - b).
If a point X(x, y) is rotated 90° clockwise about the origin, the new location is X'(y, -x)
From the image attached, ∆ABC is at A(0, 0), B(1,3) C(1, 1)
If ∆ABC is translated 2 units down and 1 unit to the left (x - 1, y - 2), the vertices would be A*(-1, -2), B*(0, 1), C*(0, -1)
If it is then rotated 90° clockwise about the origin, the new location is A'(-2, 1), B'(1, 0), C'(-1, 0)
Answer:
The coordinates of vertex A′ of ∆A′B′C′ are (-2, 1) .
The coordinates of vertex B′ of ∆A′B′C′ are (1, 0) .
The coordinates of vertex C′ of ∆A′B′C′ are (-1, 0) .
Step-by-step explanation:
3x+29>4(x+7)
how do I solve this and the answer is NOT x<8 the answer is supposed to be x<1 but I don't know how to get there.
Mr. Davis has 30 baseballs and 12 footballs. What is the ratio of all balls
to baseballs?
Answer: 5:2 Ratio
Step-by-step explanation:
Answer:
8:5
Step-by-step explanation:
total no of balls= 30+12=42
ratio of all ball to baseballs= 42:15
simplified it would be= 8:5
what is the y-intercept of the graph of the equation 3x+y=6
Answer:
Slope: − 3
y-intercept: ( 0 , 6 )
Step-by-step explanation:
Use the slope-intercept form y = m x + b to find the slope m and y-intercept b .
What the is mean absolute deviation of these numbers: 10 4 2 4?
Answer: 4
Step-by-step explanation:
10 + 4 + 4 +2 = 20/4 = 4
what is x
8(3x+6)=168
Answer:
x=-5
Step-by-step explanation:
24x+48=168
24x-120
x=5
8(15+6)=168
120+48=168
168=168
Answer: 5
Step-by-step explanation: 8 (3x+6)= 168/ 8 (3 x5+6)= 168; so 8(3x5+6)=168
In February, you have a balance of $135 in your bank account. Each month you deposit $45. Write an equation to describe the situation.
Answer:
135+45x
Step-by-step explanation:
9 divided by 2,488 ??????
Answer: 0.0036173633440514 = [tex]\frac{9}{2,488}[/tex]
Answer:
00.0036173633
Step-by-step explanation:
use calculator
is -4 irrational or rational
Answer:
irrational
Step-by-step explanation:
Which equation represents a line with a slope
of 2 that passes through the point (1, 5)?
Answer:
y=2x+3
Step-by-step explanation:
Point-Slope Equation: y=m(x-x1)+y1
y=2(x-1)+5
2x-2+5
2x+3 (y=mx+b)
Are the two triangles similar? If so, state the reason and the similarity statement. (See attached image)
A. Yes; AA; ΔLFT ∼ ΔORT
B. The triangles are not similar.
C. Impossible to Determine
D. Yes; SSS; ΔLFT ∼ ΔORT
Answer: They are not similar
Step-by-step explanation: Only way is AAA and AAA doesn’t prove triangles congruent or similar
Option (C) impossible to determine is the correct answer.
What is triangle similarity?Two triangles are said to be similar, if corresponding sides of the two triangles has same ratio or the corresponding angles of the two triangles are equal.
For the given situation,
The diagram has two triangles but the length of the sides and the angles of the triangles are not provided. So we cannot find the similarity between these two triangles.
Hence we can conclude that option (C) impossible to determine is the correct answer.
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pleassssssssse help
Answer:
Positive; Negative
Step-by-step explanation:
That is what mine showed for the same question and answer options.
As x approaches positive infinity, m(x) approaches positive infinity.
As x approaches negative Infinity, m(x) approaches negative Infinity.
The function f(x) = x^3 has been transformed m(x) = 1/3x^3+ 6. Than the blank space to be field.
Range of the function is the output value of the function.
Here, f(x) = x^3 transformed to m(x) = 1/3x^3+ 6,
The range of the transformed function is given by for its Domain x = (-∞,∞) is (-∞, ∞).
Thus, the range of the of m(x) for x =(-∞, ∞) is (-∞, ∞).
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3 3/5 divided by 18/25
-18 (-3) answer explain
Answer:
54
Step-by-step explanation:
18(3) = 18+18+18 = 54
But remember that we have two negatives
When you multiply two negative numbers, they become positive, therefore your answer is 54
A square undergoes a dilation with k=3/5.
What is the ratio of the image area to the preimage area?
A. 3:5
B. 6:10
C. 9:25
D. Cannot be determined
SUPER EASY
How do I rewrite x + y = -3 in slope intercept form.
Answer:
y =-x-3
Step-by-step explanation:
slope intercept/ y-intercept form is y=mx+b
you have to isolate y here
x+y=-3 subtract x from both sides
y=-x-3
8(k - 6) +58 = 2(4k + 5)
one solution
no solutions
infinite solutions
Answer:
infinite solutions
Step-by-step explanation:
Given
8(k - 6) + 58 = 2(4k + 5) ← distribute parenthesis on both sides
8k - 48 + 58 = 8k + 10 , that is
8k + 10 = 8k + 10
Since both sides are equal then any value of x will make the equation true.
There are an infinite number of solutions
Which are the ordered pairs?
which value of n makes the equation true
Answer:
n = - 16
Step-by-step explanation:
What is 5 + 100 + 300,909,786
Answer:
300909891
Step-by-step explanation:
Answer:
300,909,891
Step-by-step explanation:
determine if the equation y=2/7x represents a direct variation
Answer:
Represents a direct variation
Step-by-step explanation:
y = 2/7x
To find x-intercept/zero, substitute
y = 0
0 = 2/7x
Multiply both sides of the equation by 7/2
0 = x
Swap the sides of the equation
x = 0
Solution
x = 0
This is a direct variation because when x = 0. Y has to = 0 as well and it is so that makes this equation a direct variation.
direct variation - mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other
(2n-9)-(-2.4n+4) Please help!
Answer: =4.4n-13
Step-by-step explanation:
Let's simplify step-by-step.
2n−9−(−2.4n+4)
Distribute the Negative Sign:
=2n−9+−1(−2.4n+4)
=2n+−9+−1(−2.4n)+(−1)(4)
=2n+−9+2.4n+−4
Combine Like Terms:
=2n+−9+2.4n+−4
=(2n+2.4n)+(−9+−4)
=4.4n+−13
Which recursive formula can be used to determine the total amount of money earned in any year based on the amount earned in the previous year?
f(n + 1) = f(n) + 5
f(n + 1) = 5f(n)
f(n + 1) = 1.05f(n)
f(n + 1) = 0.05f(n)
Answer:
f(n + 1) = 1.05f(n)
Step-by-step explanation:
The total amount of money earned in any year based on the amount earned in the previous year is f(n+1) = 1.05f(n).
What is annual interest rate?The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.
What is principal?Principal is the money that you originally agreed to pay back. Interest is the cost of borrowing the principal.
According to the question,
The annual interest rate is 5%
So, suppose the amount earned in the previous year is f(n).
The total amount of money earned in any year based on the amount earned in the previous year is
f(n+1) = f(n) + 5%f(n) (principal + interest)
f(n+1) = 1.05f(n)
Hence, the total amount of money earned in any year based on the amount earned in the previous year is f(n+1) = 1.05f(n).
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You send 12 text messages in one day. The total cost $2.28. How much does each text message cost
Answer:
.19
Step-by-step explanation:
Answer:
Step-by-step explanation:
2.28 divided by total messages
2.28÷12= 0.19
Correct answer 19 cents for each text.