Given :
In the early spring, the trout at Big Blue Lake swim at a depth of 30 feet below sea level.
When the lake warms up in the summer, the trout swim 20 feet deeper than that , d = 20 feet .
To Find :
At what position relative to sea level do the trout swim in the summer.
Solution :
Depth in spring from surface , [tex]D_s=30\ feet[/tex] .
Let , depth in summer is D .
Now , depth in summer relative to sea-level is :
[tex]D=D_s+d\\\\D=30+20\ feet\\\\D=50\ feet[/tex]
Therefore , trout swim 50 feet deep below the sea level in the summer .
Hence , this is the required solution .
Answer:
-50
Step-by-step explanation:
bcuz it is
Point g is on line segment FH. Given FG=5x+2, GH= 3x-1, and FH= 9, determine the numerical length of FG.
Answer:
Step-by-step explanation: fg + Gh = fh
8x+1=9
8x=8
X=1
The numerical length of the line segment FG is 7 units.
Given that, FG=5x+2, GH= 3x-1, and FH= 9.
We need to find the numerical length of FG.
What is a line segment?A line segment is a part of a line that has two endpoints and a fixed length. It is different from a line that does not have a beginning or an end and which can be extended in both directions.
Now, FH=FG+GH
⇒9=5x+2+3x-1
⇒8x+1=9
⇒8x=8
⇒x=1
So, FG=5x+2=7
Therefore, the numerical length of the line segment FG is 7 units.
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The function f is defined by the following rule.
f(x) = 3x - 3
Complete the function table,
X
- 4
2
5
3/5(1 + p) = 21/20
find the solution to p
Answer:
3/4
Step-by-step explanation:
3/5(1+p)-21/20
3/5+3/5p=21/20
3/5p=21/20-3/5
3/5p=21/20-12/20
3/5p=9/20
p=9/20÷3/5
p=9/20*5/3
p=45/60
p=3/4
9) What two operations are needed to solve 2x - 4 = 16?
a. Addition & division
b. Addition & subtraction
c.Multiplication & subtraction
Answer:
a. Addition & division
Step-by-step explanation:
2x - 4 = 16 (adding 4 to both sides)
2x = 16 + 4
2x = 20 (dividing both sides by 2)
x = 20/2 = 10
Hence we can see that the two operations are addition and then division
Which of the following expressions are equivalent to 3V 2 ? Select all that apply.
Answer: A C and D
Step-by-step explanation:
find the value of f(3) for the function f(x)=-4(x+3) f(3)=
Answer:
-24Step-by-step explanation:
Given function
f(x)= -4(x+3)To find
f(3)=?Solution
Substitute x with 3 in the equation to find f(3)
f(3) = -4(3+3) = -4*6 = -24Karen owns a seafood restaurant. She orders trout from an online retailer.
Each pound of trout costs $30, and the company charges a $2 fee for
shipping the order. However, if Karen orders 10 or more pounds, the trout
costs only $24 per pound, but the shipping fee is $6.
Which piecewise function models the cost of x pounds of trout?
A. f(x) =
30x + 2, 0 < x < 10
24x + 6, 2 > 10
O B. f(2)=
24x + 6, 0 << < 10
30% +2, 2 > 10
O c. f() =
{
30x + 2, 0 << < 10
24x + 6, 3 > 10
D. f(x) =
24x + 6, 0 < x < 10
30x + 2, 3 > 10
< PREVIOUS
Answer: 30x+2, 0<x<10
24x+6, x>10
Step-by-step explanation:
Make sure the x>6 has the line under the >. It would not let me enter it like that.
The piecewise function that models the cost of x pounds of trout is: [tex]\bold{f(x)=\left \{ {{30x + 2,~~0 < x < 10} \atop {24x + 6,~~~x > 10}} \right. }[/tex],
What is piecewise function?"It is a function that is defined on a sequence of intervals."
For given question,
'x' represents number of pound of trout.
Each pound of trout costs $30, and the company charges a $2 fee for
shipping the order.
We write this in equation form as,
f(x) = 30x + 2
This is possible if Karen orders less than 10 pounds.
So, the function would be,
f(x) = 30x + 2, 0 < x < 10
If Karen orders 10 or more pounds, the trout costs only $24 per pound, but the shipping fee is $6.
This means, the function would be,
f(x) = 24x + 6, x > 10
Hence, the piecewise function that models the cost of x pounds of trout is: [tex]\bold{f(x)=\left \{ {{30x + 2,~~0 < x < 10} \atop {24x + 6,~~~x > 10}} \right. }[/tex]
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Dominic placed the following pieces of lumber in order from shortest to longest 23 over three 7 and 7/8 7.9 to 68 square root
Answer:
23/3
7 7/8
7.9
Step-by-step explanation:
which expression is equivalent to 42+90?
Step-by-step explanation:
42+90 can be written in many ways.
Fore example, it can be written with double negatives, or even commutative property.
42-(-90) or 90+42
(21x2)+(45x2) or (6x7)+(3x30)
Sorry if it's wrong...
can someone help me with this question? I keep on getting it wrong.
Answer:
102
Step-by-step explanation:
Let x be the amount of money John spends.
x/2-5=46
x/2=51
x=102
The ratio of dogs to cats is 3:8 there are a total of 99 dogs and cats in the shelter. How many are cats.
Answer:
72 cats
Step-by-step explanation:
sum the parts of the ratio, 3 + 8 = 11 parts
Divide the total by 11 to find the value of one part of the ratio.
99 ÷ 11 = 9 ← value of 1 part of the ratio, then
8 parts = 8 × 9 = 72 ← number of cats
Melissa made a total of 14 baskets during her last basketball game. She made a number of 2-point baskets and a number of 3-point baskets for a total of 33 points. Using matrices to solve, how many 3-point baskets did Melissa make in her last basketball game? 3 5 9 11
Answer:
The answer should be 5
Step-by-step explanation: cause 3x5=15 which leaves 9 more shots that are equal to 2 2x9= 18 and 18+15= 33 which means the answer is 5
Answer:
B.) 5
Step-by-step explanation:
Edge2021
i have a zero in the ones place. i am greater than 20 but less the 39 what am i
Answer:
30
Step-by-step explanation:
I need help ASAP PLEASE!
Determine whether this statement is true or false. If the statement is false, give a counterexample.
Statement: All integers are rational numbers.
¿Cuál es el valor de 0.1561 redondeado a la décima más cercana?
A 0.15
B 0.16
C 0.1
D 0.2
Answer:
A0.15
Step-by-step explanation:
A pound is approximately 0.45 kilogram. A person weighs 87 kilograms. What is the person's weight, in pounds, when rounded to the nearest
whole number?
ОА
39 lb
OB. 52 lb
OC 193 lb
OD. 180 lb
Answer:
OC 193 lb is correcte!
The person's weight, in pounds, when rounded to the nearest
the whole number is equal to [tex]1.9\times10^{2} pound[/tex]
We have given that, A pound is approximately 0.45 kilogram.
0.45 kg = 1 pound
Thus if 0.45 kg is equal to= 1 pound
87 kg will be equal to [tex]=\frac{1}{0.45} \times 87=1.9 \times 10^2 pound[/tex]
What are the significant digits?The number of significant digits in an answer should be equal to the least number of significant digits in any one of the numbers being multiplied, divided, etc.
Thus the answer should contain 2 significant digits.
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If mZA = (8x + 6)° and m
ZB = (7x + 24)', then find the measure of ZB
2(3-p)=17=41 show answer.
this is what I found hope its correct!♀️
DOES ANYONE KNOW THIS?????
Answer:
if i;m right its 45 degrees
Step-by-step explanation:
Answer:
28
Step-by-step explanation:
alternative angle theorem lets you know that angle acb is equal to cae and you can find acb since you know all angles add up to 180. 180-105-47=28
Hi May I know how to solve this question
a ball is thrown straight up from a height of 3 ft with a speed of 32 ft/s.
A scale on a blue print drawing of a house shows that 10 centimeters represents 2 meters. What number of actual meters are represented by 18 centimeters on the blue print?
Answer:3.6 m
Given:10cm=2m
Then, 5cm=1m
Therefore, (18/5)= lenght I'm meters on blueprint scale
(18/5)=3.6m
What is the unit rate (words per 1 minute) for
this scenario?
Lucy can type 300 words in 5 minutes. How many words can Lucy type in 27 minutes.
Kesha drives 26 miles in 48 minutes. Keeping the same rate, how many miles does she drive in 12 minutes
NEED HELP ASAP!!!
TEN POINTS!
state the domain, the range, and the intervals on which function is increasing, decreasing, or constant in interval notation
Answer:
domain (-∞, ∞)range (-∞, 4]increasing (-∞, 0)decreasing (0, ∞)constant (only at x=0, not on any interval)Step-by-step explanation:
The graph is of the equation y = -x^2 +4. It is a polynomial of even degree, so has a domain of all real numbers: (-∞, ∞).
The vertical extent of the graph includes y=4 and all numbers less than that:
range: (-∞, 4]
The graph is increasing to the left of its vertex at x=0, decreasing to the right.
increasing (-∞, 0); decreasing (0, ∞)
There is no interval on which the function is constant. It has a horizontal tangent at x=0, but a single point does not constitute an interval.
5t+1= 9
Please help me
Exact Form: t = 8/5
Decimal Form: t = 1.6
Mixed Number Form: t = 1 3/5 (one and three fifths)
Answer:
t = 8/5 or t = 1.6
This will be a fraction buh can be turned into a decimal
Step-by-step explanation:
subtract 1 on both sides 5t + 1 - 1 = 9 - 1
then simplify 5t = 8 after det divide both side 5t/5 = 8/5 and den your answer is t = 8/5...
HOPE DIS HELPS YU OR IS RIGHT!!!!!
f(0) = x - 9
Help if you can?!
Answer:
Substitute the given value into the function and evaluate is
− 9
Which of the following equations has been vertically stretched by a factor
of 5?
A) Y=|x+5|
B) Y=|x-5|
C) Y=5|x|
Please help me to prove this!
Answer: see proof below
Step-by-step explanation:
Given: A + B + C = π → A = π - (B + C)
→ B + C = π - A
Use the Pythagorean Identity: cos² A + sin² A = 1 → sin² A = 1 - cos² A
Use Double Angle Identities: cos 2A = 2 cos² A - 1 → cos² A = (cos 2A + 1)/2
→ cos A = 1 - 2 sin² (A/2)
Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · cos [(A - B)/2]
Use Cofunction Identities: cos (π/2 - A) = sin (A)
sin (π/2 - A) = cos A
cos (-A) = cos (A)
Proof LHS → RHS:
[tex]\text{LHS:}\qquad \qquad \sin^2\bigg(\dfrac{B}{2}\bigg)+\sin^2 \bigg(\dfrac{C}{2}\bigg)-\sin^2\bigg(\dfrac{A}{2}\bigg)[/tex]
[tex]\text{Pythagorean:}\qquad 1-\cos^2 \bigg(\dfrac{B}{2}\bigg)+1-\cos^2 \bigg(\dfrac{C}{2}\bigg)-\bigg[1-\cos^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1-\cos^2 \bigg(\dfrac{B}{2}\bigg)-\cos^2 \bigg(\dfrac{C}{2}\bigg)+\cos^2 \bigg(\dfrac{A}{2}\bigg)[/tex]
[tex]\text{Double Angle:}\quad 1-\bigg(\dfrac{\cos(2\cdot \frac{B}{2})+1}{2}\bigg)-\bigg(\dfrac{\cos (2\cdot \frac{C}{2})+1}{2}\bigg)+\bigg(\dfrac{\cos (2\cdot \frac{A}{2})+1}{2}\bigg)\\\\\\.\qquad \qquad \qquad =1-\dfrac{\cos B}{2}-\dfrac{1}{2}-\dfrac{\cos C}{2}-\dfrac{1}{2}+\dfrac{\cos A}{2}+\dfrac{1}{2}\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}[1-(\cos B+\cos C)+\cos A][/tex]
[tex]\text{Sum to Product:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\cos \bigg(\dfrac{B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]
[tex]\text{Given:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\cos \bigg(\dfrac{\pi -A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]
[tex]\text{Cofunction:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]
[tex]\text{Double Angle:}\qquad \dfrac{1}{2}\bigg[1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)+1-2\sin^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg[2-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)-2\sin^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1-\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin^2 \bigg(\dfrac{A}{2}\bigg)[/tex]
[tex]\text{Factor:}\qquad \qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin \bigg(\dfrac{A}{2}\bigg)\bigg][/tex]
[tex]\text{Given:}\qquad \qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin \bigg(\dfrac{\pi -(B+C)}{2}\bigg)\bigg][/tex]
[tex]\text{Cofunction:}\qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)+\cos \bigg(\dfrac{B+C}{2}\bigg)\bigg][/tex]
[tex]\text{Sum to Product:}\ 1-\sin \bigg(\dfrac{A}{2}\bigg)\cdot 2 \cos \bigg(\dfrac{(B-C)+(B-C)}{2\cdot 2}\bigg)\cdot \cos \bigg(\dfrac{(B-C)-(B+C)}{2\cdot 2}\bigg)\\\\\\.\qquad \qquad \qquad =1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(-\dfrac{C}{2}\bigg)[/tex][tex]\text{Cofunction:}\qquad =1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)[/tex]
[tex]\text{LHS = RHS:}\quad \checkmark\\\\\quad 1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)=1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)\quad[/tex]