Given:
Consider the tank that is filled with water drains at a rate of [tex]\dfrac{d^2}{16}+4d-100[/tex] gallons per minute where d is the depth of the tank in feet.
Depth of tank = 120 feet.
To find:
The rate of water drain for that tank.
Solution:
We have, rate of water drain in gallons per minute.
[tex]r=\dfrac{d^2}{16}+4d-100[/tex]
where, d is the depth of the tank in feet.
Put d=120, to get the rate of water drain for the tank.
[tex]r=\dfrac{120^2}{16}+4(120)-100[/tex]
[tex]r=\dfrac{14400}{16}+480-100[/tex]
[tex]r=900+380[/tex]
[tex]r=1280[/tex]
Therefore, the rate of water drain is 1280 gal/min. Hence, the correct option is B.
what is the length, in centimeters, of EF
Answer:
8
Step-by-step explanation:
1. Use the Pythagorean theorem: a^2+b^2=c^2.
You are already given c (which is always the longest side of the triangle) and one of the legs, which can be either a or b.
2. Put the numbers into the equation and square them.
6^2+b^2=10^2
When you square the numbers, it becomes 36 + b^2 = 100.
3. Subtract 36 from both sides and take the square root of the difference.
b^2 = 64
[tex]\sqrt{64}[/tex] = 8
Answer: 8cm
Step-by-step explanation: Let’s use the Pythagorean Theorem! 6^2+x^2=10^2
36+x^2=100
x^2=64
X=8
The approximate areas of two states are listed below. Texas: 2.69\times10^5 square miles Rhode Island: 1.21\times10^3 square miles Determine the difference, in square miles, between the area of Texas and the area of Rhode Island. Write your answer in scientific notation.
Answer:
10 times 5 =50 (2.69 x 50) = 134.5
10 times 3=30 (1.21x30)= 36.3
Step-by-step explanation:
The difference between the area of Texas and Rhode Island in square miles and scientific notation should be (2.68 × 10⁵) square miles.
Calculation of the area:Area of Texas = (2.69 × 10⁵) square miles = 269000 square miles
Area of Rhode Island = (1.21 × 10³) square miles = 1210 square miles
Now
Difference between the Area of the Texas and Rhode Island should be
= 269000 - 1210
= 267,790 square miles
= (2.68 × 10⁵) square miles.
Learn more about an area here: https://brainly.com/question/4329157
1 is 25% of what number
Answer:
4
Step-by-step explanation:
4 x .25 = 1
Answer:
its 4
Step-by-step explanation:
1÷4×100
=25%
(1×100)÷25
=4
Graph g(x) = –2x – 3
Answer:
The slope would be -2 with a y-intercept of (0, -3).
I hope this helped to answer your question.
please help! 1 quick question! xoxo
For f(x) = 5x and g(x)= x + 9, find
(fog)(x); b. (gof)(x); (fog)(3)
a.
C.
a.
(fog)(x)=
(Simplify your answer.)
Answer:
(fog)(x) = 5x+45(gof)(x) = 5x+9(fog)(3) = f(g(3)) = f(12) = 60Step-by-step explanation:
Given
f(x) = 5xg(x) = x + 9Finding (fog)(x)
(fog)(x) = f(g(x))
(fog)(x) = f(x+9)
(fog)(x) = 5(x+9) ∵ substitute x as x+9 in the f(x)
(fog)(x) = 5x+45
Finding (gof)(x)
(gof)(x) = g(f(x))
(gof)(x) = g(5x)
(gof)(x) = 5x+9 ∵ substitute x as 5x in the g(x)
Finding (fog)(3)
(fog)(3) = f(g(3))
substitute x = 3 in the g(x)=x+9
g(x) = x+9
g(3) = 3+9
g(3) = 12
so
(fog)(3) = f(g(3)) = f(12)
now substitute x = 12 in f(x) = 5x
f(x) = 5x
f(12) = 5(12)
f(12) = 60
Thus,
(fog)(3) = f(g(3)) = f(12) = 60
Which function is equivalent to g (k) = -k'+ 6k-9?
a g(k) = -(k- 3)
g(k) = (-k+ 3)(k+ 3)
© g(k) =-(k+3)
O
g(k) = (-k- 3)(–k+ 3)
Answer:
I believe it’s g(k)=(-k- 3)(-k+3)
Step-by-step explanation:
The equivalent function is g(k) = -(k - 3)².
The correct option is A.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
We can start by completing the square of the quadratic function g(k) = -k² + 6k - 9:
g(k) = -(k² - 6k + 9 ) = -(k - 3)²
Option A can be simplified as:
g(k) = -(k - 3)²
Compared with the completed square form of g(k), we can see that option A is equivalent to g(k).
Therefore, the answer is A. g(k) = -(k - 3)²
To learn more about the quadratic function;
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The complete question:
Which function is equivalent to g (k) = -k²+ 6k-9?
A. g(k) = -(k- 3)²
B. g(k) = (-k+ 3)(k+ 3)
C. g(k) = -(k+3)²
D. g(k) = (-k- 3)(–k+ 3)
I need help please #19
Answer:
40
Step-by-step explanation:
what is the formula for 1, -3, 9, -27?
arithmetic or geometric?
Answer:
The formula of the geometric sequence is a[tex]_{n}[/tex] = [tex](-3)^{n-1}[/tex]
Step-by-step explanation:
The terms of the sequence are 1, -3, 9, -27
∵ -3 ÷ 1 = -3
∵ 9 ÷ -3 = -3
∵ -27 ÷ 9 = -3
∴ There is a common ratio between each two consecutive terms
∴ The sequence is geometric
∵ The formula of the geometric sequence is a[tex]_{n}[/tex] = a [tex]r^{n-1}[/tex], where
a is the first term r is the common ratio∵ The first term is 1
∴ a = 1
∵ The common ratio is -3
∴ r = -3
→ Substitute them in the formula above
∵ a[tex]_{n}[/tex] = (1) [tex](-3)^{n-1}[/tex]
∴ a[tex]_{n}[/tex] = [tex](-3)^{n-1}[/tex]
∴ The formula of the geometric sequence is a[tex]_{n}[/tex] = [tex](-3)^{n-1}[/tex]
PLEASE HELP I BEG OF YOH
Answer:
second
Step-by-step explanation:
their angles are equal and their sides are proportional if the figures are similar
Answer:
B, Their angles are equal and their sides are proportional.
Step-by-step explanation:
Two figures that have the same shape are said to be similar. When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles below are similar, compare their corresponding sides.
What is the value ofx in the equation X=-45
O -75
O -27
O 27
O 75
Sheila has 14 1/2 pounds of potato salad. She wants to divide the potato salad into containers, each of which holds 1 1/4 pounds. How many containers does she need? Complete the explanation.
Answer:
11 3/5 containers
Equivalent to 11.6 containers
Step-by-step explanation:
Total pounds of potato salad = 14 1/2 pounds
Pounds in each container = 1 1/4 pounds
How many containers does she need?
Number of containers needed = Total pounds of potato salad / Pounds in each container
= 14 1/2 ÷ 1 1/4
= 29/2 ÷ 5/4
= 29/2 × 4/5
= (29×4) / (2×5)
= 116/10
= 11 6/10
= 11 3/5 containers
Equivalent to 11.6 containers
ASAP solve 21x+6=300 30 points
Answer:
X = 14
Step-by-step explanation:
Answer:
x-14
Step-by-step explanation:
-21+(-59) what is the answer
Answer:
-80
Step-by-step explanation:
Which of the following is the linear parent function?
A. F(x) = x
B. F(x) = x^2
C. F(x) = |x|
D. F(x) = 2x
Answer:
A. F(x)=x
Step-by-step explanation:
can someone help plz
Answer:
I think it B
Step-by-step explanation:
I think it is B
y=-4x+2
At point (1,y), what is y?
Parker grew
21 inches each year for the past 3 years. How many inches total has Parker grown in the past 3 years
Answer:
63
Step-by-step explanation:
21*3
Laura bought a bike on sale for $7.16 off the list price. The discount was 8%. What was the list price?
please help me! (will mark branliest)
Answer:
0.5728
Step-by-step explanation:
8*7.16/100 =0.5728
Plz help I’m am getting timed
Answer:
2/8
Step-by-step explanation:
2/8 or 1/4
Answer: 2/8
Step-by-step explanation:
yuh
One to one function and value
Answer:
yes
Step-by-step explanation:
no two points have the same y value
why is -16 the leading coefficient in quadratic applications
Answer:
Step-by-step explanation:e equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find solutions. ... Another method for solving quadratics is the square root property. The variable is squared.
1. Angelina received 10% off a $50 pair of shoes. How much did she save?
Answer:
$5
Step-by-step explanation:
Multiply 0.10 by $50
5
So Angelina saved $5
Hope this helped :)
Can anyone simplify this??
Answer:
[tex]3^{12}[/tex]
Step-by-step explanation:
[tex]([/tex][tex]3^{5}[/tex][tex])^{2}[/tex]
You multiply the exponents to get:
[tex]3^{10}[/tex]
Then you divide it by [tex]3^{-2}[/tex]
When dividing exponents, you subtract.
10 - - 2 = 12 so the exponent is 12.
That leaves us with:
[tex]3^{12}[/tex]
Tom will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of and costs an additional per mile driven. The second plan has an initial fee of and costs an additional per mile driven. How many miles would Tom need to drive for the two plans to cost the same?
Complete question :
Tom will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $57.98 and costs an additional $0.14 per mile driven. The second plan has an initial fee of $53.98 and costs an additional $0.16 per mile driven. How many miles would Tom need to drive for the two plans to cost the same?
Answer:
200 miles
Step-by-step explanation:
Let miles driven = x
First option :
57.98 + 0.14x
Second option :
53.98 + 0.16x
First option = second option
57.98 + 0.14 = 53.98 + 0.16x
57.98 - 53.98 = 0.16x - 0.14x
4 = 0.02x
x = 200
200 miles
PLEASE PLEASE HELP I NEED THE ANSWER SOON
9514 1404 393
Answer:
A, C
Step-by-step explanation:
The domain is the list of x-values in the table. Choice A correctly lists the domain values.
The range is the list of y-values in the table. Choice B incorrectly describes the domain.
For x = -1, the table tells you f(x) = 6, so f(-1) = 6.
For x = 5, the table tells you f(x) = 12, so f(5) = 12, not -2.
Choices A and C are correct.
A rectangular garden is divided into four sections. Some dimensions are shown in the diagram, and the distance
from point A to point C is 16 ft.
A
12 ft
B
15 ft
С
What is the distance from point A to point B in feet?
Answer:7
Step-by-step explanation:
Ms. Walch works as a car salesperson. She earns a monthly base salary of $ 4,000 Plus $ 500 commission for each car she sells. How many cars does Ms. Walsh need to sell in a given month to earn a total salary of $ 10,000 for that month?
Answer:
20 cars
Step-by-step explanation:
10,000 ÷ 500 = 20
Answer:
2 cars
Step-by-step explanation:
4,000 + 500 = 4,500 x 2 =10,000
thus its 2 cars
HELP ASAP PLEASE!!!!
Hii
(x-2)(x+2)/x(x+5)
=(-4-2)(-4+2)/-4(-4+5)
=(-6)(-2)/-4(1)
=12/-4
=-3
HOPE IT HELPS YOU OUT PLEASE MARK IT AS BRAINLIEST AND FOLLOW ME PROMISE YOU TO FOLLOW BACK ON BRAINLY.IN
Due in 20 mins pls help!
Answer:
A.
Step-by-step explanation:
it is in y=mx+b format