An equation is formed of two equal expressions. The original height of the water in the pool in feet is 5.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the equation, 4.75 = x + (-0.25) can be used to find x, the original height of the water in a pool. Therefore, the height of the fool in the beginning is,
4.75 = x + (-0.25)
4.75 + 0.25 = x
x = 5
Hence, the original height of the water in the pool in feet is 5.
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Please help with these 2 questions and explain why it's the answer
First, let's edit the given equations.
In 9:[tex]2(32-x^2)=4x4-2\\\\64-2x^2=14[/tex]
Then, to check if [tex]x=5[/tex] is a solution to this equation, let's put the [tex]5[/tex].
[tex]64-2(5)^2=14\\\\64-50=14[/tex]
That's correct!
In 10:[tex]4^2-x\leq x(6-5)\\\\16-x\leq 6x-5x\\\\16-x\leq x\\\\16\leq 2x\\\\x\geq 8[/tex]
Then, we must put [tex]15[/tex].
[tex]15\geq 8[/tex]
That's correct!
Good luck! If you have any question(s), then feel free to ask in comments!
Hi Student!
Let us first look at what the first question is asking for us to do and what is provided to do that. Looking at the first question we see that they are asking if x = 5 is a solution to the expression that they provided. This type of problem is fairly simple and what we basically do is just plug in the value 5 for the variable x in the expression and the simplify both sides to see if they are the same.
Plug in the values
[tex]2(32 - x^2) = 4 * 4 - 2[/tex][tex]2(32 - (5)^2) = 4 * 4 - 2[/tex]Simplify the square and subtract inside of the parenthesis
[tex]2(32 - 25) = 4 * 4 - 2[/tex][tex]2(7) = 4 * 4 - 2[/tex]Simplify both sides
[tex]2 * 7 = (4 * 4) - 2[/tex][tex]14 = (16) - 2[/tex][tex]14 = 14[/tex]Looking at the final expression that we have, we can see that we have 14 is equal to 14 which is true and therefore x = 5 is a solution of the expression provided.
Moving onto the next question, we can see that it asks for us to do something really similar to the previous question but this time to check if x = 15 is a solution of a different expression. Let's follow the same steps that we did last time.
Plug in the values
[tex]4^2 - x \le x(6 - 5)[/tex][tex]4^2 - (15) \le 15(6 - 5)[/tex]Distribute the x
[tex]4^2 - (15) \le (15 * 6) + (15 * -5)[/tex][tex]4^2 - (15) \le 90 - 75[/tex]Simplify both sides
[tex]16 - 15 \le 90 - 75[/tex][tex]1 \le 15[/tex]Looking at the final expression that we have, we can see that it states that 1 is less than or equal to 15 and that is true. Therefore, x = 15 is a solution of the expression that was provided.
F(1) =3 and f (n+1)= f(n)^2+3 then find the value of f(4)
Answer:
f(4) = 1612
Step-by-step explanation:
using the recursive formula and f(1) = 3 , then
f(2) = f(1)² + 3 = 3² + 3 = 9 + 3 = 12
f(3) = f(2)² + 3 = 144 + 3 = 147
f(4) = f(3)² + 3 = 147² + 3 = 1609 + 3 = 1612
What is the volume of the rectangular prism?
Find the value of each variable
Answer:
x = 10[tex]\sqrt{2}[/tex] , y = 10[tex]\sqrt{6}[/tex]
Step-by-step explanation:
using the sine and cosine ratios in the right triangle and the exact values
cos60° = [tex]\frac{1}{2}[/tex] , sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{20\sqrt{2} }[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 20[tex]\sqrt{2}[/tex] ( divide both sides by 2 )
x = 10[tex]\sqrt{2}[/tex]
and
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{20\sqrt{2} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2y = 20[tex]\sqrt{2}[/tex] × [tex]\sqrt{3}[/tex] = 20[tex]\sqrt{6}[/tex] ( divide both sides by 2 )
y = 10[tex]\sqrt{6}[/tex]
Figure the amount of concrete (in cubic yards) required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′. Show both exact and rounded figures in the blanks provided
The amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.
What is a Cuboid ?A cuboid is a three dimensional shape , with 6 faces , each face is a rectangle.
The concrete can be considered as in the shape of a cuboid.
Length = 18
Breadth = 24'
Height = 4"
Volume of Cuboid = Length * Breadth * Height
Volume of the cuboid = 18 * 24 * 4 *12*12 *(0.0278)³
=5.34 cu.yard.
Therefore the amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.
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Can someone help me? I’ll give brainliest to whoever gets it right first
Answer:
108°
Step-by-step explanation:
From the diagram,
Angle X + Angle CXD = 180°
Angle X + 72° = 180°
Angle X = 180° - 72° = 108°
−13x + 2/5 − 3 (2x + 4)
Kevin sold a house and receives a 6 1/2% commission he gave the listing broker 30% or 3,575 what was the price of the house
Answer:
12 just because I need the free credit things sorry this ain't gonna be helpful lol
help me solve this pls
Answer:
B.) f(x) = |x| , g(x) = 9x + 2
Step-by-step explanation:
The expression f о g = H is identical to f(g(x)) = H. In other words, when you put the function g(x) in the "x" position of the f(x) function, it should look like the H(x) function.
If g(x) = 9x + 2, put the entire function in for "x" in f(x) = |x|. Once you do this, you get the function f(g(x)) = |9x + 2|.
Answer:B.) f(x) = |x| , g(x) = 9x + 2
Step-by-step explanation:
The expression f о g = H is identical to f(g(x)) = H. In other words, when you put the function g(x) in the "x" position of the f(x) function, it should look like the H(x) function.
If g(x) = 9x + 2, put the entire function in for "x" in f(x) = |x|. Once you do this, you get the function f(g(x)) = |9x + 2|.
Help please!!!
A school building has a 100-foot guy wire attached to the top of the building. When pulled taut it touches level ground 42 feet from the base of the school. At approximately what angle does the wire make with the ground? Give the answer in degrees.
A) 24.83° B) 65.17° C) 22.78° D) 42° E) None of these
Answer: E) None of these
As you can see in the picture below, the line falls at around 66 degrees, so it can't be any of the given choices. If this answer turns out to be wrong, then it is probably B.
Hope this helps!
Find the volume of the cone . Round your answer to the nearest tenth. Use 3.14 for 8 in. 4 in.
Answer:
see the attachment photo!
I need help please ?!!!!
Answer:
6,010 mg
Step-by-step explanation:
1 gram = 1,000 milligrams that means
(6+.01)*1000=6,010mg
consider the exponential functions below.
put the functions, with their corresponding intervals, in order from least to greatest according to their average rates of change over those intervals.
The functions in order from least to greatest according to their average rates of change are function f at the interval [1,2], function h at the interval [0,2] and function g at the interval [2,3]
How to order the functions?The rate of change is calculated using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
For function g at the interval [2,3], we have:
[tex]m = \frac{g(3) - g(2)}{3- 2}[/tex]
This gives
[tex]m = \frac{20 - 4}{3- 2}[/tex]
[tex]m =16[/tex]
For function h at the interval [0,2], we have:
[tex]m = \frac{h(2) - h(0)}{2- 0}[/tex]
Where:
h(2) = 3(3)^2 - 9 = 18
h(0) = 3(3)^0 - 9 = -6
This gives
[tex]m = \frac{18 + 6}{2 - 0}[/tex]
[tex]m = 12[/tex]
For function f at the interval [1,2], we have:
[tex]m = \frac{f(2) - f(1)}{2- 1}[/tex]
This gives
[tex]m = \frac{12 - 6}{2 - 1}[/tex]
[tex]m = 6[/tex]
Hence, the functions are function f at the interval [1,2], function h at the interval [0,2] and function g at the interval [2,3]
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How is the graph of the parent function of y = RootIndex 3 StartRoot 0.5 x EndRoot transformed to produce the graph y = RootIndex 3 StartRoot x EndRoot?
It is horizontally stretched by a factor of mc031-3.
It is vertically stretched by a factor of mc031
It is translated left by mc031-5unit.
It is translated right by mc031-6.unit.
If any constant is added in the variable of the function. Then the function will shift towards left. Then the correct option is C.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The functions are given below.
y = ∛(0.5 + x)
y = ∛x
If any constant is added in the variable of the function. Then the function will shift towards left.
Then the correct option is C.
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Answer:
Step-by-step explanation:
The statement describe g (x) = RootIndex 3 StartRoot x minus 5 EndRoot + 7 by transforming the parent function is option C; Translate the parent function 5 units down and 7 units to the right.
How does transformation of a function happens?
The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units:
y=f(x+c) (same output, but c units earlier)
The transformed function can be written as
y = ∛(x - 5) + 7
Where f(x) = ∛x, this is of the form
y = ∛(x - 5) + 7
These numbers in these places correspond to ...
The statement describe g (x) = RootIndex 3 StartRoot x minus 5 EndRoot + 7 by transforming the parent function is option C; Translate the parent function 5 units down and 7 units to the right.
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The radius of the base of a cylinder is 28 cm and its height is 48 cm. Find the surface
area of the cylinder in terms of л.
O
A.4,208 cm²
B.4,228 cm²
C.4,232л cm²
D.4,256pie cm2
Answer:
D) [tex]4256\pi\:\text{cm}^2[/tex]
Step-by-step explanation:
[tex]SA=2\pi r h+2\pi r^2\\\\SA=2\pi(28)(48)+2\pi(28)^2\\\\SA=2\pi(1344)+2\pi(784)\\\\SA=2688\pi+1568\pi\\\\SA=4256\pi\:\text{cm}^2[/tex]
Answer:
Surface Area = 2πrh
= 2×π×28cm×48cm
= 2688πcm^2
A man travelled by train and left Nsawam at 10:43am and got at Dzorwulu at 3:23pm.Find the average speed of the train in km/hr if the distance of the journey was 356,140km.
The temperature at 10:00 AM is 260 c. if temperature rises 4 degrees more each hour. What will be temperature at 1:00 pm in the Afternoon?
Answer:
272 c
Step-by-step explanation:
Roses by 4 every hour
10 to 1 can be represented in 24 hour time as 10 to 13
13 subtract 10 is 3
3 multiplied by 4 is 12
260 add 12 is 272 c
Which sentence correctly compares the two numbers 5.395 and 5.385?
5395 = 5.385
5.385>5.395
5.395<5.385
5.385<5.395
5395=5.385 TRUE OR FALSE
Inequalities help us to compare two unequal expressions. The correct option is D.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The sentence that correctly compares the two numbers 5.395 and 5.385 is 5.385<5.395. Hence, the correct option is D.
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which one is the answer
Answer:
hmmm I get 216
Step-by-step explanation:
(10×7)+(6×8) the front n back triangle +(6×7)+(8×7)
Question 32 of 40
The ratio
opposite
hypotenuse
describes which function?
The ratio [tex]\frac{Opposite}{Hypotenuse }[/tex] describes the Sine function . The correct option is C. Sine
TrigonometryFrom the question, we are to determine the function that the ratio of opposite to hypotenuse describes
By SOH CAH TOA
We have that
[tex]Sine = \frac{Opposite}{Hypotenuse }[/tex]
[tex]Cosine = \frac{Adjacent}{Hypotenuse }[/tex]
and
[tex]Tangent = \frac{Opposite}{Adjacent}[/tex]
Hence, the ratio [tex]\frac{Opposite}{Hypotenuse }[/tex] describes the Sine function . The correct option is C. Sine
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Which function has a vertex at the origin?
f(x) = (x + 4)²
f(x) = x(x-4)
f(x) = -x²
f(x) = (x-4)(x+4)
Answer:
[tex]f(x)=-x^2[/tex]
Step-by-step explanation:
Vertex form of a quadratic function:
[tex]f(x)=a(x-h)^2+k[/tex]
where:
(h, k) is the vertexa is some constantIf the vertex is at the origin, then (h, k) = (0, 0)
[tex]\implies f(x)=a(x-0)^2+0[/tex]
[tex]\implies f(x)=ax^2[/tex]
Comparing this with the answer options suggests that the function with a vertex at the origin is [tex]f(x)=-x^2[/tex]
If the given figure is sliced through points J. K. and L, which best describes the shape of the resulting cross-section?
A
OA parallelogram
OB. trapezoid
OC. rectangle
OD. triangle
The shape of the resulting cross-section will be equal to the trapezoid.
What is a trapezoid?A trapezoid is a quadrilateral having four sides whose two sides are parallel to each other and the other two sides are nonparallel to each other.
As it is given in the question the figure is sliced through points J. K. and When the shape is sliced from the given points it will create the trapezoidal shape that will have two parallel sides and the other two sides are Non-parallel
Therefore the shape of the resulting cross-section will be equal to the trapezoid.
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Answer:
Trapezoid
Step-by-step explanation:
I got it right on Edmentum
Hook me up with a 5 star and a thanks :)
Help for college scholarships! Must be a paragraph.
How has your family background affected the way you see the world?
Family background refers to the culture and tradition of the family into which a person is born.
What is family background?Family background refers to the culture and tradition of the family into which a person is born. it is worthy of note that most of this family traditions are unspoken yet are firmly entrenched in the psyche of individual as he/she grows.
My family is strictly conservative having had a Southern Baptist orientation. My dad believes deeply in religion and a moralist and perfectionist.
As a result of this, I find myself always grappling with the unfortunate disorder in the world; always trying to bring order to my world as much as I can.
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Please answer this problem!
Answer:
a. volume= 784 is the answer
I WILL GIVE YOU BRAINLIEST!!
a pet store has 8 empty fish tanks that each hold 5544 cubic inches of water one goldfish requires a minimum of 1386 cubic inches of water.
What is the greatest number of goldfish that the pet store can have given the volume of water needed for one goldfish?
Answer:
32 goldfish
Step-by-step explanation:
Given:
Number of fish tanks = 8Volume of water per fish tank = 5,544 in³Water required by 1 goldfish = min 1,386 in³Number of fish per tank = water per tank ÷ water per goldfish
= 5544 ÷ 1386
= 4
Therefore, each tank can hold a maximum of 4 goldfish.
Greatest number of goldfish = number of tanks × fish per tank
= 8 × 4
= 32
in a circle H with m angle GKJ=27 find the m angle GHJ
In a circle H with a measure of angle ∠GKJ = 27°. Then the measure of angle ∠GHJ will be 54°
What is a circle?It is the center of a line drawn from the center to an equidistant location. The space between the center and the periphery of a circle is measured in radius.
In a circle H with a measure of angle ∠GKJ = 27°.
Then the measure of angle ∠GHJ will be
We know that a chord's slope in the center is double that of the chord's slope at the perimeter.
Then we have
∠GHJ = 2 x ∠GKJ
∠GHJ = 2 x 27°
∠GHJ = 54°
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Which coordinate point is a solution to the linear equation? (The graph counts by 1s)
Answer:
the point through which it passes i.e (1,5)
Answer:
(1,5)
Step-by-step explanation:
All points on the line is solution of the equation.
(1 ,5) is on the line and so it is the solution
Help please asap aaaaaaaaaaaaaaaaaa
Answer:
Step-by-step explanation:
Your exponential formula is in the form y = ab^x. In this form, the coefficient 'a' is the initial value, the y-intercept, the value when x=0. The value 'b' is the growth factor, which is 1 more than the growth rate per increment of x. This problem is asking for the growth rate to be expressed as a percentage.
__
Given p(x) = 78500(1.02^x), we can compare to the exponential function form to see that ...
a = 78,500b = 1.02 = 1 +0.02 = 1 +2%The value of x is zero in the year 2000, so the population that year is ...
p(0) = a = 78,500
The increase per year is the value of 'b' with 1 subtracted:
growth rate = 2% per year
Which image below is an acute triangle?
Triangle A has angles measuring ninety five degrees, forty five degrees, and thirty degrees. Triangle B has angles measuring one hundred degrees, twenty five degrees, and twenty five degrees. Triangle C has angles measuring fifty degrees, sixty five degrees, and sixty five degrees. Triangle D has angles measuring thirty degrees, one hundred ten degrees, and twenty degrees.
Answer:
The answer is Triangle C
Step-by-step explanation:
Write the equation that models the height of the roller coaster
Considering the circle described, the height of the roller coaster is modeled by the following equation:
[tex]y = \sqrt{900 - x^2}[/tex]
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In this problem, the roller coaster is represented by a circle centered at the origin, with radius 30, hence:
[tex]x^2 + y^2 = 30^2[/tex]
[tex]x^2 + y^2 = 900[/tex]
The height is the value of y, hence, considering it is a positive value:
[tex]y^2 = 900 - x^2[/tex]
[tex]y = \sqrt{900 - x^2}[/tex]
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