Solve the problem. Check answers to be sure they are reasonable.
A 10-gal aquarium is 4 in. higher than it is wide. Its length is 17 in., and its volume is 4284 in.^3. What are the height and width of the aquarium?
Answer:
[tex]W = 18[/tex] -- Width
[tex]H = 14[/tex] --- Height
Step-by-step explanation:
Given
[tex]V = 4284[/tex] -- Volume
[tex]L = 17[/tex] -- Length
[tex]H = ??[/tex] -- Height
[tex]W = 4 + H[/tex] -- Width
Required:
Find the height and the width
Volume is calculated as:
[tex]V = LWH[/tex]
This gives:
[tex]4284 = 17 * (4+H) * H[/tex]
[tex]4284 = 17 * (4H+H^2)[/tex]
Open bracket
[tex]4284 = 17 * 4H+17*H^2[/tex]
[tex]4284 = 68H+17H^2[/tex]
Divide through by 17
[tex]252 = 4H+H^2[/tex]
Write as a quadratic expression
[tex]H^2 + 4H - 252 = 0[/tex]
Expand
[tex]H^2 + 18H - 14H - 252 = 0[/tex]
Factorize:
[tex]H(H + 18) - 14(H + 18) = 0[/tex]
Factor out H + 18
[tex](H - 14)(H + 18) = 0[/tex]
[tex]H -14 = 0[/tex] or [tex]H + 18 = 0[/tex]
[tex]H = 14[/tex] or [tex]H = -18[/tex]
But Height can not be negative. So:
[tex]H = 14[/tex]
Recall that:
[tex]W = 4 + H[/tex]
[tex]W = 4 + 14[/tex]
[tex]W = 18[/tex]
Use the function g () = 5x – 2 to complete the table.
-4
-7
0
23
38
How do I get the answer?
Answer:
Step-by-step explanation:
You are given the equation g(x)=5x-2. You simply take the values given and put those values into the equation.
g(-4)=5(-4)-2=-20-2=-22
g(-7)=5(-7)-2=-35-2=-37
g(0)=5(0)-2=-2
g(23)=5(23)-2=115-2=113
g(38)=5(38)-2=190-2=188
Jennifer earns $9 per hour babysitting. Use this information to answer problems 18-20.
20. Is the function increasing or decreasing?
a. Increasing
b. Decreasing
Answer:
A
Step-by-step explanation:
Answer:
Increasing
Step-by-step explanation:
We know that Jennifer earns $9 dollars per hour babysitting, this is the only information provided. Meaning that the monetary value is constantly increasing, with no fees or anything being mentioned, this means that the function is increasing. Due to the situation, the line on the graph will always go up.
Jennifer's equation could be represented as 9x.
Find a and b if the points p(6,0) and q(3,2) lie on the graph of ax + by =12
Answer:
[tex]a= 2[/tex]
[tex]b = 3[/tex]
Step-by-step explanation:
Given
[tex]p(x,y) = (6,0)[/tex]
[tex]q(x,y) = (3,2)[/tex]
[tex]ax + by = 12[/tex]
Required
Find a and b
In [tex]p(x,y) = (6,0)[/tex], [tex]x = 6[/tex] and [tex]y = 0.[/tex]
This gives:
[tex]a*6 + b*0 = 12[/tex]
[tex]6a = 12[/tex]
Divide by 6
[tex]a= 2[/tex]
In [tex]q(x,y) = (3,2)[/tex]. [tex]x = 3[/tex] and [tex]y = 2.[/tex]
This gives:
[tex]a*3 + b*2 = 12[/tex]
[tex]3a + 2b = 12[/tex]
Substitute 2 for a
[tex]3*2 + 2b = 12[/tex]
[tex]6 + 2b = 12[/tex]
Collect Like Terms
[tex]2b = 12 - 6[/tex]
[tex]2b = 6[/tex]
Divide by 2
[tex]b = 3[/tex]
need help please Choose the best graph that represents the linear equation: -X = 2y + 1 Graph A
Answer:
Please refer to the attachment
Hope it helps
Please mark me as the brainliest
Thank you
Answer:
yes a is correct on edge!
Step-by-step explanation:
What is 56 divided by 14.5
Answer:
3.86( rounded)
Step-by-step explanation:
Find c.
Round to the nearest tenth:
2 cm
с
150
1050
a
c = [? ]cm
Law of Sines: sin A
sin B
b
sin C
С
a
Enter
========================================================
Explanation:
The ultimate goal is to find the value for lowercase c, or find the length of side c. So we'll use the portion sin(C)/c as part of the law of sines.
We don't know the value of lowercase 'a', so we'll ignore the sin(A)/a portion.
This leaves sin(B)/b
We see that one side is 2 cm long, so this means b = 2. The angle opposite this is 105 degrees, so B = 105.
The angle opposite side c is 15 degrees, so C = 15.
The lowercase letters represent side lengths, while the uppercase letters are angles.
--------------------------
We have enough to apply the law of sines to solve for side c.
sin(B)/b = sin(C)/c
sin(105)/2 = sin(15)/c
c*sin(105) = 2*sin(15) ............. cross multiply
c = 2*sin(15)/sin(105) .............. dividing both sides by sin(105)
c = 0.53589838486224
c = 0.5
Side c is roughly 0.5 cm long.
Make sure your calculator is in degree mode.
9514 1404 393
Answer:
0.5 cm
Step-by-step explanation:
The Law of Sines tells you ...
c/sin(C) = b/sin(B)
c = b·sin(C)/sin(B)
c = (2 cm)sin(15°)/sin(105°) ≈ (2 cm)(0.2588/0.9659) ≈ 0.5359 cm
c ≈ 0.5 cm . . . . rounded to tenths
If Mrs. Maiers buys 24 stickers, is the cost of each sticker more then or less then 0.50
A brick has a mass of 18.4 kg and a volume of 923cm squared. Evaluate the density of the brick in g/cm cubed round?
18.4kg = 1840g
D = m / v
1840 / 923 = 1.993
#
6x²-12x-25=-7
vertex
axis of symmetry
Answer:
Step-by-step explanation:
-b
The axis of symmetry can be calculated using this formula: x = ------
2a
-(-12)
which in this case is x = ---------- = 1. The axis of symmetry is the vertical
2(6) line x = +1
Thus, x = 1 is the x-coordinate of the vertex. Normally we'd find the y-coordinate by evaluating the function at x = 1. Unfortunately your
6x²-12x-25=-7 does not have the form of a quadratic function; such a function does not have the " = " sign in it.
Example: Suppose we have 6x²-12x-25 = f(x) and we evaluate this function at x = 1: f(1) = 6(1)^2 - 12(1) - 25 = -31, which (in this example)
leads to the vertex (1, -31).
Please help me asap please
If twelve inches correspond to 30.48 centimeters, how many centimeters are there in thirty inches?
Answer:
76.2 cm
Step-by-step explanation:
Do 30.48 / 12 to find the amount of centimeters per inch. 30.48 / 12 = 2.54
So, for ever inch, there are 2.54 cm. Now to find the amount of centimeters in thirty inches, do 2.54 x 30 = 76.2.
twice the difference of a number and 8 is equal to three times the sum of the number and 8. find the number
Answer:
-24
Step-by-step explanation:
2(x-8)=3x+3
2x-16+16=3x+8+16
2x=3x+24
2x-3x=3x+24-3x
-x=24
x=-24
Mhanifa please help me with this! I will mark brainliest! Please hurry before I get a bunch of random answers! I would really appreciate it! Random answers will be reported
Answer:
1. C. Reflexive property, SSS2. A. ASA postulateStep-by-step explanation:
Question 1Blank 3 = Reflexive propertyBlank 4 = SSSCorrect choice is C
Question 2Blank 6 = ASACorrect choice is A
What is the point-slope form of a line with slope -3 that contains the point
(10, -1)?
Answer:
y + 1 = -3(x - 10)
General Formulas and Concepts:
Algebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Slope m = -3
Point (10, -1)
x₁ = 10y₁ = -1Step 2: Write Function
Substitute in variables into general form.
y - -1 = -3(x - 10)
y + 1 = -3(x - 10)
PLEASE HELP MEEEEEEEEEEEEEEEE
Answer:
89
Step-by-step explanation:
Answer: 89 metres squared
Step-by-step explanation:
large area = 13 x 8 = 104
small area = 5 x 3 = 15
104 - 15 = 89
Why is it easier to use regression to predict the behavior of an index versus an individual stock?
Hello, I am BrotherEye
Answer:
Regression models are predictive tools. If you want to use them to predict the behavior of an individual, you must set "behavior" as your dependent variable, and you must have indicators and measures for such. You must also identify your explanatory or independent variable likewise you must have indicators and measures for such.
If you have built your model on the basis of collected data, you will be able to predict the value of behavior given a value of the explanatory variable.
Step-by-step explanation:
I need this please help
how to represent with an integer mary moves 3 steps backward as she dances
Answer:
-3
Step-by-step explanation:
As she moves back, so it will be negative.
Since she moves back 3 steps, it will be -3.
Hope it helps :)
Please mark my answer as the berainliest
Answer:
-3
itwaseasy...............
The time, t, for am ice cube to melt. is inversely proportional to the temperature, T, of the water the ice cube is placed. If it takes an ice cube 2 minutes to melt in 75f water, how long will it take an ice cube of the same size to melt in 80f water?
Answer:
15/8 minutes
Step-by-step explanation:
The inverse relationship implies the following equation.
[tex]t=\frac{k}{T}[/tex]
where k is a constant.
You are given a t and T that go together, so
[tex]2=\frac{k}{75}[/tex]
This implies that k=150. Now you know that the relationship is
[tex]t=\frac{150}{T}[/tex]
Now substitute 80 for T to get the answer.
[tex]t=\frac{150}{80}=\frac{15}{8}[/tex][tex]t=\frac{150}{80}=\frac{15}{8}[/tex]
minutes.
It takes an ice cube of the same size to melt in 80f water 15/8 minutes.
We have given,
The time t for am ice cube to melt. is inversely proportional to the
temperature T of the water in the ice cube is placed.
What is the inverse relationship?The inverse relationship implies the following equation.
[tex]t=\frac{k}{T}[/tex]
Where k is a constant.
You have given a t and T that go together, so
[tex]2=\frac{k}{75}[/tex]
This implies that k=150.
Now you know that the relationship is
[tex]t=\frac{150}{T}[/tex]
Now substitute 80 for T to get the answer.
[tex]t=\frac{150}{80} =\frac{15}{8}[/tex]
It takes an ice cube of the same size to melt in 80f water 15/8 minutes.
To learn more about the temperature visit:
https://brainly.com/question/24746268
A triangle with area 40 square inches has a height that is four less than six times the base. Find the base and height of the triangle
Answer:
A = 1/2bh
Step-by-step explanation:
40 = (.5)(6x - 4)(x)
40 = (3x-2)(x)
40= 3x^2 - 2x
3x^2 -2x - 40 =0
3x^2 - 12x + 10x - 40 = 0
3x(x - 4) + 10(x -4) = 0
(3x + 10)(x - 4) = 0
x = {4 , - 10/3}
x = 4 , b = 20. h = 4
Answer:
Step-by-step explanation:
Width=4 inches
Height= 20 inches
125^-1/3 integer or a fraction.
PLEASE HELP IM FAILING MATH
Kayla wants to prove the Pythagorean theorem: if a triangle is a right triangle, then the area of the square whose side is hypotenuse is equal to the sum of the areas of the squares on the other two sides.
Answer:
in ABC,if<B=90,then AB^2+BC^2=AC^2
Step-by-step explanation:
the third option
i did that khan assignment
The appropriate rephrase statement to proof the Pythagorean theorem is
In ΔABC , if ∠B = 90°, then AB² + BC² = AC²
Pythagoras's theorem is used to calculate the sides of a right angle triangle. The formula is represented as follows
c² = a² + b²where
c = hypotenuse
a and b are either adjacent or opposite sides of the triangle.
A right angle triangle is a triangle that has one angle as 90°. Therefore, from the triangle below, the appropriate rephrase statement to proof Pythagoras theorem is as follows:
In ΔABC , if ∠B = 90°, then AB² + BC² = AC²read more: https://brainly.com/question/15546331?referrer=searchResults
Use 3.14 for Pi. *Answer choices may be rounded.* 5 points 1. 15 cm 7.5 cm 176.6 706.5 1324.7 5298.8
Answer:
C. 1324.7 cm³
Step-by-step explanation:
Volume of cylinder = πr²h
π = 3.14
radius (r) = ½ of 15 = 7.5 cm
Height (h) = 7.5 cm
Plug in the values
Volume = 3.14*7.5²*7.5 = 1324.7 cm³
Write an algebraic expression that represents the total area of the square shown
I will give brainliest
Can someone help me out
Answer:
Sorry I couldn't find it.Step-by-step explanation:
:(((((((((((((((((((a man has 290 ft of fencing to build the pen shown in the illustration. If one in is a square, find the outside dimensions.
the dimensions are feet(smaller value) by feet (larger value)
9514 1404 393
Answer:
40 ft by 85 ft
Step-by-step explanation:
The total length of the three "vertical" partitions is ...
3x = vertical partitions
The total length of the horizontal sides is ...
2(x +(x +5)) = 4x +10
Then the perimeter is ...
P = vertical partitions + horizontal sides
290 = 3x +4x +10
280 = 7x
x = 40
2x+5 = 85
The overall dimensions are 40 ft by 85 ft.
Which statement best justifies whether (x – 3) is a factor of the polynomial p(x) = x - 3x? - 2x - 6?
Answer:
It is not a factor
Step-by-step explanation:
It is because p(x)=-12 at x=3
Please will give brainliest and thanks for the problem
Answer:
y = -¼x + (-6)
Step-by-step explanation:
I was summoned?