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Related Questions
Question text
Which volume formula or formulas show(s) a joint variation?
I V=8^3
II V=πr^2h
III V=Bh
Select one:
a. III only
b. I only
c. II and III only
d. I, II, and III
Answers
2. V = pr2h
3. V = Bh
Joint variation means that V will be dependent on at least two different variables. Looking at the three choices, only 2 and 3 show this.
In 2, V varies jointly as r2 and h (assuming p is the constant of proportionality). And in 3, V varies jointly as B and h, with the proportionality constant being 1.
The correct answer is: c. II and III only
To determine which volume formula(s) exhibit joint variation, we need to consider if the volume (V) varies directly with two or more variables. In joint variation, V is directly proportional to the product of two or more variables.
Let's analyze each formula:
I. V = 8^3 → This is not a joint variation as V is solely dependent on the constant 8.
II. V = πr^2h → This shows joint variation as V varies directly with both r and h.
III. V = Bh → This also exhibits joint variation since V varies directly with both B (base area) and h (height).
Identify all the sets to which 0.41567 belongs. Choose from rational,irrational,whole,and integer
Answers
... rational because it can be expressed as a fraction (e.g., 41567/100000)
... not irrational for the same reason
... not whole (obviously)
... not integer (obviously)
Answer:
1.) D
2.) C
3.) C
4.) B
5.) A
6.) D
7.) A
8.) D
9.) A
10.) D
Step-by-step explanation:
Which graph shows a triangle and its reflection image over the x-axis?
A. first picture
B. 2nd picture
C. picture 3
D. picture 4
A. is wrong
Answers
To make sure we're on the same page, I'm attaching your fourth drawing below. It's the result of taking a triangle and reflecting it over the horizontal x axis. Think of it like mirroring an image.
Answer-
In picture 4, the triangle is reflected over x axis.
Solution-
While reflecting a point over x axis, (x, y) → (x, -y) rule is followed.
Only the sign of y-coordinate is changed, keeping x-coordinate intact.
In the first picture, though the image is reflected, but it is reflected over y axis.
In the second picture, the image is first reflected over y axis, then it is translated 1 unit down.
We rotating a point 90° clockwise, (x, y) → (y. -x) rule is followed.
In the third picture, the triangle is rotated 90° clockwise and then translated 1 unit to right.
But, in case of the fourth picture, the figure is reflected over x axis. Only the y coordinates sign are changed, all the x coordinates are same as before.
A soccer team has won 1/2 of the games they played. they won 12 games. how many games did they play? Show your working/calculations
Answers
they won 1/2 of their games and won 12 games
1/2 = 50% , multiply by 2 to make 100%
so 12 x 2 = 24 games were played
To calculate the number of games played by the soccer team, multiply the number of games they won (12) by 2, because winning 12 games represents winning [tex]\frac{1}{2}[/tex] of all games played. The soccer team thus played a total of 24 games.
To find how many games the soccer team played in total, we can set up a proportion using the information that they won [tex]\frac{1}{2}[/tex] of their games. This means for every game they won, they played two (since [tex]\frac{1}{2}[/tex] represents one out of two games). If the team won 12 games, and that represents [tex]\frac{1}{2}[/tex] of the total games, we can use a simple equation to solve for the total number of games (T).
The proportion is as follows: [tex]\frac{1}{2}[/tex] = [tex]\frac{12}{T}[/tex], where 12 is the number of games won, and T is the total number of games played.
To solve for T, we multiply both sides of the equation by T to get rid of the fraction: [tex]\frac{T}{2}[/tex] = 12. To find T, we then multiply both sides of the equation by 2 to isolate T on one side of the equation: T = 12 * 2.
Therefore, the team played a total of T = 24 games.
A round-robin tournament has 66 pairings. How many teams are in the tournament?
Answers
I hope this helps.
Consider the trinomial x2 – 9x + 18. Which pair of numbers has a product of ac and a sum of b? What is the factored form of the trinomial?
Answers
AC = 18
Factors of AC: 1 * 18, 2 * 9, 3 * 6, -1 * -18, -2 * -9, -3 * -6
Sum to -9: 19, 11, 9, -19, -11, -9
(x - 3)(x - 6)
The required pair of number are -3 and -6
The factored form of the trinomial is (x-3) and (x-6)
The standard form of a quadratic equation is expressed as:
[tex]ax^2+bx+c=0[/tex]
Given the expression [tex]x^2 - 9x + 18.[/tex]
[tex]a=1\\b=-9\\c=18[/tex]
We are to get two values that we must add to get b, and that we will multiply that will give c.
The given values are -6 and -3
Check:
[tex]-6+(-3)=-6-3=-9\\-6(-3) = 18[/tex]
Factorize the trinomial
[tex]x^2-9x+18\\x^2-6x-3x+18\\x(x-6)-3(x-6)\\(x-3)(x-6)[/tex]
Hence the factored form of the trinomial is (x-3) and (x-6).
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a game spinner has regions that are numbered 1 through 8. if the spinner is used twice, what is the probability that the first number is a 3 and the second is a 7?
Answers
P(3) = 1/8
P(7) = 1/8
(1/8) * (1/8) = 1/64
The probability that the first number is a 3 and the second is a 7 is 1/64
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given:
spinner had region numbered from 1 to 8
So, the probability on the spinner has an equally likely chance of being selected= 1/8.
P(3) = 1/8
P(7) = 1/8
Thus, probability that the first number is a 3 and the second is a 7
=(1/8) * (1/8)
= 1/64
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For one photography session, Dexter earns no less than $50, but no more than $100. Which inequality can be used to represent his earnings, e?
e ≥ 50 or e ≤ 100
e > 50 or e < 100
50 < e < 100
50 ≤ e ≤ 100
Answers
50 ≤ e ≤ 100
Answer:
The answer is D.
Step-by-step explanation:
We know this because it is an "and" problem because it is numbers in between, not outside.
We also know it is "no less" or "no more" than 50 or 100. so we use a less than and equal too. Not just a less than sign.
Really hoped this helped, kind of in a test right now so just giving a brief way of how to figure this stuff out.
Continue and have fun learning!
Which expression is equivalent to (5^-2) (5^-1)
-1/125
-1/5
1/125
1/5
Answers
5^(-1)=1/5
1/25*1/5=1/125
A recipe for pastry has flour, butter and water mixed in the ratio 24 : 8 : 3 if fiona follows the recipe and uses 3 cups of flour, how many cups of butter should she use?
Answers
Ratio = amount of flour / amount of butter
Ratio = 24 / 3 = 8
This means that there is 8 cups of flour in every cup of butter.
Amount of butter = (3 cups of flour) x (1 cup of butter / 8 cups of flour)
Amount of butter = 3/8 cups of butter
Hence, the amount of butter needed is 3/8 cups.
The same can be done in order to determine the amount of water needed to be mixed for the recipe.
Fiona should use 1 cup of butter when using 3 cups of flour, according to the recipe's ratio of 24:8:3 for flour to butter to water.
Explanation:The question asks how much butter Fiona should use if she's using 3 cups of flour and the recipe calls for flour, butter, and water in the ratio of 24:8:3. To solve this, we take the ratio for butter (which is 8) and divide it by the flour ratio (which is 24), then multiply by the number of cups of flour Fiona is using (which is 3 cups).
Step-by-step Solution:
Write down the original ratio: 24 parts flour : 8 parts butter : 3 parts water.Calculate the ratio of butter to flour, which is 8/24. This simplifies to 1/3.Since Fiona is using 3 cups of flour, multiply the simplified butter ratio by the amount of flour: (1/3) * 3 cups = 1 cup. Thus, she would need 1 cup of butter.A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6 find the toal area of the pyramid
Answers
so.. then we end up with the a 30, 60, 90 angles triangle, and thus we apply the 30-60-90 rule, to get the apothem.
now the area of a regular polygon is just (1/2) (apothem)(perimeter).
now, we know the apothem, the perimeter of the hexagon is just 4+4+4+4+4+4. So, just get those values, plug them in to get the area of the hexagonal base.
if you look at the picture bottom-side, the slant-height of the pyramid, is just the altitude/height of the triangular face. So, you really have 6 triangles whose base is 4 and height is 6, and you know how to get the area of a triangle.
so, just get the area of the base, plus the area of the triangular faces, sum them up, and that's the total area of the hexagonal pyramid.
which rectangular equation is equivalent to the polar equation r sin theta=-2
Answers
r2 = x2 + y2
x = rcos∅
y = rsin∅
Since the equation is rsin∅=y, then rsin∅=-2 is equivalent to y=-2.
Answer:
The rectangular equation that is equivalent to the given polar equation is:
y= -2
Step-by-step explanation:
We know that the polar coordinate of a equation are related to the rectangular coordinates of the equation as:
[tex]x=r\sin \theta\\\\y=r\cos \theta[/tex]
where,
[tex]r=\sqrt{x^2+y^2}[/tex]
Now we are given that:
[tex]r\sin \theta=-2[/tex]
Also,
[tex]\theta=\arctan \dfrac{y}{x}[/tex]
Hence, on converting the given polar equation to the rectangular equation we get:
[tex]y=-2[/tex]
Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6). Match each set of vertices of quadrilateral EFGH with the transformation that shows it is congruent to ABCD.
Answers
Translation 7 units right gives E(4, 4), F(8, 3), G(10, 6), and H(8, 6) as shown in brown in the diagram below
Reflection on the y-axis gives E(3, 4), F(-1, 3), G(-3, 6) and H(-1, 6) as shown in green in the diagram below
Reflection on the x-axis gives E(-3, -4), F(1, -3), G(3, -6) and H(1, -6) as shown in red in the diagram below
Translation 5 units down gives E(-3, -1), F(1, -2, G(3, 1) and H(1, 1) as shown in purple in the diagram below
Answer:
Answers a little bit more simplified, all credit to the expert :)
E(4, 4), F(8, 3), G(10, 6) and H(8, 6) <-----> a translation 7 units right
E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6) <-----> a reflection across the y-axis
E(-3, -1), F(1, -2), G(3, 1), and H(1, 1) <-----> a reflection across the x-axis
E(-3, -1), F(1, -2), G(3, 1) and H(1, 1) <-----> a translation 5 units down
Step-by-step explanation:
Solve for x.
The length of a rectangle is equal to 2 times the width plus 3 feet. If the area of the rectangle is 20 square feet, what are the dimension of the rectangle?
Answers
l=2w+3
20/w=2w+3
20=2w^2+3w
2w^2+3w-20=0
Slip and slide
w^2+3w-40
(w+8)(w-5)
(w+8/2)(w-5/2)
(w+4)(2w-5)
w= -4 or 5/2, but since width must be positive, it is 5/2
(5/2)*l=20
l=8
Final answer: Length= 8, Width= 5/2
then the length = 2x + 3 feet
then the area = x(2x + 3) = 20
2x^2 + 3x - 20 = 0
(2x - 5)(x + 4) = 0
x = 2.5 or -4 ( ignore the negative value)
so the deimnasions are width = 2.5 feet and length = 2(2.5) + 3 = 8 feet
what is the length of a circle that has a central angle of 98 degrees and 6 cm rounded to the nearest 100th. using 3.14
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so...
If we take pi to be 3.14,
Arc length = 2(3.14)(6) * 98/360
= 37.68 * 98/360 = 10.26 cm
what is the algebraic expression for the product of 9 and a number t
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[tex]3x^5+8x^2y^3+xy+8[/tex], [tex]x^2+2xy+y^3[/tex], [tex]a^3b+a^b+2ab-4[/tex],
so they are expressions made from integers, integers multiplying variables of different degrees, and algebraic operations like addition, subtraction etc...
thus, the algebraic expression for the product of 9 and a number t is 9t.
Answer: 9t
What would you do to isolate the variable in the equation below, using only one step? x + 5 = -12 Select one: a. Add 5 to both sides of the equation. b. Subtract 5 from both sides of the equation. c. Add 12 to both sides of the equation. d. Subtract 12 from both sides of the equation.
Answers
To isolate the variable in x + 5 = -12, subtract 5 from both sides of the equation. This leads to the equation x = -12 - 5.
Explanation:In order to isolate the variable x in the equation x + 5 = -12, you should subtract 5 from both sides of the equation. This gives us the equation in a simplified form that allows us to determine the value of x. The idea here is to cancel out the +5 on the left side by subtracting 5 from both sides, resulting in x = -12 - 5. Hence, the answer is option b.
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a scale model of a school building is 5 inches tall. If the building is 100 feet tall, find the scale of the model
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Answer with Step-by-step explanation:
A scale model of a school building is 5 inches tall.
Actual size of the school building is 100 feet.
1 feet=12 inches
100 feet=12×100 inches
= 1200 inches
5 inch is representing 1200 inches
1 inch represents 1200/5 inches
1 inch represents 240 inches
or 1 inch represents 12×20 inch
or 1 inch represents 20 feet
Scale of the model is:
1 inch represents 240 inches
1 inch represents 20 feet
Evaluate the function rule for the given value. Y=6*4^x for x=-3
Answers
you change x in the equation for -3
y= 6 x 4^ -3
if you do it in the calculator, remember to put parenthesis in between -3
y = 6 x 1/64
y = 3/32 or 0.09375
Answer:
[tex]y = \frac{3}{32}[/tex]
Step-by-step explanation:
Using the exponent rule:
[tex]a^{-n} = \frac{1}{a^n}[/tex]
Given the function:
[tex]y = 6 \cdot (4)^x[/tex] ......[1]
To evaluate the function rule for x = -3.
Substitute x = -3 in [1] we have;
[tex]y = 6 \cdot (4)^{-3}[/tex]
⇒[tex]y = 6 \cdot \frac{1}{4^3} = 6 \cdot \frac{1}{64}=\frac{3}{32}[/tex]
Therefore, the function rule for the given value when x = -3 is:
[tex]y = \frac{3}{32}[/tex]
Identify the values of a, b, and c that would be used in the quadratic formula to solve the equation 3x2− 5x + 5 = 0. A. a = 3, b = 5, c = 5 B. a = 3, b = −5, c = 5 C. a = 5, b = −5, c = 0 D. a = −3, b = 5, c = −5
Answers
a=3 b=-5 c=5
A. a = 3, b = 5, c = 5
B. a = 3, b = −5, c = 5
C. a = 5, b = −5, c = 0
D. a = −3, b = 5, c = −5
answer is B
How many cubes with 5 inches side Will completely fill a cube that is 10 inches on each side
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how many times does 125 go into 1000? that many will fill it up.
Factor completely 36x2 − 49.
A (3x + 7)(12x − 7) B (3x − 7)(12x + 7) C (6x − 7)(6x − 7) D (6x + 7)(6x − 7)
A B C D ?
Answers
6x * 6x = 36x^2
6x * -7 = -42x
6x * 7 = 42x
-7 * 7 = -49
The -42x and 42x cancel each other out, resulting in 36x^2 - 49.
Answer:
The correct option is D.
Step-by-step explanation:
The given expression is
[tex]36x^2-49[/tex]
It can be written as
[tex](6x)^2-(7)^2[/tex]
Using the formula
[tex]a^2-b^2=(a-b)(a+b)[/tex]
[tex](6x)^2-(7)^2=(6x+7)(6x-7)[/tex]
Therefore the complete factor form of given expression is (6x+7)(6x-7). The correct option is D.
what is the average rate of change for this quadratic function please help
Answers
---------------------------------------------------
---------------------------------------------------
Explanation:
When x = 0, the value of y is y = -6. You can see this as you draw a vertical line through x = 0. This vertical line is the y axis. The parabola crosses the y axis at -6. This point is the y intercept.
When x = 3, the value of y is y = 0. This is one of the two x intercepts. An x intercept is a location where the graph crosses the x axis.
So we have the two points (0,-6) and (3,0). Let's find the slope of the line through these two points
(x1,y1) = (0,-6)
(x2,y2) = (3,0)
Slope:
m = (y2-y1)/(x2-x1)
m = (0-(-6))/(3-0)
m = (0+6)/(3-0)
m = 6/3
m = 2
The slope of the line through those two point is m = 2.
What is a quartic function with only the two real zeros given?
x = -4 and x = -1
A.
y = x4 + 5x3 + 5x2 + 5x + 4
B.
y = x4 - 5x3 - 5x2 - 5x - 4
C.
y = -x4 + 5x3 + 5x2 + 5x + 4
D.
y = x4 + 5x3 + 5x2 + 5x - 5
Answers
So, you need to factor the polynomials given or divide them by (x+1)(x+4).
(x+1)(x+4) = x^2 + 5x + 4
Using the first function you get:
(x^4 + 5x^3 + 5x^2 + 5x + 4) / ( x^2 + 5x + 4) = x^2 + 1
And you know that x^2 + 1 does not have a real solution, so the function
x^4 + 5x^3 + x^2 + x + 4 has the two real solutions given, x = -1 and x = -4, and two not real solutions.
Now you know that the answer is the first option.
If you want to check the other functions you just must divide and analyze the quotient obtained.
Answer: option A. x^4 + 5x^3 + 5x^2 + 5x + 4.
How can ΔABC be mapped to ΔXYZ?
First, translate .
Next, rotate ΔABC about B to align the sides and angles.
Answers
To map ΔABC to ΔXYZ, you need to translate the triangle and then rotate it about a point.
Explanation:In order to map ΔABC to ΔXYZ, you can follow these steps:
First, translate ΔABC by moving it horizontally and vertically to a new position.Next, rotate ΔABC about point B to align the sides and angles with ΔXYZ.By performing these steps, you can map one triangle to another.
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Can someone please help me
Answers
B = area of base
h = height of cylinder
It turns out that
V = B*h
In a similar way to that of a cube
If we know that V = 84pi and h = 7, then we can plug those values into the formula above, and solve for B
V = B*h
84pi = B*7
84pi/7 = B*7/7 ... divide both sides by 7
12pi = B
B = 12pi
Therefore the base is 12pi square units
if the lateral surface area of a square pyramid is 84ft^2 and the base edge is 6, what is the slant height?
Answers
lateral area is given by:
Area=[area of the base]+4[area of triangular sides]
area of the base will be:
Area=length*width
=6*6=36 ft^2
area of triangular sides will be:
[84-36]
=48 ft^2
area of one triangle will be:
48/4=12 ft^2
but
area of triangle is given by:
area=1/2bh
hence the height will be:
12=1/2*6*h
12=3h
h=12/3
h=4 ft
the answer is 4 ft
Which of the following is a solution of x2 + 5x = −2?
5 plus or minus the square root of 33 divided by two.
5 plus or minus the square root of 17 divided by two
negative 5 plus or minus the square root of 33 divided by two.
negative 5 plus or minus the square root of 17 divided by two.
Answers
x^2 + 5x + 2 = 0
x = -b (+-) sqrt (b^2 - 4ac) / 2a
a = 1, b = 5, and c = 2
x = -5 (+-) sqrt (5^2 - 4(1)(2)) / 2(1)
x = -5 (+-) sqrt (25 - 8) / 2
x = -5 (+-) sqrt (17) / 2
answer is : negative 5 plus or minus the square root of 17 divided by 2
Answer:
negative 5 plus or minus the square root of 17 divided by two: [tex]x=\frac{-5\pm\sqrt{17}}{2}[/tex].
Step-by-step explanation:
We have the equation
[tex]x^2+5x=-2[/tex]
[tex]x^2+5x+2=0[/tex].
To solve it, we are going to use the general formula. This formula is used to find the solutions of quadratic equations.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
where a is the coefficient of [tex]x^2[/tex], in this case a=1, b is the coefficient of x, in this case b=5 and c is the independent term, in this case c=2.
[tex]x=\frac{-5\pm\sqrt{5^2-4(1)(2)}}{2(1)}[/tex]
[tex]x=\frac{-5\pm\sqrt{25-8}}{2}[/tex]
[tex]x=\frac{-5\pm\sqrt{17}}{2}[/tex].
Diana can earn money for the tickets she sells. Which of the following statements describes the variables in this situation correctly?
Answers
The variables in this situation are the price of the tickets and the quantity of tickets sold. The relationship between price, quantity, and revenue can be analyzed using the concept of price elasticity of demand. Diana should lower the price if demand is elastic, raise the price if demand is inelastic, and can maintain the same revenue if demand has unitary elasticity.
Explanation:The variables in this situation are the price of the tickets and the quantity of tickets sold. These two variables directly affect the total revenue generated by Diana from ticket sales. The relationship between price, quantity, and revenue can be analyzed using the concept of price elasticity of demand.
If demand for tickets is elastic, Diana should lower the price to increase total revenue. A decrease in price will result in a larger percentage increase in the quantity sold, leading to a higher total revenue. On the other hand, if demand is inelastic, Diana should raise the price to increase revenue. A certain percentage increase in price will result in a smaller percentage decrease in quantity sold, ultimately raising total revenue.
If demand has unitary elasticity, an equal percentage change in quantity will offset a moderate percentage change in price. In this case, Diana can earn the same revenue regardless of a moderate increase or decrease in ticket price.
What is the midpoint of GH? G(7,-5) H(9,-1)