The ratios 9:6 and 12:8 does not form a proportion, since the products of the two are not equal.
Given we have two ratios:
9:6 and 12:8
An equation in mathematics that shows that two ratios expressed in fraction form are equivalent is known as a proportion. The rule that says a/b= c/d if and only if ad=bc allows us to assess whether two ratios, a: b and c: d, constitute a proportion.
To determine if 9:6 and 12:8 form a proportion, we use the rule of proportion.
That is, 9/12 = 8/6
If only if 9×6=12×8
Therefore, 9×6=54
and 12×8=96
since these two products are not equal, we have that 9:12 and 8:6 do not form a proportion.
Hence the ratios 9:6 and 12:8 are not in proportion.
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A solid oblique pyramid has a regular pentagonal base. the base has an edge length of 2.16 ft and an area of 8 ft2. angle acb measures 30°. a solid oblique pyramid has a regular pentagonal base. the base has an edge length of 2.16 feet and an area of 8 feet squared. point a is the apex and point c is the center of the hexagon. line a b shows the vertical height of the pyramid. triangle a b c is a right triangle with base length of 7 startroot 3 endroot feet. what is the volume of the pyramid, to the nearest cubic foot? 5 ft3 9 ft3 14 ft3 19 ft3
The volume of the Oblique pyramid is 19 [tex]ft^{2}[/tex]
We know, the volume of a pyramid is [tex]\frac{1}{2}[/tex] × B × h
where B is the area of the base and h is the height of the pyramid.
Given: The pentagonal base has an edge length of 2.16 ft and an area of 8 [tex]ft^{2}[/tex] and angle ACB measures 30°.
Consider triangle ACB
tan30° = [tex]\frac{AB}{CB}[/tex]
[tex]\frac{1}{\sqrt{3} }[/tex] = [tex]\frac{AB}{7\sqrt{3} }[/tex]
AB = 0.58 × [tex]7\sqrt{3}[/tex]
AB = 0.58 × 12.12
AB = 7.03
Now, the volume of the oblique pyramid will be
V = [tex]\frac{1}{2}[/tex] × 8 × 7.03
V = 18.75
V ≈ 19 [tex]ft^{2}[/tex]
Refer to the complete question given below.
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Answer:19
Step-by-step explanation:
The truth table represents statements p, q, and r. p q r A T T T B T T F C T F T D T F F E F T T F F T F G F F T H F F F Which statements are true for rows A and E? Select two options. p ↔ q q ↔ p q ↔ r r ↔ p r ↔ q
For the truth, table represented the statements that are true for rows A and E are
p ↔ qq ↔ rThis is further explained below.
What is a truth table?Generally, A truth table is a mathematical table that is used in logic, more specifically in linkage with Boolean algebra, boolean functions, and propositional calculus.
It is used to set out the design strength of logical gestures on each of their functional arguments, such that, for each combination of numbers taken by their logical variables.
A truth table is also known as a truth matrix.
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CQ in the correct order is given below
A car travels at 1/2t^2+55 mph for 0≤x≤5 hours. Approximately how far does it travel?
Twenty-four equals the sum of 10.5 and the quotient of a number and 4.5.
Twenty-four equals the sum of 10.5 and the quotient of a number and 4.5 is given by 24 = 10.5 + x/4.5
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
What is quotient?Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number. As a general rule, the smaller the divisor (denominator) of an expression, the larger would be the quotient.
In order to translate this word problem, we would assign a variable to the unknown number and then translate the word problem into algebraic equation as follows:
Let n represent the unknown number.
Translating the word problem into an algebraic equation, we have;
24 = 10.5 + x/4.5
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write a new function that is a horizontal stretch of f(x)=(x+2)^3+5
New function that is a horizontal stretch of F(x)=[tex](x+2)^{3} + 5[/tex] is F([tex]\frac{x}{k}[/tex])=[tex](\frac{x}{k} +2)^{3} + 5[/tex]
What is horizontal stretch ?The point (x, y) on the graph of f(x) is changed to the point (x/k, y) on the graph of g when the graph is stretched or contracted horizontally by a factor of 1/k (x).Only when the input value is also increased by a, can a graph be stretched horizontally by a factor of 1/a. The x-coordinates should be multiplied by a once f(x) has been stretched horizontally to f(ax). Keep the y-intercepts where they are. The resulting function might have a different domain, but it will have the same range. If a point (m, n) is stretched horizontally, it becomes (am, n).
F(x)=[tex](x+2)^{3} + 5[/tex]
F([tex]\frac{x}{k}[/tex])=[tex](\frac{x}{k} +2)^{3} + 5[/tex]ch visit :
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Could someone help me with this?
When the person picks 170 beads, the number of red beads will be 57.
How to calculate the value?It should be noted that based on the information, the following can be deduced:
Number of red beads = 139
Number of yellow beads = 167
Number of green beads = 107
Total number of beads = 139 + 167 + 107 = 413
Therefore, when one selects 170 beads, the number of red beads will be:
= Number of red beads / Total number × 170
= 139 / 413 × 170
= 57
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Find the distance between the two points in simplest radical form.
The distance between the two points is 13 unit.
What is triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the display style for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.
Given that,
A right triangle can be drawn using the grid lines for legs and the line segment between the two points as the hypotenuse. You can count grid squares or subtract coordinates to find the vertical leg is 12 units and the horizontal leg is 5 units. The Pythagorean theorem tells you the length of the hypotenuse (distance between the points) is d² = 12² +5² = 144 +25 = 169
d = √169 = 13
The distance between the two points is 13 unit
This set of dimensions, {5, 12, 13}, is one of several "Pythagorean triples" that often show up in math problems. Other common triples are {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}, and multiples of these.
Therefore, distance between the two points is 13 unit.
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1 find the slope of the slope of the line
2 write an wquation for the like
3 what is the value of a
4 what is the value of b
Answer:
1. Slope= 2
2. [tex] \frac{b - 2}{4 - 2} = 2[/tex] or [tex] \frac{8 - 2}{a - 2} = 2[/tex]
3. a= 5
4. b= 6
Step-by-step explanation:
The slope of a straight line between any two points of the line would be the same. This means that calculating the slope of the line using point (2, 2) and (6, 10) would give us the same slope value when calculating with points (4, b) and (6, 10) for example.
Formula
[tex]\boxed{\text{slope} = \frac{y_1 - y_2}{x_1 - x_2} }[/tex]
Q1. Since we two pairs of known coordinates, let's make use of them in the slope calculation.
Slope of line
[tex] = \frac{10 - 2}{6 - 2} [/tex]
[tex] = \frac{8}{4} [/tex]
= 2
Q2-4. Since in the subsequent parts we will eventually have to find the value of a and b, let's form an equation for each of them.
Slope between (2, 2) and (4, b)= slope between (2, 2) and (6, 10)
[tex] \frac{b - 2}{4 - 2} = 2[/tex]
[tex] \frac{b - 2}{2} = 2[/tex]
Multiply both sides by 2:
b -2= 2(2)
b -2= 4
b= 4 +2
b= 6
Using (2, 2) and (a, 8):
[tex] \frac{8 - 2}{a - 2} = 2[/tex]
Multiply both sides by (a -2):
6= 2(a -2)
Expand:
6= 2a -4
Add 4 to both sides:
2a= 10
Divide both sides by 2:
a= 10 ÷2
a= 5
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what is the length of the course from point A to point W?
The length of the course is 480 m.
Length is used to measure distance. According to the International System of Quantities, length has the dimension of distance. In most measurement systems, length is represented by a base unit from which all other units are derived. The International System of Units (SI) system's fundamental unit of length is the meter.
Nevertheless, depending on the item's position, this is not always the case. A fixed object's length is commonly understood to be its greatest extended dimension.The length of a fixed object is referred to by a number of names, including height, also referred to as vertical length or vertical extension, and width, breadth, or depth.From the given figure we can infer that W is the mid-point of AB. Therefore we know that AW = WB
Now the distance is given by
5x -110 = 2x +100
or, 5x - 2x = 100 + 110
or, 3x = 210
or, x = 70
Therefore total length = 5x -110 + 2x +100 = 7x - 10 = 490 - 10 = 480 m
Therefore the length is 480 m.
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Gil is shopping for books and CDs. He buys 4 books and no CDs for a total of $32. Write an equation that represents the relationship between the cost of a book, y, and the cost of a CD, x, in standard form.
Gil is out purchasing CDs and books. He spends $32 on 4 books but not any CDs. A standard form equation y=-8n and x=0.
Given that,
Gil is out purchasing CDs and books. He spends $32 on 4 books but not any CDs.
We have to create a standard form equation to show the connection between the price of a book (y) and the price of a CD (x).
The equations in standard form for Gil's change in money after purchasing a book (y) and his change in money after selling a CD (x).
Gil spends $32 on 4 books.
4 books = $32
1 book = $8
If n is the total number of books bought, the change in currency equals
y=-8n.
Here, the negative sign stands for a decline in currency. Here, a slope of -8 indicates that after purchasing each book, the money declined by $8.
There are no CDs so x=0.
Therefore, y=-8n and x=0.
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a cell phone user wants to determine what data plan she should get on her new contract. she selects a random sample of 15 months and finds her average usage to be 11.25 gb with a standard deviation of 2.5 gb. she wants to test h0: µ ≥ 12 gb versus ha: µ < 12 gb. what is the p-value for this test? (round your answer to 3 decimal places.)
The p value of the test when the cell phone user wants to determine what data plan she should get is 0.1324.
What is a P value?The p-value is a figure that, when generated from a statistical test, indicates how likely it is that, if the null hypothesis were true, you would have discovered a certain collection of observations. In order to determine whether to reject the null hypothesis, P-values are utilized in hypothesis testing.
The following can be deduced from the information:
Number = 15
Mean = 11.25
Standard deviation = 2.5
Test statistics = -1.162
This is the left tailed test.
The p value will be:
P(z < -1.162 )
This will be looked at in the distribution table
= 0.1324
P-value = 0.1324
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the schools newspaper staff is selling cookies to raise money for the next school year. the first student who sells 252 boxes earns a laptop. eva sells on average 7 boxes per hour, while Sylvia sells on average 3 boxes every 30 minutes. How much time, in hours, will pass until at least one of the students sells enough boxes to earn a laptop?
A.) 10
B.) 15
C.) 23
D.) 36
E.) 42
Which value is a zero of the function f(x) = x³ − 5x² − 8x + 12?
1 )-1
2)2
3)6
4) 12
Answer:
Only 6 match your answer choices.
Step-by-step explanation:
Solve for x:
x^3 - 5 x^2 - 8 x + 12 = 0
The left-hand side factors into a product with three terms:
(x - 6) (x - 1) (x + 2) = 0
Split into three equations:
x - 6 = 0 or x - 1 = 0 or x + 2 = 0
Add 6 to both sides:
x = 6 or x - 1 = 0 or x + 2 = 0
Add 1 to both sides:
x = 6 or x = 1 or x + 2 = 0
Subtract 2 from both sides:
Answer: x = 6 or x = 1 or x = -2
A fair cost $33 for admission plus $8 for each roller coaster ride.
Given that n represents the number of roller coaster rides, choose the algebraic expression that models this situation.
A
B
D
41n
33n +8
41
33 + 8n
A group of friends decided to buy bulk chocolate from a candy store. If some friends
each want 1/7 of a kilogram of chocolate of the 10 kilograms of chocolate
purchased, then how many people can get a share of chocolate?
Answer:
Your answer is [tex]70[/tex].
Step-by-step explanation:
[tex]10[/tex] ÷ [tex]\frac{1}{7}[/tex] [tex]= 70[/tex]
Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
[tex]\sqrt{2x-7} =1[/tex]
Determine the solution for 0.3(6y + 15) = 1.8y + 4.5. A y=2.5 B y=4.9 C infinite solutions D no Solutions
Answer:
C) infinite solutions
Step-by-step explanation: hope this helps have an amazing rest of ur day <3 ^ ^ :>
Any value of y makes the equation true. All real numbers Interval Notation: (−∞,∞)
The equation given has no solution because they will cancel out each other.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation is;
0.3(6y + 15) = 1.8y + 4.5.
Solving for the variable y;
0.3(6y + 15) = 1.8y + 4.5
Open the bracket;
1.8y + 4.5 = 1.8y + 4.5
Here we can conclude that the equation given has no solution because they will cancel out each other.
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i need help with this, thanks
Answer:
151, 29, 151
Step-by-step explanation:
[tex]m\angle 2=29^{\circ}[/tex] (vertical angles)
[tex]m\angle 1=m\angle 3=151^{\circ}[/tex] (linear pair)
Answer:
[tex]m \angle 1= \boxed{151}\;^{\circ}\\\\m \angle 2= \boxed{29}\;^{\circ}\\\\m \angle 3= \boxed{151}\;^{\circ}[/tex]
Step-by-step explanation:
Angles on a straight line sum to 180°.
⇒ m∠3 + m∠4 = 180°
⇒ m∠3 + 29° = 180°
⇒ m∠3 = 151°
Vertical Angle Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Applying the Vertical Angle Theorem:
m∠2 = m∠4 = 29°m∠1 = m∠3 = 151°1.9 Which of the following expressions is equal to -12? Select ALL that apply.
A.-15-3
B.-13-(-1)
C.-8-4
D.-3-(-9)
E.5-17
F. 6-(-6)
213313
The expressions that are equal to -12 are present in Options(B,C, and E).
Solutions of the given expressions are:
A. -15-3
To Add two negative numbers together, start by adding the absolute value of each number together and precede it with a negative sign.
-15-3 = -18
B. -13-(-1)
Proceed by opening the parentheses and modifying the sign in front of it.
-13-(-1) = -13 + 1 = -12
C. -8-4 = -12
D. -3-(-9) = -3 + 9 = 6
E. 5-17
Use the sign of the larger number and subtract to determine the sum of a negative and a positive number.
5-17 = -12
F. 6-(-6) = 6 + 6 =12
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If sin 25=cos T, what is the value of T?
The value of angle T is 65°
In this question, we have been given sin 25=cos T
We need to find the value of T.
Assuming angle in degrees the value of trigonometric function would be,
sin 25 = 0.4226
As we have been given sin 25=cos T,
cos T = 0.4226
So angle T would be,
⇒ T = arccos( 0.4226)
⇒ T = cos^(-1)( 0.4226)
⇒ T = 65°
Therefore, the value of angle T is 65°
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Select the correct answer.
The sine of the angle based on the information about the cosine is D. ✓91 / 10.
How to illustrate the information?It should be noted that cos is calculated as:
= adjacent / hypothenuse.
This was given as 3/10.
It should be noted that sine = Opposite / Hypothenuse
The opposite will be:
Opp² + Adj² = Hyp²
Opp² + 3² = 10²
Opp² + 9 = 100
Opp² = 100 - 9
Opp² = 91
Opp = ✓91
Therefore, the sine of the angle will be ✓91 / 10
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What is 183 divided by 13
Answer:
14.077 appr. 14.1
Step-by-step explanation:
183/13=
18÷13=1 remainder 5
53÷13=4 remainder 1
therefore the answer is 14.1
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x = ____ ( look at photo)
Julian is making potato salad for his family picnic. At the market, he spends $5.58 on red potatoes and $4.68 on yellow potatoes. If each type of potato cost $0.90 per pound, how many total pounds of potatoes does he buy
Answer:
11.4 pounds
Step-by-step explanation:
1. $20 haircut; 10% tip
Solve for x in the equation below 3(x-5)=5x-(3-x)
Answer:
x = -4
Step-by-step explanation:
3(x-5) becomes 3x-15
5x-(3-x) becomes 6x-3
3x - 15 = 6x - 3
+ 15 + 15
3x = 6x + 12
-6x -6x
-3x = 12
divide -3 on both sides
X = - 4
Answer:
x = -4.
Step-by-step explanation:
3(x-5) = 5x-(3-x)
3x - 15 = 5x - 3 + x
3x - 5x - x = -3 + 15
-3x = 12
x = -4.
Find the slope of the line that passes through (1, 9) and (8, 1).
Answer:
Slope = -1
Step-by-step explanation:
m = second y - first y / second x - first x
second y = 1
first y = 9
second x = 9
first x = 1
1 - 9 = -8
9 - 8 = 8
-8/8 = -1
Find the slope of a line.
We mark the points: (x₁ = 1, y₁=9) and (x₂ = 8, y₂ = 1)
X₁ = 1X₂ = 8Y₁ = 9Y₂ = 1We have that the formula is:
[tex]\boldsymbol{\sf{m=\dfrac{Y_{2}-Y_{1} }{X_{2}-X_{1}} }}[/tex]
Now we apply the formula and solve:
[tex]\boldsymbol{\sf{m=\dfrac{1-9}{8-1} =\dfrac{-8}{7} }}[/tex]
[tex]\boldsymbol{\sf{m=\dfrac{-8}{7} }}[/tex]
The slope of the line through (1, 9) and (8, 1) is -8/7.
A cyclist's speed is 1.5 times faster than a walker's. starting at the same point, after 1.5 hours, they were 12.5 miles apart. what were both of their speeds?
The speed of the cyclist and the walker is 25 miles per hour and 16.67 miles per hour, respectively.
Speed describes how fast an object moves. It can be measured as distance over time.
speed = distance / time
Let x be the speed of the walker and 1.5x is the speed of the cyclist.
If they start "moving simultaneously in the same direction" from the same point and, after 1.5 hours, the distance between them is 12.5 miles, then
distance traveled by cyclist = distance traveled by the walker + 12.5 miles
cyclist's speed(time) = walker's speed(time) + 12.5
1.5x(1.5 hours) = x(1.5 hours) + 12.5
2.25x - 1.5x = 12.5
x = 50/3
walker's speed = 50/3 or 16.67miles per hour
cyclist's speed = 1.5(50/3)
cyclist's speed = 25 miles per hour
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Super Confused I don’t know what to do right now
Answer:
p=+/- 5/3 or
p =+/- 1 2/3 or
p = +/- 1.66666667
Step-by-step explanation:
Equation
What you have is a quadratic. I am taking the 9 to be a 9 and not a q. So the equation, as I read it, is
9p^2 - 9 = 16 Add 9 to both sides of the equation
Solution
-9+9 + 9p^2 = 16 +9 Combine
9p^2 = 25 Divide by 9
9 p^2 /9 = 25/9 Combine
√p^2 = √(25/9) Take the Square Root of both sides.
p = +/- 5/3
f(t) = -3t+4
f( )=19
Answer:
-5
Step-by-step explanation:
[tex]-3t+4=19 \\ \\ -3t=15 \\ \\ t=-5[/tex]