Number 7 is not a factor of the number 49t + 30.
What is defined as the factor?A factor is a number which divides another number by itself and leaves no remainder.
In other sayings, if multiplying 2 whole numbers yields a product, the numbers being multiplied are factors of a product because of product is divisible by them.
Every integer has a limited number of factors.The factor of a number is often less than or equal to that number; it can never be greater than the number.With the exception of 0 and 1, each integer has at least two factors: 1 as well as the number itself.Division and multiplication are used to find factors.For the given problem,
The equation is given as 49t + 30
For any value of t the number (49t will get completely divide by 7 leaving no remainder behind).
But 30 is not the factor of 7 as it will leave the remainder 2.
Thus, adding number 30 with 49t will result in a number which is not completely divisible by 7.
Thus, 7 is not a factor of number 49t + 30.
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f(t) = -3t+4
f( )=19
Answer:
-5
Step-by-step explanation:
[tex]-3t+4=19 \\ \\ -3t=15 \\ \\ t=-5[/tex]
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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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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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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If an airplane rises at a rate of 42 meters per second, how high will it be flying after 3 minutes?
Answer:
7560 meters
Step-by-step explanation:
42 meters a second -> 2520 meters a minute -> 7560 meters for 3 minutes
Answer:
The airplane will be 7560 meters after three minutes of flying.
Step-by-step explanation:
one minute= sixty seconds
42*1800=7560
3*60=1800
Not sure if I did the math right but I'm positive I got the right answer.
1. $20 haircut; 10% tip
steve and elsie are camping in the desert, but have decided to part ways. steve heads north, at 8 am, and walks steadily at 2 miles per hour. elsie sleeps in, and starts walking west at 2.5 miles per hour starting at 11 am.
After 2.57 hours, the distance between Steve and Elsie will be 25 miles.
What exactly is the distance?Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending point. Use the formula d = st, or distance equals speed times time, to find the distance. Since both represent a certain amount of distance per unit of time, such as miles per hour or kilometers per hour, rate and speed are comparable.So, let t (hours) represent the amount of time Elsie needs to travel before they are 25 miles apart.
Steve takes longer because he is 2 hours earlier, so his time is t + 2.
Steve travels x[tex]s_s=2(t+2)[/tex] miles to the north.Elsie travels a distance [tex]s_c=2.5 t[/tex] to the west.So, according to the formula the distance between Steve and Elsie will be:
[tex]\sqrt{s_s^2+s_c^2}=\sqrt{(2(t+2))^2+(2.5 t)^2}=25[/tex]Solve for t as follows:
[tex]\begin{aligned}&(2(t+2))^2+(2.5 t)^2=25^2=625 \\&4(t+2)^2+6.25 t^2=625 \\&4\left(t^2+4 t+4\right)+6.25 t^2=625 \\&10.25 t^2+16 t-609=0 \\&t=\frac{-b \pm \sqrt{t^2-4 a x}}{2 a} \\&t=\frac{-16 \pm \sqrt{(16)^2-4 *(10.25) *(-109)}}{2 *(10.25)} \\&t=\frac{-16 \pm 68.74}{20.5}\end{aligned}[/tex]
So, t = 2.57 or t = -4.13.
As we know that time can only be positive so it t = 2.57.Therefore, after 2.57 hours, the distance between Steve and Elsie will be 25 miles.
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The correct question is given below:
Steve and Elsie are camping in the desert, but have decided to part ways. Steve heads north, at 8 AM, and walks steadily at 2 miles per hour. Elsie sleeps in and starts walking west at 2.5 miles per hour starting at 10 AM. When will the distance between them be 25 miles?
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:
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:
how would i write The product of 2 and the cube of a number. if a number is x
the Algebraic representation of the expression "product of 2 and the cube of a number" is 2x³
How to write Algebraic expression?Algebra is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
The product of 2 and the cube of a number
The unknown number = xProduct means MultiplicationSo,
product of 2 and the cube of a number
= 2 × x³
= 2x³
For instance, if x = 2
2x³
= 2×(2)³
= 2 × (2 × 2 × 2)
= 2 × 8
= 16
Therefore, the expression "product of 2 and the cube of a number" can be written as 2x³
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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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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.
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
PLEASE MARK BRAINLEST
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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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
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°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.
What value of b will cause the system to have an infinite number of solutions?
y = 6x – b
–3x + StartFraction one-half EndFractiony = –3
b =
2
4
6
8
The value of b that will cause the system to have an infinite number of solutions is 6.
System of equationGiven the following system of equation expressed as:
y = 6x – b
-3x + 1/2 y = -3
Rewrite equation 2:
1/2 y = 3x - 3
y = 6x - 6
Equate the right hand side of both equations
6x - b = 6x - 6
For the equation to have infinite number of solutions, the expression on both sides must be the same.
Comparing both sides;
-b = -6
b = 6
This gives the required value of b
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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
There are 15 year 12 pupils in a football club, out of a total of 46 pupils. write this proportion as a percentage. give your answer correct to 1 decimal place when appropriate.
In the football club, the percentage of 15-year 12 pupils out of 46 pupils is equal to 30%.
The proportion can be found by dividing the number of 15-year pupils by the total number of pupils. Therefore;
number of 15-year pupils / total number of pupils = 12 / 46 = 0.260
Rounding it to one decimal;
0.260 = 0.3
Percentage in mathematics can be defined as a number or a rate in each hundred. A decimal value can be converted into a percentage by multiplying the decimal value by 100.
0.3 × 100 = 30%
Therefore, the proportion of the 15-year pupils in the football club is 12/46 and this proportion can be written in percentage as 30%.
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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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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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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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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]
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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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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Simplify.
3c + 6d + 3d
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3c + 6d + 3d}\\\large\text{COMBINE the LIKE TERMS}\\\mathsf{= (3c) + (6d + 3d)}\\\mathsf{= 3c + 6d + 3d}\\\mathsf{= 3c + 9d}\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{3c + 9d}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
x = ____ ( look at photo)
A car travels at 1/2t^2+55 mph for 0≤x≤5 hours. Approximately how far does it travel?