Answer:
5/14
Step-by-step explanation:
-5*-1/7*4/8=5/7*4/8=20/56=5/14
Which other angles could be in that triangle?
The other angles in the isosceles triangle with an angle of 100° will be 40°
Step-by-step explanation:
Lets define an isosceles triangle first.
"An isosceles triangle is a triangle with two equal sides and two equal angles.
Given that an angle of the triangle is 100°
We know that the sum of internal angles of a triangle is 180°
The sum of remaining two angles is:
=180°-100°
=80°
As the triangle is an isosceles triangle, the two angles will be equal.
So the angles will be:
[tex]=\frac{80}{2}\\=40[/tex]
The other angles in the isosceles triangle with an angle of 100° will be 40°
Keywords: Triangle, isosceles triangle
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find the equation of a straight line passing through the point (3,3) which is perpendicular to the line y=-1/2x-4
Answer:
y = 2x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{2}[/tex] x - 4 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2, thus
y = 2x + c ← is the partial equation
To find c substitute (3, 3) into the partial equation
3 = 6 + c ⇒ c = 3 - 6 = - 3
y = 2x - 3 ← equation of perpendicular line
The equation of the line passing through (3, 3) and perpendicular to y = -1/2x - 4, is y = 2x - 3.
To find the equation of a straight line passing through the point (3, 3) which is perpendicular to the line y = -1/2x - 4, follow these steps:
Determine the slope of the given line. The slope of y = -1/2x - 4 is -1/2.Find the slope of the perpendicular line. The slope of the perpendicular line is the negative reciprocal of -1/2, which is 2.Use the point-slope form of the equation of a line, y - y₁ = m(x - x₁), where (x₁, y₁) is the point (3, 3) and m is the slope (2).Substitute the values 2 for m and (3, 3) for (x₁, y₁): y - 3 = 2(x - 3).Simplify the equation: y - 3 = 2x - 6.Rewrite it in slope-intercept form: y = 2x - 3.Therefore, the equation of the line passing through the point (3, 3) and perpendicular to the line y = -1/2x - 4 is y = 2x - 3.
Which of the following equals 8 when you evaluate f(2) ? Select all that apply
A) f(x)=2x+1
B) f(x)=3x-2
C) f(x)=x(5x-2)
D) f(x)=3x-2x+4
E) f(x)=|x-8|+2
Answer:
E) [tex]f(x)=|x-8|+2[/tex]
Step-by-step explanation:
We will check each of the given choices by finding [tex]f(2)[/tex] of the given functions.
In order to find [tex]f(2)[/tex], we plugin [tex]x=2[/tex] in the function.
A) [tex]f(x)=2x+1[/tex]
[tex]f(2)=2(2)+1[/tex]
[tex]f(2)=4+1[/tex]
[tex]f(2)=5[/tex]
B) [tex]f(x)=3x-2[/tex]
[tex]f(2)=3(2)-2[/tex]
[tex]f(2)=6-2[/tex]
[tex]f(2)=4[/tex]
C) [tex]f(x)=x(5x-2)[/tex]
[tex]f(2)=2(5(2)-2)[/tex]
[tex]f(2)=2(10-2)[/tex]
[tex]f(2)=2(8)[/tex]
[tex]f(2)=16[/tex]
D) [tex]f(x)=3x-2x+4[/tex]
[tex]f(2)=3(2)-2(2)+4[/tex]
[tex]f(2)=6-4+4[/tex]
[tex]f(2)=6[/tex]
E) [tex]f(x)=|x-8|+2[/tex]
[tex]f(2)=|2-8|+2[/tex]
[tex]f(2)=|-6|+2[/tex]
[tex]f(2)=6+2[/tex] [Since absolute value of any number is positive]
[tex]f(2)=8[/tex]
So, the function in E has value =8 for [tex]f(2)[/tex]
The St. Louis Cardinals play 160 games in a season. So far, they have won 50 games. How many more games must they win in order to win at least 68% of all games for the season?
Answer:
More wins required = 59 wins
Step-by-step explanation:
Given:-
Total numbers of games played = 160.
Total games won = 50.
Total win percentage required = 68 %
Now,
Total percentage of games won = [tex]\frac{50}{160} \times 100[/tex]
Total percentage of games won = 0.312 [tex]\times[/tex]100
Total percentage of games won =31.25% ------------(equation 1)
Balance percentage of wins required = total win percentage required - total percentage of games won
Balance percentage of wins required = 68 - 31.25 -----(from equation 1)
Balance percentage of wins required = 36.75%
More wins required = [tex]\frac{Balance\ percentage\ of\ win\ required}{100} \times 160[/tex]
More wins required =[tex]\frac{36.75}{100}\times 160[/tex]
More wins required = 0.368 [tex]\times[/tex] 160
More wins required =58.88
More wins required = 59 wins --------------(rounded value)
St. Louis Cardinals need to win 59 more games to achieve at least a 68% winning percentage for the season.
To determine how many more games the St. Louis Cardinals must win in order to achieve at least a 68% winning percentage for the season, let's go through the calculations step by step.
Total Games: The Cardinals play a total of 160 games in a season.
Current Wins: The Cardinals have currently won 50 games.
Winning Percentage Goal: We want the Cardinals to win at least 68% of their games.
The formula to calculate the winning percentage is:
[tex]\text{Winning Percentage} = \frac{\text{Wins}}{\text{Total Games}} \times 100\%[/tex]
Therefore, the number of wins needed to achieve at least a 68% winning percentage can be calculated as follows:
[tex]\text{Wins Needed} = 0.68 \times 160 = 108.8 \text{ (approximately 109 games)}[/tex]
Calculating Additional Wins Needed: To find out how many more games the Cardinals need to win, we'll subtract the current wins from the wins needed:
[tex]\text{Additional Wins Needed} = \text{Wins Needed} - \text{Current Wins}[/tex]
[tex]\text{Additional Wins Needed} = 109 - 50 = 59[/tex]
a file that is 261 megabytes is being downloaded if the downloaded is 16.6% complete how many megabytes have been downloaded
43.326 megabytes has been downloaded
Solution:
Given that a file that is 261 megabytes is being downloaded
16.6 % of download is complete
To find: megabytes that have been downloaded
From given question,
16.6 % of 261 megabytes has been downloaded
Let us find 16.6 % of 261
We know that,
a % of b can be written in fraction as [tex]\frac{a}{100} \times b[/tex]
So 16.6 % of 261 is calculated as:
[tex]16.6 \% \text{ of }261 = 16.6 \% \times 261\\\\\rightarrow \frac{16.6}{100} \times 261\\\\\rightarrow 0.166 \times 261\\\\\rightarrow 43.326[/tex]
Thus 43.326 megabytes has been downloaded
The statements below can be used to prove that the triangles are similar.
On a coordinate plane, right triangles A B C and X Y Z are shown. Y Z is 3 units long and B C is 6 units long.
StartFraction A B Over X Y EndFraction = StartFraction 4 Over 2 EndFraction
?
StartFraction A C Over X Z EndFraction = StartFraction StartRoot 52 EndRoot Over StartRoot 13 EndRoot EndFraction
△ABC ~ △XYZ by the SSS similarity theorem.
Which mathematical statement is missing?
StartFraction Y Z Over B C = StartFraction 6 Over 3 EndFraction
∠B ≅ ∠Y
StartFraction B C Over Y Z EndFraction = StartFraction 6 Over 3 EndFraction
∠B ≅ ∠Z
Answer:
BC/YZ=6/3
Step-by-step explanation:
Doing the quiz rn
The similarities of triangles can be proved using SSS theorem.
The missing mathematical statement is: [tex]\mathbf{\frac{BC}{YZ} = \frac 63}[/tex]
Because the similarities of both triangles is being proved using SSS, then only the sides would be compared
Sides AB, AC, XY and XZ have already been compared.
So, the missing mathematical statement is the ratio of sides BC and YZ
From the question, we have:
[tex]\mathbf{BC = 6}[/tex]
[tex]\mathbf{YZ = 3}[/tex]
So, the missing statement is:
[tex]\mathbf{\frac{BC}{YZ} = \frac 63}[/tex]
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A cuboid with a volume of 924cm^3 has dimensions
4cm,(x+1)cm and (x+11)cm
Clearly show that x^2+12x-220=0
Solve the equation by factorising,make sure you show your factorisation.
State both values of x on the same line
Finally,find the dimensions of the cuboid,writing all three on one line
The values of x are -22 and 10
The dimensions are 4 cm , 11 cm , 21 cm
Step-by-step explanation:
The given is:
A cuboid with a volume of 924 cm³It has dimensions 4 cm , (x + 1) cm and (x + 11) cmWe want to show that x² + 12x - 220 = 0, and solve the equation to find its dimensions
The volume of a cuboid is the product of its three dimensions
∵ The dimensions of the cuboid are 4 , (x + 1) , (x + 11)
∴ Its volume = 4(x + 1)(x + 11)
- Multiply the two brackets and then multiply the product by 4
∵ (x + 1)(x + 11) = (x)(x) +(x)(11) + (1)(x) + (1)(11)
∴ (x + 1)(x + 11) = x² + 11x + x + 11 ⇒ add like terms
∴ (x + 1)(x + 11) = x² + 12x + 11
∴ Its volume = 4(x² + 12x + 11)
∴ Its volume = 4x² + 48x + 44
∵ The volume of the cuboid = 924 cm³
- Equate the expression of the volume by 924
∴ 4x² + 48x + 44 = 924
- Subtract 924 from both sides
∴ 4x² + 48x - 880 = 0
- Simplify it by dividing all terms by 4
∴ x² + 12x - 220 = 0
Now let us factorize it into two factors
∵ x² = x × x
∵ 220 = 22 × 10
∵ 22(x) - 10(x) = 12x ⇒ the middle term
∴ x² + 12x - 220 = (x + 22)(x - 10)
∴ (x + 22)(x - 10) = 0
- Equate each factor by 0 to find x
∵ x + 22 = 0 ⇒ subtract 22 from both sides
∴ x = -22
∵ x - 10 = 0 ⇒ add 10 to both sides
∴ x = 10
∴ The values of x are -22 and 10
We can not use x = -22 because there is no negative dimensions, then we will use x = 10
∵ The dimensions are 4 , (x + 1) , (x + 11)
∵ x = 10
∴ The dimensions are 4 , (10 + 1) , (10 + 11)
∴ The dimensions are 4 cm , 11 cm , 21 cm
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Answer: Showed that: [tex]x^2+12x-220=0[/tex].
Both values of x are -22 and 10.
The dimensions are: 4 cm, 11 cm, 21 cm.
The given dimensions are 4cm,(x + 1)cm and (x + 11)cm.
So the volume is = [tex]4(x+1)(x+11)[/tex].
Given that volume= 924 [tex]cm^3[/tex].
Equating the volumes we get:
[tex]4(x+1)(x+11)=924\\4(x^2+12x+11)=924\\x^2+12x+11=\frac{924}{4}\\ x^2+12x+11=231\\x^2+12x+11-231=0\\x^2+12x-220=0\\[/tex]
Then we factor and solve the equation:
[tex]x^2+12x-220=0\\x^2+22x-10x-220=0\\x(x+22)-10(x+22)=0\\(x+22)(x-10)=0\\x=-22,10\\[/tex]
Since x can not be negative, so x = 10.
So the dimensions are: 4 cm, (x + 1) = (10 + 1) = 11 cm, (x + 11) = (10 + 11) = 21 cm.
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Tony made this diagram
of his vegetable garden. What is the total area?
Explain your reasoning.
Answer:
The total area of Tony's vegetable garden is 124 square feet
Step-by-step explanation:
The total area of Tony's vegetable garden is composed by three rectangles.
1st rectangle
Length = 10 feet
Width = 6 feet (14 - 8)
Area = 6 * 10 = 60 square feet
2nd and 3rd rectangles are equals
Length = 4 feet
Width = 8 feet (14 - 6)
Area = 2 * 4 * 8 = 2 * 32 = 64 square feet
Total area
Area of the three rectangles
60 + 64 = 124 square feet
The total area of the vegetable garden is 124 ft.
A rectangle is a quadrilateral in which opposite sides are parallel and congruent to each other.
The area of a rectangle is the product of its length and width. It is given by:
Area = length * width
Area of the vegetable garden = (8 ft * 4 ft) + (8 ft * 4 ft) + (10 ft * (14 - 8)ft)
Area of the vegetable garden = 32 ft + 32 ft + 60 ft = 124 ft.
Therefore the total area of the vegetable garden is 124 ft.
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Toby divided 59.50 by 6.8, as shown. But he forgot to put a decimal point in the answer. Complete the sentence below
Answer:
The decimal point should be placed between the digits 8 and 7 because the quotient should be greater than 56 ÷ 7 and less than 63 ÷ 7.
Step-by-step explanation:
The division of the number 59.50 by 6.8 is equal to 8.75.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The division is one of the four basic operations of arithmetic, which are the methods by which numbers are combined to form new numbers. Addition, subtraction, and multiplication are the other operations.
Given that the number 59.50 is divided by the number 6.8. The division will be done as below,
Division = 59.50/6.8
Division = 8.75
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Can someone pls help
Answer:
square so all sides are equal
bc^2+mc^2=bm^2
16x^2+4x^2=20x^2=2root5x
nd^2+dm^2=nm^2
x^2+4x^2=5x2=root5x
then:-
1/2*b*h=1/2*2root5x*root5x
=1/2*10x^2=5x^2
==================================
Work Shown:
ND = x
AN = 3x
MD = 2x
MC = 2x
BC = 4x
AB = 4x
-------
P = Area of square ABCD
P = (AB)^2
P = (4x)^2
P = 16x^2
-------
Q = Area of triangle ABN
Q = (1/2)*base*height
Q = (1/2)*AN*AB
Q = (1/2)*3x*4x
Q = 6x^2
-------
R = Area of triangle MBC
R = (1/2)*base*height
R = (1/2)*BC*MC
R = (1/2)*4x*2x
R = 4x^2
-------
S = Area of triangle MND
S = (1/2)*base*height
S = (1/2)*ND*MD
S = (1/2)*x*2x
S = x^2
-------
T = Area of triangle BMN
T = P - Q - R - S
T = 16x^2 - 6x^2 - 4x^2 - x^2
T = 5x^2
-------
An alternative method is to use the pythagorean theorem to find the lengths of BM and MN. Then you can directly compute the area of triangle BMN. You should find that BM = sqrt(20)*x and MN = sqrt(5)*x.
Roger drew one card from a standard deck of 52 cards. What is the probability that the card Roger drew is not a seven?
Answer: 12/13
Step-by-step explanation:
In a deck of cards there are 4 of each number. Therefore there are 4 sevens in the deck. 4/52 are 7, but you want the probability of getting a card that IS NOT 7. That means there are 48 cards that aren’t a 7. 48/52 is the probability. But you can simplify this by finding a number that divides evenly into both, which in this case is 4. This simplifies to 12/13.
р
с
о
1.
Convert the following equation to standard form: y = -3x + 2
— у = 2
3х + y = 2
о 3х + y = -2
о — 3 — у. = 2
ОО
в
9514 1404 393
Answer:
3x +y = 2
Step-by-step explanation:
Standard form is ...
ax +by = c
where a, b, c are mutually prime integers and the leading coefficient is positive.
We can put the equation in this form by adding 3x to both sides.
y = -3x +2
3x +y = 2 . . . . . add 3x to both sides. This is standard form.
if the velocity of the car at t=2 is 4, find the velocity equation
Answer:
Velocity equation
[tex]v=\frac{d}{t}[/tex]
Step-by-step explanation:
Given:
Velocity of the car v = 4 units
and time t = 2 seconds
Let d = distance
Find the velocity equation.
The equation of the velocity is given below.
[tex]velocity=\frac{distance\ travelted}{time\ to\ distance\ travel}\ unit/sec[/tex]
[tex]v=\frac{d}{t}[/tex]
The above equation says, the distance travelled in t times is called velocity.
The unknown value in given question is distance. so, we find distance by given value.
[tex]d = v\times t[/tex]
[tex]d = 4\times 2[/tex]
[tex]d = 8\ units[/tex]
Therefore, the distance travelled by car is 8 units.
Formula for velocity: V = d/t
V = velocity
d = distance
t = time traveled
We are given the variables t = 2 and v = 2.
Substitute these values into the formula.
4 = d/2
Solve for d (d = distance).
4 = d/2
4 * 2 = d/2 * 2
8 = d
Therefore, the car traveled a distance of 8 units.
Best of Luck!
The highest temperature ever recorded on earth was 136 ferinheit the lowest was -129 ferinheit plot each temperature as an integer on a number line and use absolute value to determine the difference between the two temperatures
Answer:
265 Fahrenheit.
Step-by-step explanation:
It is given that,
Highest temperature ever recorded on earth = 136 Fahrenheit
Lowest temperature = -129 Fahrenheit
We need to plot these temperature as an integer on a number line.
136 is a positive integer. So, it lies 136 units on the right side of zero.
-129 is a negative integer. So, it lies 129 units on the left side of zero.
According to absolute values, |x|=|-x|=x.
Absolute value of 136 and -129 are
[tex]|136|=136[/tex]
[tex]|-129|=129[/tex]
The difference between he two temperatures is
[tex]|136-(-129)|=|136+129|=265[/tex]
Therefore, the difference between he two temperatures is 265 Fahrenheit .
If s store is selling boxes of pudding at 3 for $0.99,how much would 12 boxes cost
Answer:
The cost price of 12 boxes of pudding is $3.96
Step-by-step explanation:
Given as :
The quantity of pudding boxes = 3
The cost price for 3 boxes = $0.99
Again ,
The quantity of pudding boxes = 12
Let The cost price for 12 boxes = $x
Now, According to question
Using Unitary method
∵ The cost price of 3 boxes of pudding = $0.99
or,The cost price of 1 boxes of pudding = [tex]\dfrac{0.99}{3}[/tex] = $0.33
∴The cost price of 12 boxes of pudding =$0.33 × 12
I.e x =$3.96
So,The cost price of 12 boxes of pudding = x =$3.96
Hence,The cost price of 12 boxes of pudding is $3.96 Answer
Simplify (3a^n)^3 times (1/3a^n)^3
Answer:
3
Step-by-step explanation:
From the given indices
(3a^n)^3 X (1/3a^n)^3
We can rewrite the equation to be
(3a^n)^3 X (3a^-n) ^3
We father simplify;
3a^3n X 3a^-3n
Since we have same base, we add their relative powers, we solve thus,
3a^(3n-3n)
= 3a^0
= 3 X a^0 = 3 X 1
=1
Word problem for distributive property
Answer:
To build a computer, you need to buy a motherboard for 120 dollars, a CPU for 100 dollars, RAM memory for 45 dollars, storage for 30 dollars, a case for 15 dollars, and a power supply for 50 dollars. What is the cost of building 10 computers? Hope this helps, if so then please mark brainliest.
The distributive property allows for the distribution of multiplication over addition within an expression and is key in algebra and vector operations.
The distributive property is a fundamental algebraic property used in mathematics, especially when dealing with expressions containing variables and constants. This property allows one to distribute multiplication over addition within an expression, helping simplify and solve equations. For example, using the distributive law, the expression A(A + B) can be expanded to AA + AB. Due to the idempotency theorem, which states that A times A is equal to A (AA = A), the result simplifies to A + AB = A. Furthermore, the distributive property is also a key concept in vector operations, such as the cross product, and is critical for proving various mathematical axioms and properties, such as the associative and commutative laws.
Carlos has saved 19.80. Shaq saved 5/6 of the amount that Carlos saved. Deontae
saved 4 times as much as Shaq. What is the total saved amount of all three
Answer:
$102.30
Step-by-step explanation:
Carlos: 19.80
Shag: 19.80 x 5/6 = 16.5
Deontae: 16.5 x 4 = 66.0
Total: 19.80 + 16.50 + 66.00 = 102.30
The total amount saved by Carlos, Shaq, and Deontae is $102.30.
Explanation:To find the total amount saved by Carlos, Shaq, and Deontae, we first need to understand how much each of them saved individually. Carlos saved $19.80. Shaq saved 5/6 of the amount that Carlos saved, which we can calculate as (5/6) * $19.80 = $16.50. Deontae saved 4 times as much as Shaq, which we can calculate as 4 * $16.50 = $66. Finally, we add all these amounts together to get the total saved amount.
So, the total saved amount of all three is $19.80 (Carlos) + $16.50 (Shaq) + $66 (Deontae) = $102.30
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Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations).
The question focuses on Mathematics, specifically Geometry and Calculus. It requires calculating the area of geometric figures especially circles and disks in terms of π, often via the formula A=πr² or integration.
Explanation:From the question, we are required to find the area of shaded parts, which essentially associates with geometric figures and their properties in Mathematics. Specifically, this question appears to focus on areas related to circles and spheres, as it mentions calculations in terms of π, radius (r) and certain formulas like A=πr², which is the formula for the area of a circle.
When asked to express something in terms of π, it typically means leaving the answer as multiples of π, rather than using its decimal equivalent. So for instance, if we calculated the area of a circle with a radius of 3 using A=πr², we would say that the area is 9π.
Another crucial information that surfaced in the materials provided is the area calculation using integration, which involves adding up the individual areas of 'thin rings' from r=0 to r=R where R is the total radius of the disk or circle. This is an important aspect of finding areas under curves or finding areas enclosed by curves in Calculus.
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The area of the shaded regions is [tex]\(8\pi - 8\)[/tex] square centimeters.
To find the area of the shaded regions in the circle with the inscribed triangle, we'll follow these steps:
1. Calculate the Area of Sector AOC:
- The sector's central angle is 90° because triangle AOC is right-angled at C.
- The area of a sector is [tex]\( \frac{\theta}{360} \times \pi \times r^2 \)[/tex], where [tex]\( \theta \)[/tex] is the central angle and [tex]\( r \)[/tex] is the radius.
- Here, [tex]\( r = 4 \) cm and \( \theta = 90° \).[/tex]
- So, the area of sector AOC is [tex]\( \frac{90}{360} \times \pi \times 4^2 = \pi \times 4 \) cm^2.[/tex]
2. Calculate the Area of Triangle AOC:
- The area of a triangle is [tex]\( \frac{1}{2} \times \text{base} \times \text{height} \).[/tex]
- For triangle AOC, the base and height are both equal to the radius, which is 4 cm.
- So, the area of triangle AOC is [tex]\( \frac{1}{2} \times 4 \times 4 = 8 \)[/tex] cm².
3. Calculate the Area of the Shaded Segment on the Opposite Side:
- Subtract the area of triangle AOC from the area of sector AOC.
- This gives us the area of the shaded segment: [tex]\( \pi \times 4 - 8 \)[/tex] cm².
Combining both shaded areas, the total area of the shaded regions is [tex]\( \pi \times 4 + (\pi \times 4 - 8) \)[/tex] cm², which simplifies to [tex]\( 8\pi - 8 \)[/tex] cm². Therefore, the area of the shaded regions is [tex]\( 8\pi - 8 \)[/tex] cm².
There are 12 men who may be elected to the council. If there are only 5 members of the council, how many different combination of council members are possible?
Answer:
252 different combinations
Step-by-step explanation:
There are 12 men who may be elected to the council. If there are only 5 members of the council (the order doesn't matter), then there are
[tex]C^{10}_5\\ \\=\dfrac{10!}{5!(10-5)!}\\ \\=\dfrac{10!}{5!\cdot 5!}\\ \\=\dfrac{5!\cdot 6\cdot 7\cdot 8\cdot 9\cdot 10}{5!\cdot 5!}\\ \\=\dfrac{6\cdot 7\cdot 8\cdot 9\cdot10}{1\cdot 2\cdot 3\cdot 4\cdot 5}\\ \\=7\cdot 4\cdot 9\\ \\=252[/tex]
different combinations of council members.
Jordan bikes at a speed of 8 2/3 mph. How many miles will he bike in:
45 minutes?
Answer:390 miles
Step-by-step explanation:
speed*time=distance (keep that in mind)
8 2/3 is also equal to 26/3
take that number and multiply that by 45 min
45*26/3
that equall 390 miles
(I tried my best, I might be wrong)
Answer:
13/2
Step-by-step explanation:
Keep in mind that speed*time=distance
ok so, if you convert 8 2/3 in to a improper fraction you'll get 26/3. Now we have to turn 45 minutes into a fraction so it's easier to multiply, that would be 45/60 because 1 hour has 60 minutes. Now, we would multiply 26/3 and 45/60 and get 78/12. Simplify that and get 13/2
fifteen friend want to share 3 watermelons equally. what fraction of a watermelon will each friend get?
Answer: 3/15 or 1/5
Step-by-step explanation:
Each person will get 1/15 of each watermelon so 3/15 of watermelon that can be simplified to 1/5
Final answer:
Each of the fifteen friends will receive ⅔ of a watermelon when 3 watermelons are shared equally among them.
Explanation:
If fifteen friends want to share 3 watermelons equally, we need to divide the total number of watermelons by the number of friends to find out what fraction of a watermelon each friend will get.
To find the answer, you start with 3 watermelons and divide them by 15 friends, which is:
3 watermelons ÷ 15 friends = ⅔ of a watermelon per friend.
Thus, each friend will get ⅔ of a watermelon.
what is 5 inches to centimeters
Find the solution of this system of equations
8x - 5y = -8
-7x - 5y = 82
Answer:
x=-6, y=-8. (-6, -8).
Step-by-step explanation:
8x-5y=-8
-7x-5y=82
---------------
-(8x-5y)=-(-8)
-7x-5y=82
---------------------
-8x+5y=8
-7x-5y=82
---------------
-15x=90
x=90/-15
x=-6
8(-6)-5y=-8
-48-5y=-8
5y=-48-(-8)
5y=-48+8
5y=-40
y=-40/5
y=-8
Your class has 18 students. Exactly 23
2
3
of them say that, out of all their subjects, they like science the most. Which model shows 23
2
3
of 18 circled?
Answer:
Sample model as the picture attached, which shows 2/3 of 18 are circled.
Step-by-step explanation:
Here is the correct question: Your class has 18 students. Exactly 2/3
of them say that, out of all their subjects, they like science the most. Which model shows 2/3 of 18 circled?
Given: Total number of student is 18.
2/3 of the total students like science the most.
Now, calculating the number students like the science the most.
∴ Number of students who like the science most= [tex]\frac{2}{3} \times 18= 12 \ students[/tex]
12 students like the science most out of total students.
Sample model are shown in the picture attached, where out of 18 students only 12 are inside the circle to show they like science the most.
Simplify the expression
Answer:
A)
Step-by-step explanation:
How does h(x)=-2x+5 change over the interval from x=1 to x=2?
As the rate of change of function is negative from x=1 to x=2, the function decreases at this interval.
Step-by-step explanation:
We have to find the rate of change of the function
The rate of change of function is given by:
[tex]Rate\ of\ change = \frac{h(b)-h(a)}{b-a}[/tex]
Given function is:
[tex]h(x) = -2x+5[/tex]
Here
a =1
b = 2
So,
[tex]h(2) = -2(2) +5\\= -4+5\\= 1\\h(1) = -2(1) +5\\= -2+5\\= 3[/tex]
Putting the values in the formula
[tex]Rate\ of\ change = \frac{1-3}{2-1} = -2[/tex]
As the rate of change of function is negative from x=1 to x=2, the function decreases at this interval.
Keywords: Functions, rate of change
Learn more about functions at:
brainly.com/question/9323337brainly.com/question/9381080#LearnwithBrainly
How do you know what angles they are talking about when they say some like ∠OCA ∠CAO ∠OAB
Answer:
You would know what people would say by saying that because they mean that you were to match up the letters into a shape in that order
Step-by-step explanation:
Hopefully this helps, give me a brainliest
Answer:
The given angles are
[tex]\angle BOA\\\angle AOC[/tex]
When we write down angles, we have different notations to do it.
In this case, we have angles with three letter, each one indicates a specific element.
The first letter indicate the initial point where the angle starts, for example, [tex]\angle BOA[/tex], beginas at point B, the middle letter indicates the vertex where the angle is at, so [tex]\angle BOA[/tex] indicates is at vertex O, at last, the third letter A indicates the final point where the angle goes.
Having said that, [tex]\angle BOA[/tex] is the opening from point B, then goes to vertex O and finally goes to point A, in the image attached you can see this angle highlighted.
Using the same reasoning, we have that [tex]\angle AOC[/tex] starts at points A, goes to vertex O, and ends at point C. Refer to the image attached.
Two perpendicular lines have opposite y-intercepts. The equation of one of these lines is
y=mx+b. Express the x-coordinate of the intersection point of the lines in terms of m and b.
The x-coordinate is x =_____
Plz help me and fast!
Answer: The required x-co-ordinate of the point of intersection of two lines is [tex]-\dfrac{2bm}{m^2+1}.[/tex]
Step-by-step explanation: Given that two perpendicular lines have opposite y-intercept and the equation of one of the lines is
[tex]y=mx+b.[/tex]
We are to express the x-coordinate of the intersection point of the lines in terms of m and b.
Let the slope and y-intercept of the other line be s and c respectively.
Since the product of the slopes of two perpendicular lines is -1 and -b is the opposite of b, so we have
[tex]ms=-1~~~\Rightarrow s=-\dfrac{1}{m}[/tex]
and c = -b.
That is, the equation of the other line is
[tex]y=sx+c\\\\\Rightarrow y=-\dfrac{1}{m}-b.[/tex]
Comparing the equations of both the lines, we get
[tex]mx+b=-\dfrac{1}{m}x-b\\\\\\\Rightarrow mx+\dfrac{1}{m}x=-2b\\\\\\\Rightarrow \dfrac{m^2+1}{m}x=-2b\\\\\\\Rightarrow x=-\dfrac{2bm}{m^2+1}.[/tex]
Thus, the required x-co-ordinate of the point of intersection of two lines is [tex]-\dfrac{2bm}{m^2+1}.[/tex]
Final answer:
The x-coordinate of the intersection point for two perpendicular lines with opposite y-intercepts can be expressed as x = -2b/(m + 1/m), where m is the slope and b is the y-intercept of one of the lines.
Explanation:
When we have two perpendicular lines with opposite y-intercepts, and one of the lines has the equation y = mx + b, we can find the x-coordinate of the intersection point by expressing the other line's equation.
Since the other line is perpendicular, its slope will be the negative reciprocal of m. Therefore, if the first line's slope is m, the second line's slope will be -1/m. Also, if the y-intercept of the first line is b, the y-intercept of the second line will be -b, given that they are opposite.
The equation of the second line will then be y = (-1/m)x - b. To find the intersection point, we set the y-values of both equations equal to each other:
mx + b = (-1/m)x - b
Now, let's solve for x:
mx + (1/m)x = -2b
x(m + 1/m) = -2b
x = -2b/(m + 1/m)
Thus, the x-coordinate of the intersection point in terms of m and b is x = -2b/(m + 1/m).
For the school play, the advance tickets cost $3, while tickets at the door cost $5. Thirty more tickets were sold at door in advance, and $2630 was collected. How many of each kind of ticket was sold?
Answer:
310 tickets were sold in advance before school pay and 340 door tickets were sold in advance.
Step-by-step explanation:
Given:
Let number of tickets sold in advance be 'x'.
Cost of advance ticket = $3
Cost of door tickets = $5
Also given:
Thirty more tickets were sold at door in advance
Hence number of door tickets sold = [tex]x+30[/tex]
Total Money Collected = $2630
Now we can say that Total Money Collected is equal to sum of number of tickets sold in advance multiplied by Cost of advance ticket and number of door tickets sold multiplied by Cost of door tickets.
Framing in equation form we get;
[tex]3x+(x+30)5=2630[/tex]
Solving the equation to find the value of x we get;
[tex]3x+5x+150=2630[/tex]
Combining the like terms we get;
[tex]3x+5x=2630-150\\\\8x= 2480[/tex]
Now Dividing 8 on both side using division property we get;
[tex]\frac{8x}{8} =\frac{2480}{8}\\ \\x=310[/tex]
Substituting the value of x to find number of door tickets been sold.
number of door tickets sold = [tex]x+30=310+30 =340[/tex]
Hence, 310 tickets were sold in advance before school pay and 340 door tickets were sold in advance.