The answer is true.
Step-by-step explanation:
To find the points all lie on the same line, we need to substitute the points in the equation of the line, to determine if the values on both sides of the equation are equal.
Substituting the point [tex](6,13)[/tex] in the equation of the line, we get,
[tex]\begin{aligned}y &=\frac{4}{3} x+5 \\13 &=\frac{4}{3}(6)+5 \\&=4(2)+5 \\&=8+5 \\13 &=13\end{aligned}[/tex]
Thus, the values on both sides are equal. The point [tex](6,13)[/tex] lie on the same line.
Substituting the point [tex](21,33)[/tex] in the equation of the line, we get,
[tex]\begin{aligned}y &=\frac{4}{3} x+5 \\33 &=\frac{4}{3}(21)+5 \\&=4(7)+5 \\&=28+5 \\33 &=33\end{aligned}[/tex]
Thus, the values on both sides are equal. The point [tex](21,33)[/tex] lie on the same line.
Substituting the point [tex](99,137)[/tex] in the equation of the line, we get,
[tex]\begin{aligned}y &=\frac{4}{3} x+5 \\137 &=\frac{4}{3}(99)+5 \\&=4(33)+5 \\&=132+5 \\137 &=137\end{aligned}[/tex]
Thus, the values on both sides are equal. The point [tex](99,137)[/tex] lie on the same line.
Thus, all the three points lie on the same plane.
Hence, the answer is true.
All three points (6 , 13), (21 , 33), and (99 , 137) lie on the line y = [tex]\frac{4}{3}[/tex]x + 5. Thus, the statement is True, all three points make the equation true. Option 3 is the correct answer.
To determine whether the points (6,13), (21,33), and (99,137) all lie on the line y = [tex]\frac{4}{3}[/tex]x + 5, we need to substitute the x-values of each point into the equation and see if the corresponding y-values match.
1. For the point (6,13):
Substitute x = 6 into the equation.
⇒ y = ([tex]\frac{4}{3}[/tex]) × 6 + 5
⇒ y = 8 + 5
⇒ y = 13
Since the y-value matches, the point (6,13) is on the line.
2. For the point (21,33):
Substitute x = 21 into the equation.
⇒ y = ([tex]\frac{4}{3}[/tex]) × 21 + 5
⇒ y = 28 + 5
⇒ y = 33
Since the y-value matches, the point (21,33) is on the line.
3. For the point (99,137):
Substitute x = 99 into the equation.
⇒ y = ([tex]\frac{4}{3}[/tex]) × 99 + 5
⇒ y = 132 + 5
⇒ y = 137
Since the y-value matches, the point (99,137) is on the line.
All three points satisfy the equation y = [tex]\frac{4}{3}[/tex]x + 5. Therefore, the statement is True: all three points make the equation true option (3).
Complete question:
True or False:
The points (6,13), (21,33) and (99,137) all lie on the same line. The equation of the line is y = [tex]\frac{4}{3}[/tex]x + 5.
Select the correct explanation.
False, all three points do not make the equation true.True, all three points are positive.True, all three points make the equation true.False, all three points are positive.Convert to scientific notation
Answer:
5.7* 10 to the power of 4
Answer:
57,000 = 5.7 × 10⁴Step-by-step explanation:
[tex]\text{The scientific notation}:\\\\a\times10^k\\\\\text{where}\\\\1\leq a<10,\ k\in\mathbb{Z}\\\\================================[/tex]
[tex]57,000=5.7\times10000=5.7\times10^4\\\\-----------------------\\\\57000=5\underbrace{7000}_{\leftarrow4}=5\times10^4[/tex]
If there are 12 people sitting at a round table how many different pairs of people can have conversations assuming they can all talk to each other?
Answer: 6
Step-by-step explanation: 12/2 because a pair is 2 people and there are 12 people in total.!
The number of different pairs of people who can have conversations at a round table with 12 people is 66. This is calculated using the combination formula C(n, 2).
The student asks about the number of different pairs of people who can have conversations at a round table with 12 people, assuming that everyone can talk to each other. The problem is a combinatorial one and can be solved by using the formula for combinations. The formula for the number of combinations of pairs from a set of n items is [tex]C(n, 2) = \frac{n! }{2! * (n - 2)!}[/tex], where n! (n factorial) is the product of all positive integers up to n, and C denotes the combination.
To find how many different pairs can have conversations, we plug in n = 12 into the combination formula:
[tex]C(12, 2) = \frac{12! }{2! * (12 - 2)!} = \frac{12 * 11}{2 * 1} = 66[/tex]
So, there are 66 different pairs of people that can have conversations at a round table with 12 people.
Louis wants to carpet the rectangular floor of his basement.The basement has a area 432 square feet,The width of the basement is 1/3 its length.What's the length of Louis's basement.
Answer:
36 ft
Step-by-step explanation:
Let L represent the length of Louis's basement. The area is the product of length and width, so is ...
A = L(L/3)
432 = L²/3 . . . . . fill in area value
1296 = L² . . . . . . multiply by 3
36 = L . . . . . . . . . take the square root
The length of Louis's basement is 36 feet.
Input the expression x +9/2
Answer:um where is the constant
Step-by-step explanation:
The expression 'x + 9/2' involves adding a variable 'x' to the fraction 9/2. In an example situation, if you substitute x with the number 5, the result would be 9.5. Remember, x can represent any number.
Explanation:The expression you provided is x + 9/2. In mathematics, this is an algebraic expression which comprises of a variable x and a fraction 9/2. It means that you're adding the x variable to the fraction 9/2. For example, if you were to substitute x with a number, let's say 5, the answer would then be 5 + 9/2 = 9.5. It's important to remember that variables can represent any number, and in this case, the variable is x.
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9 cm
3 cm
AB is parallel to DC.
AD = 9 cm, DC = 3 cm. Angle BCD = 35°
Angle ABD = 90°
Calculate the size of angle BAD.
Give your answer correct to one decimal place.
Answer:
∴ ∠BAD = [tex]sin^{-1}[/tex](0.2044) = 11.8°
Step-by-step explanation:
i) AD = 9 cm
ii) DC = 3 cm
iii) ∠BCD = 35°
iv) Since AB is parallel to DC and ∠ABD = 90° then we can conclude that ∠BDC = 90°.
v) [tex]\frac{BD}{DC} = \frac{BD}{3\hspace{0.1cm}cm} = tan(35)[/tex] = 0.6128 ∴ BD = 3 [tex]\times[/tex] 0.6128 = 1.84 cm
vi) ∴ sin(∠ BAD ) = [tex]\frac{BD}{AD}[/tex] ⇒ sin(∠ BAD ) = [tex]\frac{1.84}{9}[/tex] = 0.2044
∴ ∠BAD = [tex]sin^{-1}[/tex](0.2044) = 11.8°
Answer:
Step-by-step explanation:
The image below represents a 12 x 16 room with an 8 x 10 piece of linoleum centered in the room . The yellow and blue rectangles extend the length of their respective sides. Where these two rectangles overlap, there is a green rectangle.
What is the area of the portion of the room shown in gray? _____ sq. ft.
The area of the gray portion in the room, after subtracting the area of the central linoleum from the total area of the room, is 112 sq. ft.
Explanation:To calculate the area of the gray portion in the room, first subtract the area of the linoleum from the total area of the room. The area of the room is given as 12 x 16 sq. ft. and the linoleum is 8 x 10 sq. ft.. To find the total area of the room, multiply the length by the width (12 x 16 = 192 sq. ft.). Then do the same for the linoleum (8 x 10 = 80 sq. ft.). Subtracting the area of the linoleum from the total area of the room gives us the gray area (192 - 80 = 112 sq. ft.). Hence, the area of the gray portion is 112 sq. ft.
How do I find the area
Answer:
For the smaller rectangle: 9 x 19.8 = 178.2
For the bigger rectangle: 27 x 10.8 = 291.6
NEED HELP ASPA PLS HELP WITH THIS
SEE IMAGE FOR A, B, C, D REFERENCE
A- 3
B- 3
C- 6
D- 3x+6
On the board you should have 6 of the orange + tiles and 3 of the orange x tiles.
Write the equation for a parabola that has x-intercepts (−4.5, 0) and (−2.8, 0) and y-intercept (0, 37.8).
Answer:
[tex]y=3(x+4.5)(x+2.8)[/tex] or [tex]y=3x^2+21.9x+37.8[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola in factored form is equal to
[tex]y=a(x-x_1)(x-x_2)[/tex]
where
a is a coefficient
x_1 and x_2 are the roots or x-intercepts of the quadratic equation
In this problem we have
[tex]x_1=-4.5\\x_2=-2.8[/tex]
substitute
[tex]y=a(x+4.5)(x+2.8)[/tex]
Find the value of a
we have the y-intercept (0,37.8)
substitute the value of x and the value of y of the y-intercept in the equation and solve for a
[tex]37.8=a(0+4.5)(0+2.8)[/tex]
[tex]a=37.8/12.6\\a=3[/tex]
so
[tex]y=3(x+4.5)(x+2.8)[/tex]
Convert to expanded form
[tex]y=3(x^2+2.8x+4.5x+12.6)[/tex]
[tex]y=3x^2+21.9x+37.8[/tex]
Answer:
Go to the link below :)
Step-by-step explanation:
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Passes through (3,-7), m=-2
If you are trying to find the equation of a line:
The equation of a line is y = mx + b [m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y) or the point where the line crosses through the y-axis]
Since you have m = -2, plug it into the equation
y = mx + b
y = -2x + b To find b, plug in the point they gave you (3, -7)
-7 = -2(3) + b
-7 = -6 + b Add 6 on both sides
-1 = b Now that you have b, plug it into the equation
y = -2x - 1
Jacksonville to Atlanta: 4 routes Atlanta to Knoxville: 3 routes Knoxville to Indianapolis: 2 routes Sammy is traveling from Jacksonville to Atlanta to Knoxville to Indianapolis. He can choose from several different routes. How many different routes can Sammy take on his trip? A) 9 B) 11 C) 12 D) 24
Answer:
D) 24.
Step-by-step explanation:
The solution is 24 routes. To determine the number of different routes we multiply the routes for each part of the trip. 4(3)(2) = 24 routes.
He can take 24 different routes for his trip
The correct option is option D)
What is permutation and combination?
an arrangement of objects in a definite order is known as permutation. The members or elements of sets are arranged here in a sequence. a combination is a selection of items from a set which has distinct members, and the order of selection does not matter. even though the terms are used together they are different and formula for calculating them is also different
We are given that,
Jacksonville to Atlanta: 4 routes
Atlanta to Knoxville: 3 routes
Knoxville to Indianapolis: 2 routes
Also Sammy is traveling from Jacksonville to Atlanta to Knoxville to Indianapolis
To find the different routes sammy can take can be computed as
4*3*2=24ways
Hence Sammy can take 24 routes
The correct option is option D)
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Square root of one hundred and twenty three
what is the quotient of m^6/5 divided by 5/m^2
Answer:
[tex]\large\boxed{\dfrac{m^8}{25}}[/tex]
Step-by-step explanation:
[tex]\dfrac{m^6}{5}\div\dfrac{5}{m^2}\\\\\text{Divide by a fraction is the same as multiply by its reciprocal}\\\\=\dfrac{m^6}{5}\times\dfrac{m^2}{5}=\dfrac{m^6\times m^2}{5\times5}\\\\\text{use}\ a^n\times a^m=a^{n+m}\\\\=\dfrac{m^{6+2}}{25}=\dfrac{m^8}{25}[/tex]
Find the product. Simplify your answer.
(4z–1)(z–3)
Answer: 4z (to the 2 power) - 13z + 3
Step-by-step explanation:
WHat is the property for 5x+10=24-2x
Final answer:
The correct solution to the equation 5x+10=24-2x is x=2, which is verified by substitution and results in an identity, confirming the solution is accurate.
Explanation:
The equation 5x+10=24-2x is a simple linear equation that can be solved by collecting like terms and isolating the variable x. Begin by adding 2x to both sides to get 7x + 10 = 24, then subtract 10 from both sides to obtain 7x = 14. Dividing both sides by 7 yields x = 2, which is the sole solution to the equation. Checking the solution, 24 - 2(2) does indeed equal 5(2) + 10, giving an identity of 20 = 20. This illustrates the solution is correct and verifies our process.
OK it has 5 g Of sugar per serving. A banana has 15 g of sugar per serving.
1/3 banana hgfdsedcrtvfybgunhimjnyhtbgvfdcvfbgnhmij,omhnbvdcrmjytgvg
For the function f defined by f(x)=3x2−2x+5 find f(−x),−f(x) , and −f(−x).
Step-by-step explanation:
[tex]f(x)=3x^2-2x+5\\\\f(-x)=\text{substitute (-x) instead x in f(x)}\\\\f(-x)=3(-x)^2-2(-x)+5=3x^2+2x+5\\\\-f(x)=-(3x^2-2x+5)=-3x^2-(-2x)-5=-3x^2+2x-5\\\\-f(-x)=-(3x^2+2x+5)=-3x^2-2x-5[/tex]
The answers are:
[tex]\begin{aligned}& f(-x)=3 x^2+2 x+5 \\& -f(x)=-3 x^2+2 x-5 \\& -f(-x)=-3 x^2-2 x-5\end{aligned}[/tex]
Let's find f(−x), −f(x), and −f(−x) for the given function [tex]f(x)=3 x^2-2 x+5[/tex].
f(−x):
Replace x with −x in the function:
[tex]f(-x)=3(-x)^2-2(-x)+5[/tex]
Simplify this expression:
[tex]f(-x)=3 x^2+2 x+5[/tex]
−f(x):
Multiply the entire function f(x) by −1:
[tex]-f(x)=-\left(3 x^2-2 x+5\right)[/tex]
Distribute the negative sign:
[tex]-f(x)=-3 x^2+2 x-5[/tex]
−f(−x):
Replace x with −x in the function f(x) and then multiply the whole expression by −1:
[tex]-f(-x)=-\left(3(-x)^2-2(-x)+5\right)[/tex]
Simplify this expression:
[tex]-f(-x)=-\left(3 x^2+2 x+5\right)[/tex]
Distribute the negative sign:
[tex]-f(-x)=-3 x^2-2 x-5[/tex]
Question:
For the function f defined by [tex]f(x)=3 x^2-2 x+5[/tex] find f(−x),−f(x) , and −f(−x).
What is 967 divided by 60 equals???
Answer:
16.11(6)
Step-by-step explanation:
967/60=16 7/60
Suppose p represents the amount of air pressure in a tire and t, the time it takes for the tire to go flat, equals −8. What is the value of p, if the quotient of
p
t
is −4?
p = 32
Solution:
Given p represents the amount of air pressure in a tire.
t represents the time it takes for the tire to go flat and t = –8.
To find the value of p, if [tex]\frac{p}{t}=-4[/tex].
⇒ [tex]\frac{p}{t}=-4[/tex]
Substitute t = –8 in the above equation.
⇒ [tex]\frac{p}{-8}=-4[/tex]
Do cross multiply, we get
⇒ p = (–8) × (– 4)
⇒ p = 32
Hence, the value of p is 32 if the quotient [tex]\frac{p}{t}[/tex] is –4.
1 9/10, 1 7/10, blank, 1 3/10, 1 1/10 what is the blank
Answer:15/10
Step-by-step explanation:
You subtract the top of the fraction by 2
Answer:
1 5/10 or 1 1/2
Step-by-step explanation:
You seem to have an arithmetic sequence, with each term 2/10 less than the one before.
2/10 less than 1 7/10 is 1 5/10. The fraction can be reduced to 1 1/2, but you may not want to.
At the football game, 4 hamburgers and 6 soft drinks cost $34, and 4 hamburgers and 3 soft drinks cost $25. Which two equations can be used to determine the price of a hamburger and the price of a soft drink? Let x represent the cost of a hamburger and y represent the cost of a soft drink.
Answer:
[tex]4x+6y=34\\\\4x+3y=25[/tex]
Step-by-step explanation:
Let be "x" the cost in dollars of a hamburger and "y" the cost in dollars of a soft drink.
The cost of 4 hamburguers can be represented with this expression:
[tex]4x[/tex]
And the cost of 6 soft drinks can be represented with this expression:
[tex]6y[/tex]
Since the total cost for 4 hamburgers and 6 soft drinks is $34, you can write the following equation:
[tex]4x+6y=34[/tex] [Equation 1]
The following expression represents the the cost of 3 soft drinks:
[tex]3y[/tex]
According to the information given in the exercise, the total cost for 4 hamburgers and 3 soft drinks is $25. Then, the equation that represents this is:
[tex]4x+3y=25[/tex] [Equation 2]
Therefore, the Equation 1 and the Equation 2 can be used to determine the price of a hamburger and the price of a soft drink
A sound system has a regular price of $249. Find the total cost of it is on sale for 40% off and the sales tax is 6.25%
Answer:
$158.74
Step-by-step explanation:
A sound system has a regular price of $249. Now, we have to find the total cost of it if there is a sale for 40% off and the sales tax is 6.25%.
Now, if there is 40% off on price $249, then the discounted price will be
[tex]249(1 - \frac{40}{100}) = 149.4[/tex] dollars.
Then the after-tax value of the sound system at the rate of 6.25% will be [tex]149.4(1 + \frac{6.25}{100}) = 158.74[/tex] dollars (Approximate)
(Answer)
Substitution for {2x-3y=11 and -x + 2y = -6
Step-by-step explanation:
-x+2y=-6
x-2y=6
x=2y+6
substitute in 2x-3y=11 gives us 2(2y+6)-3y=11
4y+12-3y=11
y=-1
-x+2(-1)=-6
-x=-4
x=4
Daniel went on his bike 45 miles in four hours, what was his speed?
Answer:
11.25 miles/hour
Step-by-step explanation:
Recall, speed = Distance ÷ Time
We are given :
Distance = 45 miles
Time = 4 hours
Hence,
Speed = Distance ÷ Time
= 45 miles ÷ 4 hours
= 11.25 miles/hour
7x + 3x + 5 - 2x + 7. Select all that are equivalent.
a. 2x + 6
b. 10X + 12 - 2x
c. 12x + 12
d. 8x + 12
Answer:
d 8x+12
Step-by-step explanation:
7x+3x+5-2x+7
combine 7x+3x-2x=8x
and 5+7=12
8x+12
Answer:
Step-by-step explanation:
7x+3x-2x=8x
5+7=12
8x+12
what conclution can be drawn about lines AB and CD?
Answer:
Step-by-step explanation:
they are both equal
Answer: They are not parallel because the two given alternate interior angles are not congruent
Step-by-step explanation:
A flock of geese landed landed in a dog park. All the dogs ran to investigate. Alex counted
22 animals 64 legs. How many many geese and how many dogs did he count?
Answer:
12 geese
10 dogs
Step-by-step explanation:
We are given;
Total number of animals (dogs and geese) is 22 Total number of legs of animals is 64We are required to determine the number of geese and dogs that Alex counted;
We need to know that;
a dog has 4 legs while, a geese has 2 legs Therefore;Assuming he counted x number of geese and y number of dogs;
Then;
x + y = 22, and
2x + 4y = 64
Thus, solving the equation simultaneously;
we can multiply the first equation by 2, to get
2x + 2y = 44
2x + 4y = 64
Eliminating x (by subtracting the second eqn from the first eqn), we get;
-2y = -20
y = 10
Solving for x;
x = 22 - y
= 22 - 10
x = 12
Therefore; he counted 12 geese and 10 dogs
Lucas says his twin baby brothers have a total weight of 15 and one eighth pounds. jackson 6 and one fourth pounds and jeremy weighs 8 and seven eighths pounds. explain how you can use estemation to tell if the total weight is reasonable
By rounding each brother's weight to the nearest whole number and adding these, we get an estimate of 15 pounds. The actual total weight, 15 and one eighth pounds, is close to this estimate, indicating that Lucas' claim about his brothers' weight is reasonable. This demonstrates how estimation can be used to quickly verify the validity of a claim.
Explanation:Estimation is a valuable mathematical tool that can be used to assess the reasonableness of a solution. In the case of Lucas' twin baby brothers' weight, you can use rounding to estimate their total weight. Let's start by rounding each brother's weight to the nearest whole number. In this scenario, Jackson, who weighs 6 and one fourth pounds could be estimated to weigh 6 pounds, and Jeremy, who weighs 8 and seven-eighths pounds, could be estimated to weigh roughly 9 pounds.
Adding these together gives a total of 15 pounds. The actual weight of the twins, 15 and one eighth pounds, is very close to this estimation, indicating that Lucas' claim about his brothers' weight is reasonable. This approach makes effective use of estimation as a means to quickly and simply verify a given claim's feasibility.
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Which of the following functions has the same horizontal asymptote as the function graphed below?
f(x)=-3^x+2 +2
f(x)=2^x-3
f(x)=3^x+2 -2
f(x)=2^x+2 -3
Answer:
The functions which has the same horizontal asymptote y = -3 as given in the graph are,
f(x) = [tex]2^{x} - 3[/tex] and
f(x) = [tex]2^{(x+2)} -3[/tex]
Step-by-step explanation:
The function that is graphed has horizontal asymptote as y = -3 .
As x → -∞ f(x) → - 3 for the second and fourth function. Hence the functions which has the same horizontal asymptote y = -3 as given in the graph are,
f(x) = [tex]2^{x} - 3[/tex] and
f(x) = [tex]2^{(x+2)} -3[/tex]
Which dimensions cannot create a triangle?
three angles measuring 10°, 25, and 145º
three sides measuring 9 m, 15 m, and 9 m
three angles measuring 40°, 70°, and 65
three sides measuring 6 cm, 8 cm, and 10 cm
Answer:
Step-by-step explanation:
three angles measuring 40°, 70°, and 65 cannot create a triangle because sum of all the angles should be 180