Answer:
(b) y -16 = 3(x -9)(c) y = 3x -11Step-by-step explanation:
You are given a couple of points:
(years, heigh) = (6, 7) and (9, 16)
and asked to write a linear equation that they satisfy. In general, you need to find the slope using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (16 -7)/(9 -6) = 9/3 = 3
__
point-slope equationThe point-slope form of the equation for a line can be used with this information.
y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)
Using the given points, you can write either of the equations ...
y -7 = 3(x -6) . . . . . using the first point
y -16 = 3(x -9) . . . . . using the second point. This matches choice B.
__
slope-intercept equationEither of the point-slope equations can be rearranged to give the slope-intercept equation.
y -16 = 3(x -9)
y = 3x -27 +16 . . . . eliminate parentheses, add 16
y = 3x -11 . . . . . This matches choice C.
__
Additional comment
The first choice has the right slope, but uses a point not on the line (10, 6).
The last choice has the wrong slope and the wrong y-intercept.
A bag contains 3 red, 5 black, and 4 white marbles. What is the probability of picking a black marble, keeping it, and then picking a red marble?
Step-by-step explanation:
1/12 for black marble
1/11 for red marble
cause you kept the black marble you didn't put it back to the bag.
A box is in the shape of a rectangular prism. Andrea is trying to ship boxes of her homemade chocolate chip cookies. The box she is using to ship has the dimensions of 12in by 10in by 12in. Each cookie box has dimensions of 4in by 5in by 3in. How many cookie boxes will fit into the box to be shipped? Explain how you got your answer.
The 24 boxes which will fit into the large box if the box is in the shape of a rectangular prism.
What is a cuboid?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape.
We can find the volume of the box = length×width×height
Volume for the large box = 12×10×12 = 1440 cubic in
Volume for the small box = 4×5×3 = 60 cubic in
Number of cookie boxes will fit into the large box = 1440/60 = 24
Thus, the 24 boxes which will fit into the large box if the box is in the shape of a rectangular prism.
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the city ordered 4 1/2 of gravel and used 1/5 of that amount to repair a park road. what fraction of a ton was used for the road?
Answer:9/10ths
Step-by-step explanation:
First, convert the 4 and 1/2 tons of gravel to a fraction
You get 9/2
Multiply 9/2 by 1/5 to get your answer
You get 9/10ths of a ton of gravel
PLEASE HURRY!! I HAVE TO GET THIS DONE NOW AND IM STUCK ON IT A LITTLE. MAKE SURE TO ANSWER THEM ALL PLEASE! THXS
Answer:
v = 2419200in³
Step-by-step explanation:
v=l*b*h
=240*84*120
=2419200in³
Answer:
[tex]V_{shipping\: container}=2,419,200\:in^3[/tex]
A. 4032 boxes
SA = 460 sq in
Step-by-step explanation:
For shipping container:
l = 240 in, w 84 in, h = 120 in
[tex]V_{shipping\: container}=lwh[/tex]
[tex]\implies V_{shipping\: container}=240\times 84\times 120[/tex]
[tex]\implies V_{shipping\: container}=2,419,200\:in^3[/tex]
For box:
l = 10 in, w = 5 in, h = 12 in
[tex]V_{box}=lwh[/tex]
[tex]\implies V_{box}=10\times 5\times 12[/tex]
[tex]\implies V_{box}=600\:in^3[/tex]
[tex]\frac{V_{shipping\: container}}{V_{box}}=\frac{2,419,200}{600}[/tex]
[tex]\frac{V_{shipping\: container}}{V_{box}}=4032[/tex]
Surface area of box
= 2(lw + lh +wh)
= 2(10*5+ 10*12+ 5*12)
=2(50+120+60)
=2(230)
= 460 sq in
Reflect (-1, 4) over the x-axis.
Then translate the result up 3 units.
What are the coordinates of the final point?
If a point (-1, 4) reflected over the x-axis then translate the result up 3 units then the coordinates of the final point are (-1, -1)
What is Coordinate Geometry?A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.
Reflecting a point over the x-axis negates the y-coordinate, while leaving the x-coordinate unchanged.
Therefore, reflecting (-1,4) over the x-axis gives us the point (-1,-4).
Translating a point up 3 units means adding 3 to the y-coordinate. Therefore, translating (-1,-4) up 3 units gives us the point:
(-1, -4 + 3) = (-1, -1)
So the final point is (-1,-1).
Hence, if a point (-1, 4) reflected over the x-axis then translate the result up 3 units then the coordinates of the final point are (-1, -1)
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Find the exterior angle for each
Step-by-step explanation:
In all cases just divide 360° by the number of sides
Thus,for a. 360°/12=30°
Answer:
1. the total triangles of 12 sides are 10 triangles but the exterior angles of a 12 sided polygon is 30° because dodecagon is equal to 150°
2. the total triangles of 18 sides are 16 triangles but the exterior angles of a 18 sided polygon is 20° because octakaidecagon is equal to 360°/18=20°
3. the total triangles of 8 sides are 6 triangles but the exterior angles of a 6 sided polygon is 120° because hexagon is equal to 720°/6=120°
4. the total triangles of 3 sides are 1 triangle but the exterior angles of a 6 sided polygon is 60° because hexagon is equal to 180°/3=60°
1 + (x + 44) = (1 + x) + 44 name the property
Answer:
distribute=muev around
Step-by-step explanation:
done
Select the correct answer.
Simplify the expression.
5224x1148
Answer: The answer is C.
Step-by-step explanation:
Simplify the radical by breaking the radicals up into a product of known factors, assuming real numbers.
Factor that affect rate of dessolving
Answer:
The rate of dissolving depends on the surface area, temperature and amount of stirring.
Step-by-step explanation:
Answer:
the factors that effect rate of disssolving are as follows
Step-by-step explanation:
surface areatemperaturemomentumWhat are all values of x for which the series n 3^n/x^n converges
The interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.
What is convergent of a series?A series is convergent if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums getting closer and closer to a certain number.
We can find the interval for the convergent by root test.
Like the Ratio Test, the root Test is used to determine absolute convergence (or not) with factorials, the ratio test is useful.
For the given series:
[tex]\sum^{\infty}_{n=0}\dfrac{3^n}{x^n}[/tex]
As the series goes infinitely, we can use root test.
By the root test, the convergence interval will be;
The interval of convergence is:
x < -3 or x > 3 we can write this as:
|x| < 3
Thus, the interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.
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An architect-designed an attic space in the shape of a square pyramid. After reviewing the design, he decided to make a second design for an attic space in the shape of an oblique pyramid. He created models of both designs as shown.
Both models were cut horizontally at the same height, finding the cross-sections with the same area. Several other horizontal cross-sections were analyzed and found to have the same area. Both pyramid models also have the same height, a.
Which formula would allow the architect to calculate the volume of his second attic space design?
A.V=s^2a
B.V=1/2s2b
C.V=1/3scb
D.V=1/3s2a
The formula that would allow the architect to calculate the volume of his second attic space design is V = 1/3s²b. Option D is correct.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
The formula for the volume of an oblique pyramid is V = 1/3 * base area * height. In this case, the base of the oblique pyramid is the shape of the cross-section, which is a square. So, the formula becomes V = 1/3 * s^2 * height. The given information states that the height is "a", which is the same for both pyramid models.
Therefore, the formula for calculating the volume of the second attic space design becomes V = 1/3 * s² * a.
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Which of the following lists of ordered pairs is a function?
OA. (2, 5), (3, 6), (6, 9)
B. (1, 2), (4, 0), (3, 5), (4, 3)
C. (-1, 2), (2, 3), (3, 1), (2, 5)
D. (2,5), (3, 6), (2, 1)
Answer:
a
Step-by-step explanation:
none of the x or y values repeat
please help me with this question
The amount in the account after the given time if compounded semiannually to the nearest cent is $1104.2
Compound interestInterest is any amount added on a sum of money over a period of time. The formula for calculating the compound interest is:
A = P(1+r/n)^nt
Given
Principal = $1000
rate r = 5% = 0.05
time = 3years
n = 2 (semi annually)
Substitute the given parameters
A = 1000(1 + 0.05/3)^3(2)
A= 1000(1.1042)
A = $1104.2
Hence the amount in the account after the given time if compounded semianually to the nearest cent is $1104.20
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The volume of a right cone is 41251 unit. If its diameter measures 30 units, find its
height.
Volume is a three-dimensional scalar quantity. The height of the cone is 175.075 units.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the right cone is 41,251 unit³, while the diameter of the cone is 30 units. Therefore, the radius of the cone is 15 units. Thus, the height of the cone will be,
Volume = (1/3)×π×r²×h
41,251 = (1/3)×π×(15²)×h
h = 175.075 units
Hence, the height of the cone is 175.075 units.
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helppppppppppppppppppp
Answer:
y = 20.48
Step-by-step explanation:
[tex]\frac{y}{5.12}[/tex] = 4 ( multiply both sides by 5.12 to clear the fraction )
y = 4 × 5.12 = 20.48
heeeyy yall, how do i do this?
Answer:
72 cm²
Identify the given sides:
Length: 6 cmWidth: 3 cmHeight: 2 cmSurface area of rectangular prism:
2 * (Length * Width + Width * Height + Length * Height)2 * (6*3 + 3*2 + 6*2)2 * (18+6+12)2 * (36)72 cm²TSA
2(LB+BH+LH)2(3×6+6×2+3×2)2(18+12+6)2(36)72cm²which of the following probability models would be best for a probability calculation with two or more “and” statements
a) a systematic list
b) none of these
c) a tree diagram
d) an area model
The tree diagram would be best for a probability calculation with two or more “and” statements, option (c) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
A probability calculation can be computed using multiple models, each of which is dependent on the given parameters. A graphical model, such as a tree diagram, or an analytical model, such as the systematic list model, can be used.
Tree diagram models are useful for visually showing complex probabilities and aiding solution visualization.
Thus, the tree diagram would be best for a probability calculation with two or more “and” statements option (c) is correct.
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Please help
What association does the scatter plot show?
A - positive nonlinear association
B - positive linear association
C - no association
D - negative linear association
E - negative linear association
So you helped 69 people and you get 340 dollars so how much money you get from helping 1 person let x represent the amount of money for 1 person round to the nearest whole number (please do it )
Answer:
x = 5
Step-by-step explanation:
So you just do 340/69 which gives you 4.927536232, and you round to the nearest whole number giving you 5.
Which phrase best completes the sentence?
Renewable resources are __________.
things that cannot be replenished
things that can provide heat but not other forms of energy
things that can be naturally replaced in a short period of time
things such as petroleum and coal
Answer:
things that can be naturally replaced in a short period of time
3x^2-39+120
factor this
Answer:
[tex]9x^{2} +81[/tex]
Step-by-step explanation:
I Guess.
Answer:
3(x^2 + 27)
My answer was totally off! I just re evaluated the equation and I got this:
LMK if it's wrong :)
how many years should i study for university for architecture
Answer:
The answer is almost certainly 5 years. People might, however, pursue a Master of Architecture degree, which takes two to three years to accomplish.
Step-by-step explanation:
Architecture is a five-year degree that requires a keen interest in the topic. A five-year undergraduate architecture degree, known as a B. Arch., or a two- or three-year post-college master's program, known as an M. Arch., are the two alternatives for those who wish to get an architectural degree that will help them get licensed as an architect. You'll have to labor every day and night. Of course, your performance in class will have an impact. Some instructors may offer homework that are beyond your grasp and abilities. Everything you do must be carefully thought out, imagined, and built.
31. Which firm's design would you recommend? Why? As long as the design meets the requirements, there is no right or wrong answer. (3 points)
Answer:
I'm not really into firm design lol I don't even know what that is, I like graphic designs like patterns and stuff.
Step-by-step explanation:
SOMEONE HELP PLEASE
Simplify the expression by combining like terms:
9x + 3y + x +4-3y
(a) 10x+4
(b)10x+6y+4
(c)13x+3y
(d)9x-3y-6
Step-by-step explanation:
9x + 3y + x +4-3y
Solution ,
Organize the like terms
[tex] = 9x + x + 3y - 3y + 4[/tex]
[tex] = 10x + 4[/tex]
what is the perimeter of triangle DFG. The perimeter of triangle DFG is 54 inches. The perimeter of triangle DFG is 27 inches. The perimeter of triangle DFG is 36 inches. The perimeter of triangle DFG is 52 inches
A conducting sphere contains positive charge distributed uniformly over its surface
The potential at the center of the sphere is the same as the potential at the surface. Then the correct option is B.
What is the potential difference?The amount of labor required to move a unit signal from one part to another is defined as the potential difference between any two points.
If the conducting sphere contains a positive charge distributed uniformly over its surface
The charge inside the sphere is zero, so the electric field inside the sphere is zero
Hence potential is same ( E = - dV/dr)
The potential at the center of the sphere is the same as the potential at the surface.
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25 x 25 = ? What is the answer?
Answer:
625
Step-by-step explanation:
25x25 can be broken down into 20 x 25 and 5 x 25
20 x 25 is 10 x 25 x 2
10 x 25 is 250 and 250 times 2 is 500
25 x 5 is 125.
500+125 is 625.
what is the equation of the quadratic that models the data
Answer:
y = -5(x-5)^2+1125
Step-by-step explanation:
A small box is 1 unit long, 1 unit wide, and 1 unit high. Why is the box considered a unit cube?
The box is considered a unit cube because the volume of the cube is 1 cubic unit.
What is a volume of a cube?Suppose that: The side length of the considered cube is L units. Then, we get:
Volume of that cube = L³ cubic units.
A small box is 1 unit long, 1 unit wide, and 1 unit high.
Volume = 1³
Volume = 1 unit³
The box is considered a unit cube because the volume of the cube is 1 cubic unit.
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A food corner in disney spring has been selling 7000 hot dogs per week,
that has lead them to gaining $500 each week. according to their business
plan, their net profit increases by $5 dollars for each unit sold (15pts)
a. identify independent and dependent variable
b. write linear equation representing the dependent variable
c. find the number of hot dog sold to make profit at least $10000 per
week
is it 10000
if this is wrong sorry
