Answer:
y = − x + 7
Step-by-step explanation:
let D be the line that passes through the points (5, 2) and (10, -3)
Then D has an equation of the form D: y = mx + p
Now we need to find m and p in order to be able to write the equation of the line D:
[tex]m = \frac{2-(-3)}{5-10} = \frac{5}{-5} = -1[/tex]
Since the point (5 , 2) lies on the line D then :
2 = -1 × (5) + p
then
2 = -5 + p
then
p = 2 + 5
= 7
then
p = 7
Conclusion:
Since m = -1 and p = 7
then
[tex]D : y = -x + 7[/tex]
a .circle with diamter at (2,2) and (8,14
the equation of the circle with diameter at (2,2) and (8,14) is (x-5)^2 + (y - 8)^2 = 45
How to calculate the equation of a circle?A circle is a 2-dimensional shape with no edges.
The standard equation of a circle with centre (a, b) and radius "r" is given as:
(x-a)^2 + (y-b)^2 = r^2
Given the diameter of circle with coordinate (2,2) and (8,14), the diameter is expressed as:
D = √12² + 6²
D = √144+36
D = √180
For the radius
r = √180/2
r² = 180/4
r² = 45
Determine the centre (a, b)
(a, b) = (2+8/2 2+14/2)
(a, b) = (5, 8)
Substitute
(x-5)^2 + (y - 8)^2 = 45
Hence the equation of the circle with diameter at (2,2) and (8,14) is (x-5)^2 + (y - 8)^2 = 45
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At a restaurant, 8 plates are accidentally broken each day for a week (7 days). What number represents the change in the number of plates the restaurant has?
The original price of a computer is $579. which coupon is a better deal?
Save 25% on any computer is the better deal. Then the correct option is A.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
A) Save 25% on any computer. Then the better deal will be
→ 579 × 0.25 = $ 144.75
B) Save $150 on any computer. Then the better deal will be
→ $ 150
C) Save $75 plus 5% off on any computer. Then the better deal will be
→ 579 × 0.05 + 75 = $ 103.95
D) Save $50 plus 10% off on any computer. Then the better deal will be
→ 579 × 0.10 + 50 = $ 107.9
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On a coordinate plane, 2 straight lines are shown. The first solid line is horizontal at y = negative 1. Everything above the line is shaded. The second dashed line has a negative slope and goes through (negative 2, 1) and (0, 0). Everything below the line is shaded. A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. Which constraint could be part of the scenario? The pool is 1 meter deep. The pool is 2 meters deep. The toy falls at a rate of at least a Negative one-half meter per second. The toy sinks at a rate of no more than a Negative one-half meter per second
y≥x-2
x+2y⊂4
hoping that your answer
From a point, 50 feet from the base of a building, the angle of elevation from ground level to the top of the building is 66°. find the height of the building to the nearest hundredth of a foot
Answer:
112.30 ft
Step-by-step explanation:
The geometry can be modeled by a right triangle with a base of 50 ft, an angle adjacent to the base of 66°, and a side opposite the angle that is the height of the building. The relationship between these measures is given by the trig function ...
Tan = Opposite/Adjacent
tan(66°) = height/(50 ft)
Solving for the height gives ...
height = (50 ft)tan(66°) ≈ 112.30 ft
The height of the building is about 112.30 feet.
Write the equation of a circle whose diameter is 8 and whose center is (-8, -5)?
if the diameter is 8, then its radius is half that or 4.
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-8}{ h},\stackrel{-5}{ k})\qquad \qquad radius=\stackrel{4}{ r} \\\\[-0.35em] ~\dotfill\\\\\ [x-(-8)]^2~~ + ~~[y-(-5)]^2~~ = ~~4^2\implies (x+8)^2+(y+5)^2=16[/tex]
UNIT 5: CEREAL BOX PROJECT / PORTFOLIO
HELP
Using the formula for volume and surface area of solids, we have the following:
1. 180 in.³; 258 in.²; $12.9
2. 144 in.³; 184 in.²; $9.2
3. 75 in.³; 228 in.²; $11.4
What is Volume and Surface Area?Volume of a rectangular prism = l × w × h
Surface area of a rectangular prism = 2(wl+hl+hw)
Volume of a square pyramid = 1/3 × a² × h
Surface area of a square pyramid = a² + 2al
Volume of a cylinder = πr²h
Surface area of a cylinder = 2πr( h + r)
1. Volume of the rectangular prism cereal box = 7.5 × 2 × 12 = 180 in.³
Surface area of the rectangular prism cereal box = 2(wl+hl+hw) = 2(2 × 7.5 + 12 × 7.5 + 12 × 2) = 258 in.²
Cost of material for the the rectangular prism cereal box = 258 × 0.05 = $12.9.
2. Volume of the square pyramid cereal box = 1/3 × a² × h = 1/3 × 6² × 12 = 144 in.³
Surface area of the square pyramid cereal box = a² + 2al = 6² + 2(6)(12.3) ≈ 184 in.²
Cost of material for the the square pyramid cereal box = 184 × 0.05 = $9.2.
3. Volume of the cylinder cereal box = πr²h = π(2.5²)(12) = 75 in.³
Surface area of the cylinder cereal box = 2π(2.5)(12 + 2.5) ≈ 228 in.²
Cost of material for the the cylinder cereal box = 228 × 0.05 = $11.4.
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What attributes do squares and
trapezoids always have in
common?
Answer:
There both quadrilaterals
Step-by-step explanation:
If n is proportional to M squared and n) 27 when m=3 what is the formula for n in terms of M and what is the value of n given m=6
Answer:
n=9M, when m is 6,n=18
Step-by-step explanation:
If n is proportional to M
n=kM
27=3k
k=27/3
k=9
the formula on terms of n and M is
n= 9M
2) If m= 6,
n= 3M
n=3(6)
n=18
Answer:
n = 108
Step-by-step explanation:
given n is proportional to m² then the equation relating them is
n = km² ← k is the constant of proportion
to find k use the condition n = 27 when m = 3 , then
27 = k × 3² = 9k ( divide both sides by 9 )
3 = k
n = 3m² ← equation of proportion
when m = 6 , then
n = 3 × 6² = 3 × 36 = 108
A box of macaroni is 5 inches long, ½ inch wide and 2 ¼ inches tall. What is the volume of the box?
Answer:
5.625 cubic inches
Step-by-step explanation:
Find the number that makes the ratio equivalent to 5:6.
:66
Answer:
55 - you multiplied 6 by 11 to get 66 so you multiply by 5 by 11 to get 55.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPp
Answer:
36 in²
Step-by-step explanation:
Area of the figure
Area (small rectangle) left + Area (big rectangle) right3 x (6 - 4) + 5 x 63 x 2 + 306 + 3036 in²Answer:
The answer is 36 ft²
Step-by-step explanation:
Let us divide this whole figure into 2 rectangle, a big and a small.
Rectangle 1: (Small)
Length (l) = 2 ftBreadth (b) = 3 ft(Area 1) = l × b
A = 2 × 3 = 6 square ft
Rectangle 2: (Big)
Length (l) = 6 ftBreadth (b) = 5 ft(Area 2) = l × b
A = 6 × 5 = 30 square ft
Now,
Total Area of figure = Area of Rectangle 1 + Area of Rectangle 2.
Total Area = 6 + 30 = 36 square ft.
Thus, The area of the figure is 36 ft².
help?? its for calc please
Answer:
its logx=logy
Answer:
its logx=logy
what does T equal to?
Answer:
4/3
Step-by-step explanation:
t^3=64/27
=4^3/3^3
=index same
t =4/3
Answer:
4/3)
Step-by-step explanation:
t- 3= 64/27
= 4-3/3-3
= index same
t = 4/3
11, 20, 29, ...
Find the 43rd term.
Answer:
389
Step-by-step explanation:
20 - 11 = 9
29 - 20 = 9
This is a geometric sequence with a common difference of 9.
a_1 = 11
a_2 = 11 + 9
a_3 = 11 + 2 × 9
...
a_n = 11 + (n - 1) × 9
a_43 = 11 + (43 - 1) × 9
a_43 = 11 + 42 × 9
a_43 = 389
Hence, the [tex]43[/tex]rd term is [tex]389[/tex].
What is the sequence?
A sequence is a list of objects, typically numbers, in which order matters, repetition is allowed, and the same elements can appear multiple times at different positions in the sequence.
Here given sequence is [tex]11, 20, 29, ...[/tex]
Here,
[tex]a=11\\\\d=a_2-a_1\\d=20-11\\d=9[/tex]
The general formula is
[tex]a_n=a+(n-1)d[/tex]
where,
[tex]a_n[/tex] is the [tex]n[/tex]th term
[tex]a[/tex] is the first term
[tex]n[/tex] is the number of terms
[tex]d[/tex] is the common difference
Substituting the values in the general formula
[tex]a_n=a+(n-1)d\\\\a_{43}=11+(43-1)9\\\\a_{43}=11+(42)9\\\\a_{43}=11+378\\\\a_{43}=389[/tex]
Hence, the [tex]43[/tex]rd term is [tex]389[/tex].
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Carl wants to earn money shoveling snow from driveway this winter. The average size of a driveway in his neighborhood is 240 ft. ² it take a squirrel 45 minutes to shovel an average size driveway with 4 inches of snow. Enter the minimum number of minutes it will take her to shovel a driveway with 4 inches of snow that has an area of 720 ft. ² if he shovels at this rate. 
Using proportions, it is found that it will take him at least 135 minutes to shovel the driveway at this rate.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, it takes 45 minutes to shovel 240 ft². How long does it take to showel 720 ft²? The rule of three is given by:
45 min - 240 ft²
n min - 720 ft²
Applying cross multiplication:
240n = 45 x 720
n = 45 x 720/240
n = 45 x 3
n = 135
It will take him at least 135 minutes to shovel the driveway at this rate.
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Answer is 1, I just need the working. Thank you
there are three pictures with every step
good luck writing that on the paper bro lol
The beginning steps for determining the center and radius of a circle using the completing the square method are shown in the table.
Step 1
[original equation]: x2 + 8x + y2 − 6y = 11
Step 2
[group like terms]: (x2 + 8x) + (y2 − 6y) = 11
Step 3
[complete the square]:
Which of the following is the correct equation for Step 3? (1 point)
(x2 + 8x + 16) + (y2 − 6y − 9) = 11 + 16 − 9
(x2 + 8x + 16) + (y2 − 6y + 9) = 11 + 16 + 9
(x2 + 8x + 4) + (y2 − 6y − 3) = 11 + 4 − 3
(x2 + 8x + 4) + (y2 − 6y + 3) = 11 + 4 + 3
Answer:
(b) (x^2 + 8x + 16) + (y^2 − 6y + 9) = 11 + 16 + 9
Step-by-step explanation:
To complete the square of a binomial, the constant term of the perfect square trinomial is the square of half the coefficient of the linear term. It will always be positive.
__
Answer Choicesa) 9 is subtracted, incorrectly
b) 16 and 9 are correctly added . . . this is the correct Step 3
c) half the linear term is added, incorrectly
d) the magnitude of half the linear term is added, incorrectly
A pebble falls off the top of a cliff. Its final velocity is 58.8m/s. How long does it take to reach the ground? Show
your work.
Answer: 5.7s
Step-by-step explanation:
We are explicitly given the final velocity of 58.8m/s, and implicitly given the acceleration of 9.8m/s^2 due to gravity. We are also implicitly given the initial velocity of the pebble. The pebble was not thrown off the cliff, it simply fell off the cliff. Therefore the initial velocity is 0m/s. Using the first kinematic equation, you get:
[tex]v_f=v_i+at[/tex]
[tex]58.8=0+(9.8)t[/tex]
[tex]58.8=9.8t[/tex]
[tex]t=5.7s[/tex]
The usual price of a compact disc player was $200. At a sale, it was sold at a discount of 5%. What was the selling price
Answer:
It would be sold at 190$
Step-by-step explanation:
200x5/100 or 200 x 0.05
Hi, I need help with this math question. Can you pls help me?
The third term is 245 and the first term is 5 -> To get from the first term to the third term, we multiply it by 49.
Since in a geometric sequence, the difference between each term has to be a constant multiplier or a sequence of multipliers -> We can find the second number to be 5 x 7 = 35
So, this geometric sequence is 5 ; 35 ; 245 and so on.
-> The common ratio of this sequence is 7. (and sorry if the things above don't make sense)
Answer:
7
Step-by-step explanation:
Given:
First term = 5Third term = 245Let the second term be "x".
⇒ 5, x, 245...
Thus, the following equations:
5 × (something) = xx × (something) = 245To find the common ratio between the three terms, we need to find the value of "x". Simplify both the equations to obtain the values of (something). Then compare both the values.
⇒ [5 × (something)] = x
⇒ [5 × (something)]/5 = x/5
⇒ (something) = x/5
⇒ x × (something) = 245
⇒ [x × (something)]/x = 245/x
⇒ (something) = 245/x
Now, let's compare both the results of (something).
⇒ x/5 = 245/x
⇒ x² = 5 x 245
⇒ x² = 1225
⇒ x = √1225 = 35
Substitute the second term into the sequence.
⇒ 5, x, 245 = 5, 35, 245
Looking at the sequence formed, we can tell that 7 is being multiplied to each term. Thus, 7 is the common ratio.
PLEASE ANSWER I WILL GIVE BRAINLIEST TO CORRECT ANSWER
Answer:
6x+4y=16
Step-by-step explanation:
2 ( 3x) + 2 (2y) = 2 (8)
6x + 4y = 16 <===== add this equation to the top equation to get
11x = 22
then x = 2 use this value of x in any of the equations to calculate y
5(2) - 4y = 6
10 - 4y = 6
-4y = -4
y = 1
i honestly dont know how to answer 8+h over 10 = 1 how?
Answer:
h = 2
Step-by-step explanation:
8+h / 10 = 1
Multiply both sides by 10 to remove the denominator
10 * (8 + h / 10) = 1 * 10
8 + h = 10
Subtract 8 from both sides
8 - 8 + h = 10 - 8
h = 2
A campbell’s soup can is 6 inches tall and has a arduous of 2.5 inches how much paper is needed to make the label? How much room is there inside the can to hold the soup
Step-by-step explanation:
The label of the soup is the lateral area of the cylinder.
The formula for a cylinder is LA = ph.
The perimeter of a cylinder is the circumference of a circle, 2 times pi times r.
then multiply that answer by the height of 6.
The answer will be in square inches
an electronics company is designing a watch with a face that is in the shape of a hexagon and two congruent trapezoids attached. the heights of the trapezoids and the apothem of the hexagon measure 2 centimeters each, and the legnth of the shorter base of each trapezoid is 1.5 centimeters. what is the total area of the face of the watch to the nearest tenth of a square centimemter
Answer:
Step-by-step explanation:
The total area of the face of the watch is 9.0 cm²
What is a hexagon?The polygon with six side is called a hexagon.
Given that, a watch with a face that is in the shape of a hexagon and two congruent trapezoids attached.
height, h = apothem of the hexagon = 2 cm and
base, b = length of shorter base of trapezoid.
Area of the triangle
So, the area of this triangle is A = 1/2bh
= 1/2 × 1. 5 cm × 2 cm
= 1.5 cm × 1 cm
= 1.5 cm²
Area of the hexagon
Since there are 6 of such triangles in the hexagon, the area of the hexagon, A' = 6A
= 6 × 1.5 cm²
= 9.0 cm²
So, total area of the face of the watch is 9.0 cm²
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Please help asap
Savannah is trying to justify to her geometry class that the 2 lines she drew, line a and line b, are
parallel. Select all of the reasons that prove Savannah's lines parallel.
Answer:
2,3,4,5
Step-by-step explanation:
The ones you selected are all correct.
Hope this helps.
Parallel lines were coplanar endless straight lines in geometry that never intersect. Therefore, all the options are correct.
What are parallel lines?Parallel lines were coplanar endless straight lines in geometry that never intersect. Within a single three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.
Euclid's parallel postulate deals with parallel lines. Euclidean geometry is just a particular example of this sort of geometry, and parallelism is essentially a feature of affine geometries. Lines can have similar characteristics known as parallelism in various other geometries, including such hyperbolic geometry.
∠2≅∠8 ( alternate interior angle)
∠1≅∠8 (vertical angle)
∠1≅∠5 (corresponding angle)
∠2≅∠5 (consecutive interior angle)
∠4≅∠6 (exterior angle)
Therefore, all the options are correct.
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Find the length of the third side. If necessary, round to the nearest tenth
Pythagorean Theorem (Rounding)
Answer:
24 :)
Step-by-step explanation:
Pythagorean theorem: a^2 + b^2 = c^2
Lets solve!!
7^2 + b^2 = 25^2
49 + b^2 = 625
Now we subtract!!
625 - 49 = b^2
576 = b^2
Now we neeed to find the square root!!
[tex]\sqrt{576}[/tex] = 24
Have an amazing day!!
Please rate and mark brainliest!!
Which Line has The Greater Slope
1
2
3
4
Roberto is having his house painted. The job takes three days, and he pays the painter the same hourly rate everyday. The cost of the job is in the chart below.
Which of the following equations, where “h” represents hours worked and “p” the amount paid in dollars, represent an hourly pay rate that is Greater than the painter’s hourly rate?
Day 1: 5 hours worked; Paid $300
Day 2: 4 hours worked; Paid $240
Day 3: 6 hours worked; Paid $360
Choose all answers that apply:
A) P=6.5h
B) P=50h
C) P=65h
D) P=70h
Answer:
a is the answer
Step-by-step explanation:
Buses arrive at a stop every 18 min. Each bus waits 4 min before departing. What is the probability that a person arriving at the bus stop at a random time has to wait more than 8 min for a bus to leave?
Answer:
Socratic app
Step-by-step explanation:
it will help you
