The two numbers are 8 and 13 and the system of equations are x + y = 21 and xy = 104
System of equationsLet the two unknown numbers be x and y
If the sum of the numbers is 21, hence;
x + y = 21
x = 21 - y
If the product is 104, then;
xy = 104
(21-y)y = 104
21y - y^2 = 104
y^2-21y + 104 = 0
Factorize the result
y^2-8y - 13y+ 104 = 0
y(y-8) - 13()y-8) = 0
y = 13 and 8
Hence the two numbers are 8 and 13 and the system of equations are x + y = 21 and xy = 104
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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:
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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By finding the size of each exterior angle of a regular polygon with 24 sides, calculate the size of each interior angle of the polygon.
We can find the sum of the interior angles of a regular polygon using the formula : (n-2) x 180, where n is the number of sides.
We replaced in : (24-2) x 180 = 3960
So, all the interior angles in this polygon add up to 3960.
-> Each interior angle is equal to 3960 : 24 = 165.
3 A fashion designer checks the price of a certain fabric. Manufacturer A charges $7.50 per yard. The graph shows the price that Manufacturer B charges. a. What is the initial value of each function? b. How much does 400 yd of fabric cost at each manufacturer? How much does 800 yd of fabric cost at each manufacturer? c. What can you conclude about the two functions? Explain. d. Manufacturer C offers the fabric for $5.50/yd but you have to buy at least 500 yd. What should the designer do if she needs 400 yd? Explain.
Answer: Price of 400 yd of fabric from Manufacturer A is = $7.50 X 400= $3,000. From given graph, we can observe that the charge for 800 yards of fabric is = $6,000
Find the surface area of a rectangular prism that has the following dimensions.
length: 4.5 in.
width: 6 in.
height: 12 in.
surface area = in^2
The expression for the total surface area of rectangle was used, with all values rightly plugged in, the total surface area is 306 in^2
Surface area of SolidsGiven Data
Length = 4.5 inchWidth = 6 inchHeight = 12 inchWe know that the expression used in finding the surface area is given as
Surface area of rectangular prism =2(wl+hl+hw)
Substituting our given data into the formula we have
=2(6*4.5+12*4.5+12*6)
=2(27+54+72)
=2(153)
= 306 in^2
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Answer:
306
Step-by-step explanation:
I didn't know till I saw the other persons answer. Please give them branliest.
FREE BRAINLIEST - EZ QUESTION: Write the equation of the parabola that has the vertex at point (−2,7) and passes through the point (−1,3).
Answer:
y = -4(x +2)² + 7
formula for parabola: y = a(x-h)² + k
Where (h, k) denotes the vertex
vertex: (-2, 7) point: (-1, 3)First find a:
3 = a(-1-(-2))² + 7a + 7 = 3a = -4Thus equation:
y = -4(x-(-2))² + 7y = -4(x +2)² + 7Answer:
y = -4x^2 - 16x - 9.
Step-by-step explanation:
The vertex form is:
y = a(x - b)^2 + c where a is a constant, and (b, c) is the vertex
So we have
y = a(x + 2)^2 + 7
When x = -1, y = 3 so:
3 = a(-1 + 2)^2 + 7
3 = a + 7
a = -4.
So the equation is
y = -4(x + 2)^2 + 7
y = -4x^2 - 16x -16 + 7
y = -4x^2 - 16x - 9.
Devaughn is 7 years older than Sydney. The sum of their ages is 103. What is Sydney's age?
103-7 = 96 then 96/2 = 48 so we can say that Sydney is 48 and devaughn is 48+7 = 55 years old.
Therefore, Sydney is 48 years of age.
At a local bodega, the cost of a bottle of juice at the corner store is
$1.05, and the cost of a bag of chips is $1.10. What would it cost to get
8 bottles of juice and 4 bags of chips? What would it cost to get a
bottles of juice and y bags of chips?
Total cost, 8 bottles of juice and 4 bags of chips:
Total cost, x bottles of juice and y bags of chips:
y
Answer:
$12.80
Step-by-step explanation:
The cost to get 8 bottles of juice and 4 bags of chips will be:
= 8($.105) + 4($1.10)
= $8.40 + $4.40
= $12.80
The cost for x bottles of juice and y bags of chips will be:
= (1.05 × x) + (1.10 × y)
= 1.05x + 1.10y
If a city with a population of 52,000 doubles in size every 97 years, what will the population be 291 years from now?
Answer:
156,000
Step-by-step explanation:
291 divided by 97 is 3. 52,000 x 3 = 156,000.
Population will be 6 times of present population in 291 years.
What is the population of a city ?The number of people in the city at a particular time is called population of the city.
How to find the required population ?Present population of the city = 52000
According to the problem, Population doubles in size in every 97 years.
After 97 years, the population = Double of present population
= 2 × 52000 = 104000
Population in 97 years = 104000
Population in 1 year = [tex]\frac{104000}{97}[/tex]
So, population in 291 years = [tex]\frac{104000}{97}[/tex]× 291 = 104000×3 = 312000
Population in 291 years from now = [tex]\frac{312000}{52000}[/tex] = 6 times
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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
PLEASE HELP
You will take a test containing two types of questions, multiple choice and free response. MC questions are worth 4 points each and free response are worth 7 points each. You must answer at least 4 of the MC and no more than 10 you must answer at least 3 FR questions, but no more than 10. Total, you may only answer 18 questions. How many type of each question must you answer to maximize your score.
Answer:
I think the answer is 16 to maximize the score
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!!
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]
Which Line has The Greater Slope
1
2
3
4
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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please help me asap....
What attributes do squares and
trapezoids always have in
common?
Answer:
There both quadrilaterals
Step-by-step explanation:
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
A hotel is building a large new aquarium for their lobby. They know the length from the top corner to the opposite bottom corner is 13 feet long, the height is 12 feet and the length is 4 feet. Solve for the width and then determine the volume in cubic feet of water it will take to fill the aquarium
Answer:
3 ft, 144 ft³Step-by-step explanation:
Find the width as below
l² + w² + h² = d², where l- length, w- width, h- height, d- the distance between top and bottom cornersSubstitute the values and solve for w
4² + w² + 12² = 13²w² + 160 = 169w² = 9w = 3 feetNow find the volume
V = lwhV = 4*3*12 = 144 ft³Answer:
width = 3ft
volume = 144 ft³
Step-by-step explanation:
Pythagoras Theorem
[tex]\sf a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
The diagonal of the base of the aquarium, its height, and the length from the top corner to the opposite bottom corner forms a right triangle. As we know two of the lengths, we can use Pythagoras Theorem to calculate the unknown length (diagonal of base).
Given:
a = height of aquarium = 12 ftb = diagonal of basec = top corner to opposite corner = 13 ft[tex]\implies \sf 12^2+b^2=13^2[/tex]
[tex]\implies \sf b=\sqrt{13^2-12^2}[/tex]
[tex]\implies \sf b=5[/tex]
Now we know the length of the diagonal of the base, we can again use Pythagoras Theorem to find the width of the aquarium.
Given:
a = length of aquarium = 4 ftb = width of aquarium c = diagonal of base = 5 ft[tex]\sf \implies 4^2+b^2=5^2[/tex]
[tex]\sf \implies b=\sqrt{5^2-4^2}[/tex]
[tex]\sf \implies b=3[/tex]
Therefore, the width of the aquarium is 3 ft.
As the aquarium is modeled as a rectangular prism:
[tex]\begin{aligned}\textsf{Volume of a rectangular prism} & = \sf width \times length \times height\\ \implies \textsf{Volume of aquarium} & = \sf 3\:ft \times 4\:ft \times 12\:ft\\& = \sf 144 \:\:ft^3\end{aligned}[/tex]
A cart weighing 200 pounds rests on an incline at an angle of 40 degrees. what is the required force to keep the cart at rest? round to the thousandths place
a) 128.558 pounds
b) 133.388 pounds
c) 149.023 pounds
d) 153.208 pounds
The force needed to keep the cart at rest is 149.022 pounds
Force and MotionGiven Data
Weight of cart = 200 poundsAngle = 40 degreeThe force needed to keep the cart at rest is the vertical component of the resultant force, hence we have
Fy = Mg sin θ
Substituting our given data we have
Fy = 200 sin 40
Fy = 200 *0.74511
Fy = 149.022 pounds
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Answer:
128.558
Step-by-step explanation:
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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help?? its for calc please
Answer:
its logx=logy
Answer:
its logx=logy
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.
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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What is the cost of 10.0 gallons of gasoline priced at 1.449 per gallon?
Answer:
14.49
Step-by-step explanation:
thats all folks i don't know why though
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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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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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
A chef needs to decorate cupcakes for a birthday party. If the chef places
2
strawberry slices on top of each cupcake, which inequality represents the possible number of cupcakes,
k
, the chef could decorate with
46
strawberry slices?
The possible number of cupcakes is less than or equal to 23
How to write inequality equation?let
k = possible number of cupcakesNumber of strawberry slices = 46Number if strawberry slices on each cupcake = 2The inequality:
2k ≤ 46
divide both sides by 2
k ≤ 46 / 2
k ≤ 23
Therefore, the possible number of cupcakes is less than or equal to 23
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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
