Answers
Answer:
23. Length = 21 feet, Width = 3 feet
24. Larger Angle = 162 degrees, Smaller Angle = 18 degrees
Step-by-step explanation:
23.
Let us say: l ⇒ length of the rectangular pool, w ⇒ width of the rectangular pool
According to the problem we could formulate two equations as such:
2l + 2w = 48,
l = 15 + 2w
Now let us solve for the dimensions;
First convert the two equations to standard form:
2l + 2w = 48,
l - 2w = 15
Using process of elimination:
2l + 2w = 48
+ l - 2w = 15
Simplify:
3l = 63,
length = 21 feet
Substitute this value of length into the second equation.....:
21 - 2w = 15
.......And simplify:
-2w = -6,
width = 3 feet
24.
Let us say: L ⇒ larger angle, S ⇒ smaller angle,
According to the problem we could formulate two equations as such:
L + S = 180,
L = 9S
Now let us solve for the angles;
Let us here use substitution:
(9S) + S = 180
Simplify:
10S = 180,
Smaller Angle = 18 degrees
Substitute this value of the smaller angle into the second equation.....:
L = 9(18)
.......And simplify:
Larger Angle = 162 degrees
Related Questions
PLEASE HELP!! 25 POINTS!!!
Agnes and Jamie left the apartment at the
same time traveling in the same direction
(along the same road). Agnes is traveling
at 54 mph and Jamie at 60 mph. How
many hours will it be before Jamie is 12
miles ahead of Agnes?
Answers
Answer:
2 Hours
Step-by-step explanation:
If Jamie is going 6 miles per hour faster than Agnes, then in 2 hour Jamie should be 12 miles ahead of Agnes
What are all the simplified form of the equation 3(4x - 2) = 9 + 2x + 5
Answers
Step-by-step explanation:
Step 1: Distribute
[tex]3(4x - 2) = 9 + 2x + 5[/tex]
[tex](3 * 4x) + (3 * -2) = 14 + 2x[/tex]
[tex]12x - 6 = 14 + 2x[/tex]
Step 2: Add 6 to both sides
[tex]12x - 6 + 6 = 14 + 6 + 2x[/tex]
[tex]12x = 20 + 2x[/tex]
Step 3: Subtract 2x from both sides
[tex]12x - 2x = 20 + 2x - 2x[/tex]
[tex]10x = 20[/tex]
Step 4: Divide both sides by 10
[tex]10x / 10 = 20 / 10[/tex]
[tex]x = 2[/tex]
Answer: [tex]x = 2[/tex]
since 2010 the town of fall river has been experiencing a growth in population according to the model what will the population of fall river be in 2020
Answers
Answer:
the population of fall river will be 48558
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
Since 2010, the town of Fall River has been experiencing a growth in population. The relationship between the elapsed time, t, in years, since 2010 and the town's population, P(t left parenthesis, t, right parenthesis, is modeled by the following function. P(t)=36,800⋅[tex]2^{\frac{t}{25} }[/tex] According to the model, what will the population of Fall River be in 2020? Round your answer, if necessary, to the nearest whole number.
My answer:
Given the exponential function:
P(t)=36,800⋅[tex]2^{\frac{t}{25} }[/tex] where:
t in years, since 2010 the town's population, P(t)As we know, from 2010 to 2010 are 10 years
Hence, to find the population of fall river be in 2020, we substitute t =10 into the given function:
[tex]P(10)=36800\cdot2^{^\dfrac{10}{25}}}\\=48557.9\\\approx 48558[/tex]
So in 2020, the population of fall river will be 48558
Hope it will find you well.
Answer:
By 2020 the population of Fall River will be 48558
Step-by-step explanation:
Here, we note that the equation for the model is p(t) = 36,800×2^(t/25)
That is the format;
[tex]p(t) = 36,800 \times 2^{\frac{t}{25}[/tex]
Where:
t = Number of years since 2010
Therefore, the population of the town in 2020 can be found by first finding the number of years between 220 and 2010 and plugging the value into the equation as follows;
Number of years, t = 2020 - 2010 = 10 years
Hence;
[tex]p(t) = 36,800 \times 2^{\frac{10}{25}} = 48557.89 \approx 48558[/tex]
Therefore, according to the model, by 2020 the population of Fall River will be 48558.
A random sample of 200 teenagers participated in a taste test. Each teenager sampled four choices of fruit drink (labeled A, B, C, and D), and then were asked to pick a favorite. The table shows the results of this taste test.
Based on the information given, which of the following statements is true?
a) 40% of the participants were boys.
b) 10/35 of the participants who preferred B are girls.
c) The ratio of boys who preferred C is equal to the ratio of girls who preferred C.
d) 20/35 of the boys preferred D.
Answers
Answer:
it is c hope it helps have a good day
Answer:
(C) The ratio of boys who preferred C is equal to the ratio of girls who preferred C
Step-by-step explanation:
A is incorrect because the ratio of girls to boys in the survey is 120/80 which is 60%
B is incorrect because the ratio of girls who prefrerred B to the ratio of boys is 10/25 not 10/35
D is incorrect because once again 20/15 does not equal 20/35
C is the correct answer and the only correct answer despite the multiple choice question because the ratio of boys that preferred c to girls is the exact same
* Required
How do you name a prism or pyramid? *
10 points
O
by
by the shape of its face
O
by the number of edges it has
O
by the number of vertices it has
O
by the shape of its base
What parts of prism make up its faces? Check all that apply. *
10 points
bases
Answers
Answer:
by the number of edges it has
Step-by-step explanation:
cuz a prism has more sides than a pyramid
Highest common factor of 32,48 and 72
Answers
Answer:
the hcf of 32 48 and 72 is 8
Step-by-step explanation:
We have ,
32 = 2×2×2×2×2 = 2^{5}
48 = 2×2×2×2×3 = 2⁴×3¹
72 = 2×2×2×3×3 = 2³×3²
Now,
HCF(32,48,72) = 2³ = 8
/* Product of the smallest power of each common prime factors of the numbers */
The highest common factor of 3248 and 72 is 8.
What are LCM and HCF?The LCM of two or more numbers is the least common multiple of them.
The HCF of two or than two given numbers are the highest number that divides them completely.
Given, Are two numbers 3248 and 72.
Let us see is 3248 is completely divisible by 72, it is not.
Now, Check if 3248 is completely divisible by 36, it is not.
Other factors of 72 are 18, and 18 also does not divide 3248.
8 divides 328 complete so the HCF of 3248 and 72 is 8.
learn more about HCF here :
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2 box plots. The number line goes from 0 to 20. For East Side Middle School Debate Wins, the whiskers range from 5 to 14, and the box ranges from 10 to 12. A line divides the box at 11. For West Side Middle School Debate Wins, the whiskers range from 3 to 14, and the box ranges from 8 to 12. A line divides the box at 9. Which of these inferences about the two debate teams are true? Check all that apply. West Side is more consistent at winning. East Side is more consistent at winning. East Side typically wins more debates per year than West Side. West Side typically wins more debates per year than East Side. These graphs do not contain enough information from which to draw inferences.
Answers
B. East Side is more consistent at winning.
&
C. East Side typically wins more debates per year than West Side.
The perimeter of a rectangle is 128 cm. The length of the rectangle is three times longer than the width. What is the length and width of the rectangle?
Answers
Answer:
l=16 cm
w=48 cm
Step-by-step explanation:
perimeter of rectangle formula:
2l+2w
where
3w=l
and w=w
so
2(3w)+2w=128
6w+2w=128
8w=128
w=16
now substitute 16:
2l+2(16)=128
2l+32=128
2l=96
l=48
The length is 48 cm and width is 16 cm.
what is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values. . In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
given:
perimeter of a rectangle is 128 cm.
let the width be x
length= 3x
So, perimeter of a rectangle is 128 cm.
2( l + w)= 128
x+ 3x= 64
4x= 64
x= 16
Hence, the length is 48 cm and width is 16 cm.
Learn more about Algebra here:
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A circle of a certain radius has an area which is numerically 5 times the value of the circumference. What is the radius of the circle?
Answers
We have been given that a circle of a certain radius has an area which is numerically 5 times the value of the circumference. We are asked to find the radius of the circle.
We know that area of circle with a radius of r units is [tex]\pi r^2[/tex].
We know that circumference of a circle is [tex]2\pi r[/tex].
5 times the value of circumference would be [tex]5(2\pi r)=10\pi r[/tex].
Now we will equate 5 times circumference with area as:
[tex]\pi r^2 = 10\pi r[/tex]
Let us solve for r.
[tex]\pi r\cdot r = 10\pi r[/tex]
[tex]\frac{\pi r\cdot r}{\pi r}=\frac{10\pi r}{\pi r}[/tex]
[tex]r=10[/tex]
Therefore, the radius of the circle would be 10 units.
Find the lateral surface area of the rectangular pyramid? PLEASE HELP!! Do you have to find the slant height first?
I will award brainliest answer!! Thanks!
Answers
Answer:
The lateral surface area of the rectangular pyramid is equal to sum of area of 4 lateral triangles.
Here, the base is square, then 4 lateral triangles have equal area.
=> Lateral surface area of this rectangular pyramid:
A = (area of lateral triangle) x 4
= (12 x 14 x 1/2) x 4 = 336 (ft2)
=> Option C is correct.
Hope this helps!
:)
The lateral surface area of the given rectangular pyramid is 336 ft²
What is lateral surface area?The lateral surface of an object is all the sides of the object, excluding its base and top.
The lateral surface area is the area of the lateral surface. This is to be distinguished from the total surface area, which is the lateral surface area together with the areas of the base and top.
Given that, a rectangular pyramid, we need to find the lateral surface area of the rectangular pyramid,
The lateral surface area of the rectangular pyramid is equal to the sum of area of 4 lateral triangles.
Here, the base is square, then 4 lateral triangles have equal area.
Therefore, the lateral surface area of this rectangular pyramid:
A = (area of lateral triangle) x 4
= (12 x 14 x 1/2) x 4
= 336 ft²
Hence, the lateral surface area of the given rectangular pyramid is 336 ft²
Learn more about lateral surface area click;
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Kanesha wants to find out if people in her community would support a dog park. Which populations would be appropriate to sample for the survey?
A. People shopping at local pet store.
B. Parents of small children in the community.
C. Children attending the local school.
D. Owners of local businesses.
Answers
Answer:
a
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
A baking pantry is making packages. Each package contains 4 identical bags of flour and a 7 pound bag of sugar. The package weighs a total of 64 pounds. How much does each bag of flour way
Answers
Answer:
The answer is 14.25 pounds.
Step-by-step explanation:
If the package contains 4 bags of flour and a 7 pound bag of sugar which weighs 64 pounds in total;
The total weight of the flour bags is 64 - 7 = 57 pounds.Since the flour bags are identical, they weigh the same. If we divide 57 by 4, we can find that the weight of each bag of flour is 57 / 4 = 14.25 pounds.I hope this answer helps.
Find the circumference of the circle that has a radius measurement of 11 1/4
Answers
Answer:
22.5π units² or about 70.65 units²
Step-by-step explanation:
11 [tex]\frac{1}{4}[/tex] is equivalent to 11.25
The formula for the circumference of a circle is 2πr. Using that formula we get:
2*π*11.25 = 22.5π ≈ 70.65
Answer:
70.69 or 22.5 pi
Step-by-step explanation:
To find the circumference of a circle, you can use the formula:
2 x pi x radius
Using this formula, we can substitute the information that we already know, and solve for the circumference:
2 x pi x 45/4
6.28 x 45/4
70.69 or 22.5 pi
You are going on a field trip in a school bus. A special detector placed on one of the bus's tires counts the number of rotations completed by the tire during the journey. The tire's diameter is 1 meter, and it made 8000 rotations during the trip.
How far did the bus travel?
Answers
Answer:
25,133 m or 25.1 km
Step-by-step explanation:
The circumference of the tire is ...
C = πd
C = π(1 m)
The distance the bus traveled is 8000 times this far, so is ...
distance = (8000)(π m) = 8000π m
Using 3.14159 for π, we find the distance to be about
distance = (8000)(3.14159) m ≈ 25,133 m
The bus traveled about 25,133 meters or 25.1 km.
Answer:
25,133 m or 25.1 km
Step-by-step explanation:
The circumference of the tire is ...
C = πd
C = π(1 m)
The distance the bus traveled is 8000 times this far, so is ...
distance = (8000)(π m) = 8000π m
Using 3.14159 for π, we find the distance to be about
distance = (8000)(3.14159) m ≈ 25,133 m
The bus traveled about 25,133 meters
Hope this helps ;)
Ella bought 11/12 of a pound of green grapes and 3/4 of a pound of red grapes. How much more did the green grapes weigh than the red grapes?
Answers
Answer:
1/6
Step-by-step explanation:
11/12-3/4
=11/12-9/12
=2/12
=1/6
Answer:
2/12 or 1/6
Step-by-step explanation:
11/12-3/4
First convert the 3/4 to 9/12 becase the numbers have to have the same denominater.
3/4=9/12
11/12-9/12=2/12
Simplified would be 1/6
In ΔPQR, the measure of ∠R=90°, QP = 29, RQ = 21, and PR = 20. What ratio represents the cosine of ∠P?
Answers
Answer:
cos(P) = 20/29
Step-by-step explanation:
Given the following information:
∠R=90°,QP = 29RQ = 21PR = 20To ratio represents the cosine of ∠P we use the cosine law (please have a look at the attached photo)
[tex]RQ^{2}[/tex] =[tex]QP^{2}[/tex]+ [tex]PR^{2}[/tex] − 2QP*PRcos(P)
<=> cos(P) = ([tex]QP^{2}[/tex]+ [tex]PR^{2}[/tex] - [tex]RQ^{2}[/tex]) / 2QP*PR
<=> cos(P) =( [tex]29^{2} + 20^{2} - 21^{2}[/tex]) /2*29*20
<=> cos(P) = 20/29
Hope it will find you well.
Answer:
53/28
Step-by-step explanation:
A pole that is 3.1 m tall casts a shadow that is 1.71 m long. At the same time, a nearby tower casts a shadow that is 46.5 m long. How Tall is the tower?
roundyour answer to the nearest meter.
Answers
Answer:
84 meters.
Step-by-step explanation:
Set each tower equal to each other and you get (3.1/1.71)=(x/46.5)
Solve for X
X≈84.2982
But we want the nearest meter, so it's just 84 meters.
Answer:
84 meters
Step-by-step explanation:
The proportional value, or ratio is as the following:
[tex]\frac{3.1}{1.71} = \frac{x}{46.5}[/tex]
Now we can cross multiply in order to solve the equation...
[tex]1.71x=3.1*46.5\\1.71x = 144 \frac{3}{20}\\ x=84.3[/tex]
Rounded to the nearest meter, x is 84 meters.
PLEASEEEEEEEEE HELP 15 POINTS
Answers
Answer:
If I remember correctly,
P x 9 = $60.75 and 6 x(times) $1.25=c
Step-by-step explanation:
First problem:
Since the total price of all 9 sandwiches is $60.75, that means that the price of one sandwich nine times will equal the total price.
Second problem:
Rather than giving you the total price, it gives you the price of one drink, so to find the total price you would need to multiply the price of one drink by the number of drinks to get the total (the total being c in this case)
Find the circumference and area of a circle whose radius is 12.4 cm.Give your answer to the nearest centimeter (whole #). Circumference = cm Area = cm2
Answers
Final answer:
The circumference of the circle is approximately 78 cm and the area of the circle is approximately 484 cm².
Explanation:
The circumference of a circle can be found by using the formula:
Circumference = 2πr, where r is the radius of the circle.
Given that the radius is 12.4 cm, we can substitute this value into the formula:
Circumference = 2π(12.4 cm)
Using an approximation of π as 3.14, the calculation becomes:
Circumference = 2(3.14)(12.4 cm) = 77.9 cm
Therefore, the circumference of the circle is approximately 78 cm (to the nearest whole number).
The area of a circle can be found by using the formula:
Area = πr²
Substituting the given radius into the formula:
Area = 3.14(12.4 cm)² = 483.864 cm²
Therefore, the area of the circle is approximately 484 cm² (to the nearest whole number).
The graph of the function f(x) = x2 + 8x + 12 is shown. Which statements describe the graph? Check all that apply.
The vertex is the maximum value.
The axis of symmetry is x = –4.
The domain is all real numbers.
The range is all real numbers.
The function is increasing over (–∞, –4).
The x-intercepts are at (–6, 0) and (–2, 0).
Answers
Answer:
B C F
explanation:
Took the test
Answer:
B C F
Step-by-step explanation:
edge
Plz help meI will mark u brainliest 2.. Write an expression that represents the amount of money they collected each night. The total earned for both nights is 1,651: a. The first night, the school sold 60 adult tickets and 94 student tickets. b. The second night, the school sold 83 adult tickets and 127 student tickets.
Answers
Answer:
143a + 221b = 1,651
Step-by-step explanation
143a + 221b = 1,651
1.Add the "a"s and "b"s together seperatly.
2.Then put them together in a equation.
3.The a you added together is 143a.The b you added together is 221b.
PLEASE HELP WITH THIS QUESTION!!
Answers
Answer:
y = 2 * 3^x
Step-by-step explanation:
y = a b^x
a is the initial value ( when x = 0)
The initial value is 2
y = 2 b^x
Pick a value (1,6) and substitute it in
6 = 2 * b^1
6 = 2 * b
Divide by 2
6/2 = 2/2 b
3 =b
y = 2 * 3^x
Can someone please tell me which number belongs to each of the variables
Like is P=17 or 8 I’m confused
Answers
Answer:
The answer is PQ = 17 units, PR = 8 units, QR = 15 units .
Sin P = 15/17
Cos P = 8/17
Tan P = 15/8
Sin Q = 8/17
Cos Q = 15/17
Tan Q = 8/15
Answer:
PQ= 17
PR= 8
RQ= 15
Step-by-step explanation:
Which property can you use to show that 3x +{2x+4} is equivalent to {3x + 2x} + 4
Answers
Answer:
3x+2x=5x but 4 can't add to 3x and 2x
Answer:
6x – 3x + 9y + 4 + 11 is equivalent to 3(x + 3y + 5)
Step-by-step explanation:
On his last three tests, Mark scored 85, 95, 80. What grade must he get on his next test to have an average of 90 for all four tests
Answers
Answer: 100
Step-by-step explanation:
85+95+80=260 divided by 3 is 86.6 repeating and getting 100 on his next test would add up to 360 and 360/4 is 90
A pack of 6 cans of pop costs £1.80. A pack of 10 cans of pop costs £3.50.
Which one should you buy?
Answers
Let us look at the cost per can of both packs.
Cost of can in 6-pack = 1.80/6
= £0.30
Cost of can in 10-pack = 3.50/10
= £0.35
Since the cost of a can in the 6-pack is cheaper, it would be better to buy the 6-pack if you were looking to save money.
7.142857142857143 to the next whole number
Answers
Answer:
the answer is 7
Step-by-step explanation:
A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?
Answers
Answer:
Step-by-step explanation:
Given that,
The company makes 4 different sweat shirts
Each year they make 60,000 of each kind.
So, if they will make 60,000 sweat shirt for each brand and the company design 4 different brand.
So, number of brand is 4
n = 4.
Then,
1 brand = 60,000
Therefore, 4 brand = 60,000 × 4
4brand = 240,000 sweat shirts.
So, in a year the company will make 240,000 sweat shirts.
The company makes a total of 240,000 sweatshirts each year by producing 60,000 of each of the 4 different kinds.
The question asks for the total number of sweatshirts produced by a company each year if it makes 60,000 of each kind and there are 4 different kinds of sweatshirts.
Identify the number of different kinds of sweatshirts: 4.Determine the number of each kind of sweatshirt made annually: 60,000.Multiply the number of kinds by the number of each kind: 4 x 60,000 = 240,000.Therefore, the company makes a total of 240,000 sweatshirts each year.
The soccer balls at the sporting goods store are on sale for 20% off the regular price. What is the sale price if the regualr price is $28?
Answers
$22.40
Explanation:
20%x 28= 5.60
28-5.60=22.40
if a bicycle wheel has a diameter of 21 inches what the exact circumference?
Answers
Answer:
Circumference = 65.97344573
Step-by-step explanation:
Given the diameter of a circle, we can use the formula C = πd to find the circumference.
C = circumference
π = pi
d = diamater
Equation: 21(π) = 65.97344573
Make sure to round to whatever decimal place is asked for!