Answer:
32m²
Step-by-step explanation:
r=
[tex] \frac{c}{2\pi } [/tex]
r=20/(2×3.14)= 3.18m
A=pi r² = 3.14x3. 18² = 32m²
Stephanie read 45 pages from a book of 120 pages. Which of the following equations shows the number of pages (n) Stephanie still needs to read?
The equation of the number of pages Stephanie still needs to read will be n + 45 = 120. Then the correct option is A.
The missing options are given below.
A. n + 45 = 120
B. n - 45 = 120
C. 45ⁿ = 120
D. n/45 = 120
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Stephanie read 45 pages from a book of 120 pages.
Let n be the number of remaining pages.
Then the equation, we have
n + 45 = 120
Then the correct option is A.
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What is 6 months to 5 years expressed as a ratio
Answer:
6:5
Step-by-step explanation:
Solve for x in the equation x squared minus 12 x + 59 = 0.
The value of x in the equation is -4.92
How to solve for x?The equation is given as:
12x + 59 = 0
Add -59 to both sides of the equation
12x = -59
Divide by 12
x = -59/12
Evaluate
x = -4.92
Hence, the value of x in the equation is -4.92
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[tex]x^2-12x+59=0\\x^2-12x+36+23=0\\(x-6)^2=-23\\x\in\emptyset[/tex]
Find the Volume
I need correct answer
Answer:
70 cm^3; 1000 cm^3; 343 cm^3; 30 cm^3; 48 cm^3
Step-by-step explanation:
to find the volume to all of these shapes you can just multiply all the sides together
one looks like this
2 * 5 * 7 = 70
70 is the answer for the first one
you repeat this 4 more times
since a cube has all equal sides for 2 and 3 you can just cube your side length
10^3 = 1000
7^3 = 343
afterwards since they are all just rectangular prisms you can just multiply all the sides together
1 * 5 * 6 = 30
4 * 6 * 2 = 48
those are your answers
dont forget to add ^3 behind the cm
Step-by-step explanation:
70cm kr 5ko 12m y x W L H V
ksk
Choose the best answer. The diagonals of a square:
A. bisect each other at different angles
B. are the same length and intersect at a right angle
C. do not bisect each other and intersect at right angles
D. are the same length and intersect at different angles
Answer:
D
Step-by-step explanation:
are the same length and intersect at different angles
What are the solutions to the equation x^2+9x+12=6
Answer:
[tex]x= -\dfrac {9}2 +\dfrac{\sqrt{57}}{2},~~x = -\dfrac {9}2 - \dfrac{\sqrt{57}}{2}[/tex]
Step-by-step explanation:
[tex]~~~~~~~x^2 +9x +12 = 6\\\\\implies x^2 +9x = 6-12\\\\\implies x^2 +9x = -6\\\\\implies x^2 +2 \cdot \dfrac 92 \cdot x +\left(\dfrac 92\right)^2 -\left( \dfrac 92 \right)^2 = -6\\\\\implies \left(x+ \dfrac 92 \right)^2 -\dfrac{81}{4}= -6\\\\\implies \left(x +\dfrac 92 \right)^2 = -6 + \dfrac{81}4\\\\\implies \left(x + \dfrac92 \right)^2 = \dfrac{57}{4}\\\\\implies x+ \dfrac 92 = \pm\sqrt{\dfrac{57}4}\\\\\implies x = -\dfrac {9}2 \pm\dfrac{\sqrt{57}}{2}[/tex]
If f(x) = 1-x, which value is equivalent to fi)?
Answer:
[tex]\sqrt 2[/tex]
Step-by-step explanation:
[tex]f(x) = 1-x\\\\|f(i)| = |1-i| = \sqrt{1^2 +1^2 } =\sqrt 2[/tex]
There is a circular pool in the backyard with an approximate area of 113 square inches. What was the diameter?
A.12 inches
B.36 inches
C.48 inches
D.144 inches
A circle is a curve sketched out by a point moving in a plane. The diameter of the circular poll is 12 inches. Thus, the correct option is A.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
The area of a circle is given as πR², where r is the radius of the circle. Since the area of the pool is 113 sq. inches, therefore, the radius of the circle will be,
Area of pool = πR²
113 sq. inches. = πR²
113/π = R²
R = √35.9690
R = 5.9974 ≈ 6 inches
Now, since the diameter of a circle is twice the radius of the circle, therefore, the diameter of the circle will be,
Diameter of the circle = 2 × 6 inches = 12 inches
Hence, the diameter of the circular poll is 12 inches. Thus, the correct option is A.
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Answer:
a. 12 inches
Step-by-step explanation:
113 ÷ 3.14 = 35.98726114649682
2√35.98726114649682 = 5.998938334947011
5.998938334947011 x 2 = 11.99787666989402
keyword approximate ;)
How would you apply the fundamental counting principle to a bike lock combination with 5 numbers?
1. 10+ 10+ 10+ 10+10
2. 10x5
3. 10x10x10x10x10
4.none of these
Answer:
3
Step-by-step explanation:
write a Pythagorean triplet whose smallest member is 6
Answer:
6, 8, 10
Step-by-step explanation:
Where:
a = 6
b = 8
c = 10
Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]
[tex]6^2 + 8^2 = c^2[/tex]
[tex]36 + 64 = c^2[/tex]
[tex]100 = c^2[/tex]
c = [tex]\sqrt{100}[/tex]
c = 10
A box shaped like a rectangular prism has a length of 8 inches and width of 8 inches. Its volume is 512 cubic inches. What is the height of the box?
Many of the amenities at a local ski hill are operated using gas generators. To transport gasoline to the top of the mountain, a special trailer has been designed. The trailer bed is in the shape of a square with a side length of 1.5 m. They wish to attach a cylindrical shaped gas tank to the trailer which is as large as possible, but cannot be taller than the trailer bed is. Determine the dimensions, volume and surface area of the gas tank.
The Dimension of the Cylinder: Height = 1.5 m and radius = 0.75 m
Volume of Cylinder = 2.649 m³
Surface Area = 10.59 m²
What is Cylinder?A cylinder is a three-dimensional solid figure which has two identical circular bases joined by a curved surface at a particular distance from the center which is the height of the cylinder.
Here, Trailer bed dimension = 1.5 m X 1.5 m
So, height of the cylindrical = 1.5 m
Radius = 1.5/2 = 0.75 m
Now, Volume of Cylinder = πr²h
= 3.14 X (0.75)²X1.5
= 2.649 m³
Surface area of cylinder = 2πrh + 2πr²
= 2πr (h + r)
= 2 X 3.14 X 0.75 ( 1.5 + 0.75)
= 10.59 m²
Thus, The Dimension of the Cylinder: Height = 1.5 m and radius = 0.75 m
Volume of Cylinder = 2.649 m³
Surface Area = 10.59 m²
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The measures of the angles of a triangle are in the extended ratio 4:5:6. Find the measure of the largest angle in the
triangle.
A 60°
B. 72°
C. 120°
D. 132°
factorize that x^4+4y^4
Answer:
(x² + 2y² + 2xy)(x² + 2y² - 2xy)Step-by-step explanation:
Given binomial:x⁴ + 4y⁴
In order to factorize it, follow the steps:
Complete the square:x⁴ + 4y⁴ = (x²)² + 2*(x²)*(2y²) + (2y²)² - 2*(x²)*(2y²) = (x² + 2y²)² - (2xy)² = (x² + 2y² + 2xy)(x² + 2y² - 2xy)Used identities:
(a + b)² = a² + 2ab + b²a² - b² = (a + b)(a - b)A stright road is 1.4 long and 0.04 km wide.what area does it cover?
Step-by-step explanation:
it is a rectangle !
a straight road and its width.
so, the area is (as for any other rectangle)
length×width
in our case
1.4 km × 0.04 km = 0.056 km²
Answer:
Area formula= length x width
length of road= 1.4 km
width of road= 0.04 km
Area= 1.4 x 0.04
= 0.056 km
What’s the answer to the picture I took?
Answer:
y = - x
Step-by-step explanation:
From the given table:-
( x_1,x_2): (5,-5)
( y_1,y_2): (6,-6)
1) Let's find the slope (m):-
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{ - 6( - 5)}{6 - 5} = \frac{ - 6 + 5}{1} = \frac{ - 1}{1} = - 1[/tex]
2) Substitute x_1= 5, y_1=-5 and m=-1 into y-y_1=m(x-x_1)
[tex]y - ( - 5) = - 1(x - 5)[/tex]
[tex]y + 5 = - x + 5[/tex]
[tex]y = - x + 5 - 5[/tex]
[tex]y = - x[/tex]
This rectangle is composed of two parts, labeled 1 and 2.
5√2 in
3 in
1
3√2 in
2
What are the areas of each smaller rectangle and the large rectangle?
Drag each tile to the correct location on the image. Not all tiles will be used.
The area of part 1 is
square inches.
The area of part 2 is:
square inches.
The area of the entire rectangle is:
square inches.
The area of part 1 is 15√2 square in, the area of part 2 is 30 square in, and the area of the entire rectangle is (30 + 15√2) square in.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
The area of part 1 = 5√2×3 = 15√2 square in
The area of the part 2 = 5√2×3√2 = 15×2 = 30 square in
The area of the entire rectangle = area of part 1 + area of part 2
= (15√2 + 30) square in or
= (30 + 15√2) square in
Thus, the area of part 1 is 15√2 square in, the area of part 2 is 30 square in, and the area of the entire rectangle is (30 + 15√2) square in.
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solve 8 = 2^x + 4.
A. x=-4
B. x=-1
C. x=0
D. x=7
let A={1,2,3,4,5} and B={4,5,6} Let R is relation from A to B defined by R={(a,b):a+b ⊆ B} Then Find 1. R 2. Domain (R) 3. Range (R) 4.Inverse of R
1. Disregard my comment. Since R is said to be a relation from A to B, we take both a ∈ A and b ∈ A. Then the set R is the pairs (a, b) whose entries' sum belongs to B.
We have
• 4 = 1 + 3 = 2 + 2 = 3 + 1, so R contains (1, 3), (2, 2), and (3, 1)
• 5 = 1 + 4 = 2 + 3 = 3 + 2 = 4 + 1, so R contains (1, 4), (2, 3), (3, 2), and (4, 1)
• 6 = 1 + 5 = 2 + 4 = … = 5 + 1, so R contains (1, 5), (2, 4), …, (5, 1)
Then
R = {(1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4),
… (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1)}
2. The domain of R is the set of all values a in the pairs (a, b) belonging to R :
dom(R) = {1, 2, 3, 4, 5}
3. The range of R is the set of all values b in those same pairs:
range(R) = {1, 2, 3, 4, 5}
4. The inverse of R is the set with the same elements as R, but the entries are swapped:
inv(R) = {(3, 1), (4, 1), (5, 1), (2, 2), (3, 2), (4, 2),
… (1, 3), (3, 2), (3, 3), (1, 4), (2, 4), (1, 5)}
In this case, we have R = inv(R).
log_8(5x+4)=3x-4
Write the log equation as an exponential equation. You do not need to solve for X
The equivalent equation of the logarithmic equation is [tex]5x + 4 = 8^{3x - 4}[/tex]
How to rewrite the equation?The logarithmic equation is given as
Log_8(5x+4)=3x-4
Rewrite properly as:
[tex]\log_8(5x+4)=3x-4[/tex]
Apply the following law of logarithm
[tex]\log_a(b) = x \to a = b^x[/tex]
So, we have:
[tex]5x + 4 = 8^{3x - 4}[/tex]
Hence, the equivalent equation of the logarithmic equation is [tex]5x + 4 = 8^{3x - 4}[/tex]
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1.
In AXYZ, |XZ| = 13 cm, XY = 12 cm and
ZXYZ = 90°. Find YZ if the area of the
triangle is 30 cm².
Step-by-step explanation:
I think you mean triangle XYZ. and angle XYZ.
so, the angle at Y is 90°.
that makes XZ the Hypotenuse (baseline opposite of the 90° angle) of the right-angled triangle.
so, we can actually use Pythagoras (we don't need the area of the triangle to solve) :
13² = 12² + YZ²
169 = 144 + YZ²
25 = YZ²
YZ = 5 cm
just to check - the area of this triangle is (remember, it is a right-angled triangle, so XY and YZ serve also as baseline and height) :
area = 12 × 5 / 2 = 60/2 = 30 cm²
correct, it fits.
Which of the following values are solutions to the inequality -5 -6x > -8?
I. - 4
II. - 3
III. - 5
Answer:
I. - 4
II. - 3
III. - 5
Step-by-step explanation:
All values are the solution to the inequality
Carol buys a house for £234 900
She pays a 10% deposit.
Work out the amount of deposit paid by Carol.
Answer:
211410
Step-by-step explanation:
234900x.10
23490
234900-23490
211410
need help with this problem
Answer:
(28) 61.5, or $61,500
(29) 49.25, or $49,250
(30) the median
Step-by-step explanation:
(28) the mean can be calculated by adding together the values and then dividing by the total number of values.
(45 + 47 + 47.5 + 51 + 53.5 + 125) / 6 = 61.5
(29) the median can be calculated by crossing off the values from the outside in, alternating sides
45, 47, 47.5, 51, 53.5, 125
47, 47.5, 51, 53.5
47.5, 51
you will end with two middle values since there are six values in the set, so average these to find the median
(47.5 + 51) / 2 = 49.25
(30) The median will better reflect the value of the homes because it is not as much influenced by the outlier value, 125, as the mean is.
What is the product?
StartFraction 2 y Over y minus 3 EndFraction divided by StartFraction 4 y minus 12 Over 2 y + 6 EndFraction
Two-thirds
Ten-ninths
StartFraction 4 y Over y minus 3 EndFraction
StartFraction 4 y Over y + 3 EndFraction
The value of the product [tex]\frac{2y}{y -3} \times \frac{4y - 12}{2y + 6}[/tex] is [tex]\frac{4y}{y + 3}[/tex]
How to determine the fraction?The product expression is given as:
[tex]\frac{2y}{y -3} \times \frac{4y - 12}{2y + 6}[/tex]
Factorize each factor of the expression
[tex]\frac{2y}{y -3} \times \frac{4(y - 3)}{2(y + 3)}[/tex]
Cancel the common factors
[tex]\frac{y}{1} \times \frac{4}{y + 3}[/tex]
Evaluate the product
[tex]\frac{4y}{y + 3}[/tex]
Hence, the value of the product [tex]\frac{2y}{y -3} \times \frac{4y - 12}{2y + 6}[/tex] is [tex]\frac{4y}{y + 3}[/tex]
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Answer:
4y/y+3
Step-by-step explanation:
edge 2022
math
any help please
Step-by-step explanation:
the answer is true
the statement is true
a puppy weighs 1 pound. what does the puppy weigh after 4 weeks
A regular hexagonal prism has a height of 7 cm and base edge length of 4 cm. Identify its lateral area and surface area.
Given the base edge and the height, the lateral area and surface area of the regular hexagonal prism are 168cm² and 251.138cm² respectively.
What is lateral and surface area of the regular hexagonal prism?For a regular hexagonal prism, the Lateral surface area and the surface area is expressed as follows:
Lateral Area = 6a × h
Surface Area = 6ah + 3√3a²
Where a is base edge and h is height.
Given that;
Base edge length a = 4cmHeight h = 7cmThe Lateral Area of the regular hexagonal prism will be;
Lateral Area = 6a × h
Lateral Area = 6( 4cm ) × 7cm
Lateral Area = 24cm × 7cm
Lateral Area = 168cm²
The Surface Area of the regular hexagonal prism will be;
Surface Area = 6ah + 3(√3)a²
Surface Area = 6(4cm × 7cm) + 3(√3)(4cm)²
Surface Area = 168cm² + 3(√3)16cm²
Surface Area = 168cm² + 83.138cm²
Surface Area = 251.138cm²
Given the base edge and the height, the lateral area and surface area of the regular hexagonal prism are 168cm² and 251.138cm² respectively.
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in a circle H with m angle GKJ=27 find the m angle GHJ
In a circle H with a measure of angle ∠GKJ = 27°. Then the measure of angle ∠GHJ will be 54°
What is a circle?It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
In a circle H with a measure of angle ∠GKJ = 27°.
Then the measure of angle ∠GHJ will be
We know that a chord's slope in the centre is double that of the chord's slope at the perimeter.
Then we have
∠GHJ = 2 x ∠GKJ
∠GHJ = 2 x 27°
∠GHJ = 54°
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Hi i have exams coming up soon within 4 months time what can i don't to focus more and not be easily distracted?
i would recommend setting a schedule for each day. a to do list can also help. this can help you stay on track make a list of things you need to do and have set goals for every week or month. if you're studying something you dont like, i would recommend doing pomodoros. you can find videos to follow along to.
i hope this was helpful!