A circle is a curve sketched out by a point moving in a plane. The diameter and circumference of the circle are (x/4) units and (x/4)π units, respectively.
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.
Given that radius of the circle is x/8 units. Therefore, the diameter and the circumference of the circle can be written as,
Diameter of circle = 2 × (Radius of the circle)
= 2 × (x/8) units
= x/4 units
Circumference of circle = 2 × π × (Radius of the circle)
= 2 × π × (x/8) units
= (x/4)π units
Hence, the diameter and circumference of the circle are (x/4) units and (x/4)π units, respectively.
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Identify the vertex, the axis of symmetry, the maximum or minimum value, and the domain and the range of each function.
y=(x-125)²+125 .
Each function's vertex, axis of symmetry, maximum or lowest value, domain, and range are all described as follows: Vertex: (125,125); range: (125,125); minimum: at y=125; x=125; maximum: no., axis of symmetry is x=125.
Describe Domain and Range.The domain of a function is the set of values that we are allowed to enter into our function.
The set of values that a function can accept as input is known as its range.
According to given data;y=(x-125)²-125
we know that;
y=(x-h)²+k
Vertex: In this form, the vertex (or, in other words, the "pointy bit") is given to us in the (h ,k);here we have (125,125).
Axis of symmetry : Two equal segments of the parabola. It moves straight up and down via the vertex.
Thus, we may formulate an equation for the vertical line that passes through the vertex. It is x=125 in this query..
Maximum and lowest values: Here, we're concerned in examining the vertex to determine whether it is at the maximum or lowest of the parabola's range (i.e., when a negative sign is placed in front of the (x-h) = 0 term, respectively).
Range: The value of range is (125,∞ )
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Owen drove 9 miles total five days this week on Saturday he drove 17 miles to his grandmas house how many total miles did he drive this week
Answer:
26 miles
Step-by-step explanation:
add 9 miles to 17 miles= 26 miles
Point Q is the midpoint of GH. GQ = 2x + 3, and GH = 5x - 5. What is the length of GQ?
Enter your answer in the box.
Answer:
[tex]\displaystyle 25 = GQ[/tex]
Step-by-step explanation:
If point Q is the centre of GH, then QH and GQ are equivalent segments. So, double the length of GQ, set it equal to the length of GH, then solve for x:
[tex]\displaystyle \boxed{4x + 6} = 2[2x + 3] \\ \\ 5x - 5 = 4x + 6 \hookrightarrow -11 = -x \hookrightarrow \boxed{\boxed{11 = x}}[/tex]
Plug the result into the expression for the length of GQ to get twenty-five units.
I am joyous to assist you at any time.
Pls help with these 2 problems for 15 points
Answer:
1) 15
Step-by-step explanation:
The smallest integer is 15 because,
There are 7 consecutive integers with n + 6 being the largest, therefore:
7n + 21 = 6(6 + n)
7n + 21 = 36 + 6n
7n - 6n + 21 = 36
n + 21 = 36 ⇒ n = 36 - 21 = 15
Hope this helps!
2) -3
2/5 = .4
Under her cell phone plan, Jocelyn pays a flat cost of $35 per month and $5 per
gigabyte. She wants to keep her bill under $55 per month. Use the drop-down menu
below to write an inequality representing g, the number of gigabytes she can use
while staying within her budget.
g
Submit Answer
Answer:
< 5 gigabytes
Step-by-step explanation:
Let the number of gigabytes be represented as: g
Under her cell phone plan, Nicole pays a flat cost of $35 per month and $5 per gigabyte. She wants to keep her bill under $60 per month.
Under $60 = less than (<) $60
Hence, our inequality equation is given as:
$35 + $5 × g < 60
35 + 5g < 60
Collect like terms
5g < 60 - 35
5g < 25
g < 25/5
g < 5 gigabytes
Therefore, the number of gigabytes she can use while staying within her budget less than 5 gigabytes
The diagram below shows a large cone divided horizontally into two parts A and B. Given that the vertical height of A and B are equal, and that the volume of A is x cm³. Express the volume of the entire large cone in terms of x. [2] If the volume of part B is 3500 cm³, calculate the volume of cone A. [2]
Answer:
3500cm3
Step-by-step explanation: since A and B are equal, and B has a volume of 3500 cm3 then A will have the same.
Extra: The horizontal measure of A is 1500 and the verticle is 1500
PLEASE HELP?
Pedro went to the store and spent $36.85. He paid with a $50 bill. How much money will he get back as
change? Show All Your Work for full credit.
Answer:
Step-by-step explanation:
change = dollar_amount - spent_amount
change = 50 - 36.85
change = 13.15
Lincoln High School has 75 less than 4 times as many students as Washington High School. a. Write an expression to find the number of students at Lincoln High School if Washington High School has w students. w + b. How many students are at Lincoln High School if Washington High School has 250 students? students
Answer: A. 4w+(-75)
B. 925
Step-by-step explanation:
100 POINS 1 QUESTION!
Answer:
Step-by-step explanation:
we cant see the question :)
Answer: If you have to fill in the chart I think you just add them together so aluminum would be +3, phosphide -3, iodide -1, and tin 0
Step-by-step explanation:
Simplify by combining like terms. -a² + 2b² + (1/4) a²
The Simplified value is [tex]\frac{-3}{4} a^{2} +2b^{2}[/tex].
Like terms are defined as terms that have same variable and and same power.
For Example ; 2a² , 6a² are like terms.
In the given question ,
[tex]=-a^{2} +2b^{2} +\frac{1}{4} a^{2} \\ \\ =-a^{2} +\frac{1}{4} a^{2} +2b^{2}[/tex]
[tex]=a^{2}(-1+\frac{1}{4} )+2b^{2}[/tex] ( taking a² common )
taking LCM and solving further we get
[tex]=a^{2} (\frac{-4+1}{4} )+2b^{2}[/tex]
[tex]=\frac{-3}{4} a^{2} +2b^{2}[/tex]
Therefore , The value by combining Like terms in -a² + 2b² + (1/4) a² is [tex]\frac{-3}{4} a^{2} +2b^{2}[/tex].
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What are the solutions of the rational equation?
a. x-1 / x+2 = x² + 2 x-3/x+2
The solutions of the rational equation x-1 / x+2 = x² + 2 x-3/x+2 are x = -2 and x = 1
In this question,
We have been given a rational equation.
x-1 / x+2 = x² + 2 x-3/x+2
We need to find the solution of given rational equation.
Here, the denominator is same on the both sides.
x-1 / x+2 = x² + 2 x-3/x+2
⇒ x - 1 = x² + 2 x-3
⇒ x² + 2x - 3 - x + 1 = 0
⇒ x² + x -2 = 0
We solve above quadratic equation.
⇒ x² + 2x - x - 2 = 0
⇒ x(x + 2) - (x + 2) = 0
⇒ (x + 2)(x - 1) = 0
⇒ x + 2 = 0 or x - 1 = 0
⇒ x = -2 or x = 1
Therefore, the solutions of the rational equation x-1 / x+2 = x² + 2 x-3/x+2 are x = -2 and x = 1
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The sum of two consecutive integers is - 207. Find the two integers.
===========================================
Work Shown:
x = first integer
x+1 = second integer right after x
The two consecutive integers add to -207
(first) + (second) = -207
(x)+(x+1) = -207
2x+1 = -207
2x = -207-1
2x = -208
x = -208/2
x = -104 is the first integer
x+1 = -104+1 = -103 is the second integer
Check:
-104 + (-103) = -207
The answers are confirmed.
Earth's radius is approximately 6400 kilometers. What are the surface area and volume of the Earth? Round to the nearest tenth if necessary.
The surface area of earth is 514.4million [tex]Km^{2}[/tex] and the volume of the Earth is 1.1 ×[tex]10^{12}[/tex] [tex]Km^{3}[/tex].
Radius of Earth = 6400 (approximately).
Earth is a sphere. So by using the formula of Surface Area of sphere we can calculate the Surface area of earth as follows,
Surface Area of Earth = 4[tex]\pi r^{2}[/tex] = 4 × (3.14) × [tex](6400)^{2}[/tex]
= 4 × 3.14 × 40960000
= 514457600 [tex]Km^{2}[/tex]
= 514.4million [tex]Km^{2}[/tex]
The surface area of earth is 514.4million [tex]Km^{2}[/tex] .
Similarly, by using the formula of volume of sphere we can calculate the volume area of earth as follows,
Volume of Earth = (4/3)[tex]\pi r^{3}[/tex]
= (4/3)×(3.14)×[tex](6400)^{3}[/tex]
=(1.3333)(3.14)(2.6214 × [tex]10^{11}[/tex])
= 1.0975 × [tex]10^{12}[/tex] [tex]Km^{3}[/tex]
= 1.1 ×[tex]10^{12}[/tex] [tex]Km^{3}[/tex]
The volume of the Earth is 1.1 ×[tex]10^{12}[/tex] [tex]Km^{3}[/tex].
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Write and solve an inequality for m
Answer choices:
m + 6 > 8; m > 2
m + 6 < 8; m < 14
m + 6 > 8; m > 14
m + 6 < 8; m < 2
Based on the information, it should be noted that the inequality to solve for m will be D. m + 6 < 8; m < 2.
How to illustrate the information?It should be noted that in Mathematics, an inequality is used to show the expressions that are hot the same or equal.
Based on the information given about the triangle, it should be noted that the hypothenuse which is given as 8 is the longest side of the triangle.
Therefore, the inequality to solve for m will be:
m + 6 < 8.
Collect like term
m < 8 - 6
m < 2
Therefore, based on the information, it should be noted that the inequality to solve for m will be m + 6 < 8; m < 2.
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. If there are 4.90 Cal in 10.0 g of parsley, how many joules are in 12.1 g of parsley?
The joules are in 12.1 g of parsley is 24.806936 Joules of energy
10g has 4.9 cal
1g has 4.9/10 cal
Energy in 12.1 g = 4.9 x 12.1 / 10 = 5.929 Cal = 5.929 x 4.18400 = 24.806936 Joules of energy [1 calorie = 4.18400]
In the International System of Units (SI), a joule is a unit of work or energy equal to the work done by a force of one newton acting through one meter. It is named after the English scientist James Prescott Joule and equals 107 ergs, or about 0.7377 foot-pounds. The joule is equivalent to one watt-second in electrical terms, which is the amount of energy released in one second by a current of one ampere through a resistance of one ohm.
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Divide. State any restrictions on the variable. 3x²-9 x / x-2 ÷ x² - 9 / 4 x-8
The division of given rational expression 3x²-9 x / x-2 ÷ x² - 9 / 4 x-8 is 12x / x + 3 provided x ≠ -3
In this question,
we have been given a complex rational expression [tex]\frac{3x^{2} -9x}{x-2}\div \frac{x^2-9}{4x-8}[/tex]
We need to find the division of given rational expression.
We rewrite given rational expression as,
3x²-9 x / x-2 ÷ x² - 9 / 4 x-8
= 3x²-9 x / x-2 / x² - 9 / 4 x-8
= (3x²-9 x / x-2) × (4 x-8 / x² - 9 )
= [tex]\frac{3x(x-3)}{x-2}\times \frac{4(x-2)} {(x+3)(x-3)}[/tex]
= 12x / x + 3 .........(provided x ≠ -3)
Therefore, the division of given rational expression 3x²-9 x / x-2 ÷ x² - 9 / 4 x-8 is 12x / x + 3 provided x ≠ -3
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Find the slope of the line through each pair of points. (0,-1/2) and (7/5, 10)
The slope of the line with points (0,-1/2) and (7/5, 10) is 7.5
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope
We know that slope, slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
For the pairs of points (0,-1/2) and (7/5, 10)
⇒ m = [tex]\frac{10 - (-1/2)}{(7/5) - 0}[/tex]
⇒ m = [tex]\frac{21/2}{(7/5) }[/tex]
⇒ m = 15/2
⇒ m = 7.5
Hence, the slope of the line with points (0,-1/2) and (7/5, 10) is 7.5
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The distance from Charlotte, North Carolina, to Knoxville, Tennessee, is
2.31 × 10 miles. The distance from Charlotte, North Carolina, to El Paso,
Texas, is about 7 times that distance. What is the approximate distance
from Charlotte to El Paso?
A. 1.62 × 10 miles
B. 9.31 × 10 miles
C. 1.62 × 10 miles
D. 9.31 × 10 miles
The approximate distance from Charlotte to El Paso is 1. 62 × 10 miles . Options A and C
How to determine the distanceFrom the information given, we have that;
Distance from Charlotte, North Carolina, to Knoxville, Tennessee, is 2.31 × 10 milesDistance from Charlotte, North Carolina, to El Paso, Texas, is about 7 times that distanceTo determine the distance from Charlotte to El Pasco, we have the expression
= 7 × distance from Charlotte to Knoxville
Substitute the value
= 7 × 2.31 × 10 miles
= 1. 62 × 10 miles
Thus, the approximate distance from Charlotte to El Paso is 1. 62 × 10 miles . Options A and C
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ΔE F G is a 30°-60°-90° triangle with m∠ F=90 . Find the coordinates of E in Quadrant III for F(-3,-4) and G(-3,2).FG is the longer leg.
The coordinates of E in Quadrant lll is (3 - [tex]2\sqrt{3}[/tex], -4)
Given,
m < F = 90°
E (x, y) in quadrant lll
F(-3, 4), G(-3, 2)
FG = The longer leg.
FG = [tex]\sqrt{(-3-(-3)^{2} )+(2-(-4)^{2} }[/tex] = [tex]\sqrt{36}[/tex] = 6
FE = [tex]\frac{FG}{\sqrt{3} }[/tex] = [tex]\frac{6}{\sqrt{3} }[/tex] = 2[tex]\sqrt{3}[/tex]
GE = 2FE = 2 × 2√3 = 4√3
ΔEFG is a 30° - 60° - 90° triangle with the longest leg FG = 6.
We apply the 30° - 60° - 90° triangle theorem to determine the short side FE and the hypotenuse GE.
l = 4√3
h = 2√3
[tex]\sqrt{(x-(-3))^{2} +(y-(-4))^{2} }[/tex] = (2√3)²
[tex]\sqrt{(x-(-3))^{2} +(y-2)^{2} }[/tex] = (4√3)²
∴ (x + 3)² + ( y + 4)² = 12
(x + 3)² + (y - 2)² = 48
Solving this, we get:
Coordinates of E as (3 - 2√3, -4)
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There are 80 animals on a farm. 52 of the animals are chickens.
a) What fraction of the animals are chickens?
Give your answer in its simplest form.
b) Write your answer to part a) as a decimal.
The fraction of the animals in chickens is 52/80 which is 0.65 in decimal form.
What are fractions?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. In mathematics, there are six types of fractions: proper/improper fractions, mixed fractions, equivalent fractions, and like/, unlike fractions. A fraction has two parts: the numerator and the denominator.So, (A) The fraction of the animals is chickens: 52/80
Simplest form: 13/20
(B) In decimal form: 0.65
Therefore, the fraction of the animals in chickens is 52/80 which is 0.65 in decimal form.
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A cylindrical container if radius 4 cm and height 15 cm is half filled with water. Find the volume of water in the container
Answer:
= 0.377 liters
= 377 mililiters
Step-by-step explanation:
Volume of a regular cylindrical container = л r ² h
л = 3.1416 (aprox,)
r = radius
h = height = 15cm (half filled) = 15/2 = 7.5cm
then:
Volume = 3.1416 * (4cm)² * 7.5cm
volume = 3.1416 * 16cm² * 7.5cm
volume = 377 cm³ (aproximadly)
1 cm³ = 0.001 liters
377 cm³ = 0.001*377 = 0.377 liters = 377 mililiters
There are 8 roses and 6 daisies in a vase What is the ratio of all flowers in the vase to roses
Answer:
14 to 8
Step-by-step explanation:
8 roses+6 daisies=14 is all the flowers in the vase
Which value of p is a solution to this equation?
p–6=2
Answer:
[tex] \sf \large \: p = 8[/tex]
Step-by-step explanation:
Let's solve the equation step by step,
p – 6 = 2
Add +6 to both sides
p - 6 + 6 = + 6
p = 8
Answer:
8
Step-by-step explanation:
Find the missing term(s) of each arithmetic sequence. -1, □, 11,. . . .
The missing term is 6.
Here the sequence is -1,__, 11...
An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Here the sequence is in an arithmetic sequence, as there is a common difference between the two numbers.
To find the nth term of the sequence we have a formula:
[tex]a_{n}[/tex] = a + (n-1)d
From this we can find a common difference, as we know the 3rd term of the sequence.
[tex]a_{3}[/tex] = -1 + (3-1) d
11 = -1 + 2d
2d = 12
d = 6
Now we have to the 2nd term of the series we have
[tex]a_{2}[/tex] = -1 + (2-1) 6
= -1 + 6
= 5
Therefore the 2nd i.e., the missing term of the sequence is 5
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200 learner's in grade 10 class.107 learner's takes history.63 learners take science and 147 learner's take both history and science and how many learner's take neither of the subjects
Answer:
I believe the answer is 30.
Step-by-step explanation:
-
Please help of 3 through 6
Answer:
3, 9% more people have green as their favorite color over yellow. 4. Picture is cut off so I can't see sorry 5. science and social studies 6. Mike spends 40% more time studying math then he does science
Step-by-step explanation:
Position and label each triangle on the coordinate plane.
right ΔM N O with right angle at point M and legs of lengths a and 2 a .
We need to position the right triangle Δ MNO in the first quadrant with coordinates , M(0,0) , N (0,a) & O (2a,0).
It is given that Δ MNO with right angle at point M has legs of lengths a and 2a .
We have to position the triangle on coordinate plane.
What is a right angled triangle ?
A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.
As per the question ;
The triangle is a right angle triangle, so it's two sides can be located
on axis.
Place the right angle of the triangle Δ MNO at M.
i.e., M will have coordinates (0,0)
The origin will allow the two legs to be along the x and y-axes , so position the triangle in the first quadrant.
As N is on the y-axis ;
Its x-coordinate will be 0 and the y-coordinate will be a , because the leg is a units long.
i.e., N will have coordinates (0,a)
As O is on the x-axis,
its y-coordinate will be 0 and the x-coordinate will be 2a , because the leg is 2a units long.
i.e.,
O will have coordinate (2a,0)
We can put these coordinates after placing the triangle in the first quadrant i.e., M (0,0) , N (0,a) & O (2a,0).
Thus , we need to position the right triangle Δ MNO in the first quadrant with coordinates , M(0,0) , N (0,a) & O (2a,0).
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Given: <5=<16;<2=<4
Prove: <11 and <14 aré supplementary
Given the question, <11 and <14 are supplementary because they sum up to give 180 degrees. Detail below
What are supplementary angles?These are angles that sum up to give 180 degrees. On the other hand, angles on a straight line sum up to give 180 degrees.
Considering the question given above, we can prove that <11 and <14 are supplementary as follow:
<11 + <12 = 180 (angle on straight line)
But
<12 = <14 (corresponding angles)
Thus,
<11 + <14 = 180
Recall
Angle that sum up to give 180 are called supplementary angles
Therefore,
<11 + <14 = 180 => supplementary
From the illustrations given above, we can see clearly that <11 and <14 are supplementary angles
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What is the slope of the line that goes through the points (-4,2) and (8,5)? A. B. C. D.
Answer:
4
Step-by-step explanation:
The slope of the line with points p(x, y) and p′(x′, y′) is given by:
[tex] (\frac{x. \: - \: x}{y. \: \: - y } )[/tex]
[tex] (\frac{8 - ( - 4)}{5 - 2} )[/tex]
12/3
slope = 4
a babysitter earns $8 an hour
Answer:
8xh h=hours
Step-by-step explanation:
8 times how ever much hour than that's all if there's tips well just add it to your answer
