Answer:
The radius of the track is 32 meters
Step-by-step explanation:
Circumference
The circumference of a circle can be defined as the distance around the circle or the length of a circuit along the circle.
Given a circle of radius r, the circumference of the circle can be calculated as follows:
[tex]L=2\pi r[/tex]
If we already know the length of the circle, we can solve the above expression for r:
[tex]\displaystyle r=\frac{L}{2\pi}[/tex]
The distance given around a circular running track is L=200 m, thus:
[tex]\displaystyle r=\frac{200}{2\pi}=31.830989\ m[/tex]
Rounding to the nearest meter:
r= 32 meters
The radius of the track is 32 meters
6
13 Which statement about ş multiplied by 4 must be true?
The product is between 6 and 7.
B
6
The product is less than
7.
6
The product is between 5 and 4.
The product is greater than 4.
An ornament shaped like a sphere has a radius of 2.3 inches which measurement is closest to the volume of the ornament in cubic inches
Answer:
50.97in^3Step-by-step explanation:
Volume of a sphere
The expression for the volume of a sphere is given as
V=4/3πr^3
Given that the radius is 2.3in
Substitute r= 2.3 in the expression to find the volume of the sphere
V=4/3*3.142*(2.3)^3
V=4/3*3.142*(12.167)
V=4/3*38.23
V=152.9/3
V=50.97in^3
Therefore the volume of the ornament is 50.97in^3
Solve for x . x^2+6x+6=0
Answer:
[tex]\boxed {x = \sqrt{3} - 3}[/tex]
[tex]\boxed {x = -\sqrt{3} - 3}[/tex]
Step-by-step explanation:
Solve for the value of [tex]x[/tex]:
[tex]x^2 + 6x + 6 = 0[/tex]
-When you use the quadratic formula ( [tex]\frac{-b\pm \sqrt{b^{2} - 4ac}}{2a}[/tex] ), it would give you two solutions. So, use the quadratic formula:
[tex]x = \frac{-6\pm \sqrt{6^{2} - 4 \times 6}}{2}[/tex]
-Simplify [tex]6[/tex] by the exponent [tex]2[/tex]:
[tex]x = \frac{-6\pm \sqrt{6^{2} - 4 \times 6}}{2}[/tex]
[tex]x = \frac{-6\pm \sqrt{36 - 4 \times 6}}{2}[/tex]
-Multiply both [tex]-4[/tex] and [tex]6[/tex]:
[tex]x = \frac{-6\pm \sqrt{36 - 4 \times 6}}{2}[/tex]
[tex]x = \frac{-6\pm \sqrt{36 - 24}}{2}[/tex]
-Add [tex]34[/tex] and [tex]-24[/tex]:
[tex]x = \frac{-6\pm \sqrt{36 - 24}}{2}[/tex]
[tex]x = \frac{-6\pm \sqrt{12}}{2}[/tex]
-Take the square root of [tex]12[/tex]:
[tex]x = \frac{-6\pm \sqrt{12}}{2}[/tex]
[tex]x = \frac{-6\pm 2\sqrt{3}}{2}[/tex]
-Now solve the equation when [tex]\pm[/tex] is plus, So, add [tex]-6[/tex] to [tex]2\sqrt{3}[/tex]:
[tex]x = \frac{-6\pm 2\sqrt{3}}{2}[/tex]
[tex]x = \frac{2\sqrt{3} - 6}{2}[/tex]
-Divide [tex]-6 + 2\sqrt{3}[/tex] both sides by [tex]2[/tex]:
[tex]x = \frac{2\sqrt{3} - 6}{2}[/tex]
[tex]\boxed {x = \sqrt{3} - 3}[/tex] (Answer 1)
-Now solve the equation when [tex]\pm[/tex] is minus. So, Subtract [tex]2\sqrt{3}[/tex] from [tex]-6[/tex]:
[tex]x = \frac{-2\sqrt{3} - 6}{2}[/tex]
-Divide [tex]-2\sqrt{3} - 6[/tex] by [tex]2[/tex]:
[tex]x = \frac{-2\sqrt{3} - 6}{2}[/tex]
[tex]\boxed {x = -\sqrt{3} - 3}[/tex] (Answer 2)
Solve.
3(x-4) = -3
How do i slove this
Answer:
[tex]3(x - 4) = - 3 \\ 3x + 12 = - 3 \\ 3x = - 15 \\ x = - 5[/tex]
Firstly, multiply the number and variable in the perenthesis. Then move the variable on it's own side of the equation. The simplify.
Answer:
You need to do the Distributive Property. This means multiplying the number outside the parenthesis to each number inside.
Step-by-step explanation:
3(x)=3x
3(-4)=-12
3x+-12=-3
then evaluate using inverse operations to get x=3
How do you make comparisons between an equation and a graph?
Answer:
here is a hint
Step-by-step explanation:
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Compare slope of an equation and slope of a line on graph and compare y-intercepts.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
For linear equation,
Compare slope of an equation and slope of a line on graph and compare y-intercepts.
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Therefore, compare slope of an equation and slope of a line on graph and compare y-intercepts.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
30 POINTS! HELP ME PLZZ I NEED HELP WITH THIS!!!
Answer:3/12 is greater
Step-by-step explanation:
Since 3/12 and 2/9 have different denominators, you need to find the Least Common Multiple (LCM) of the denominators and then multiply the top and bottom of each fraction by the number of times the denominator goes into the LCM.
According to my calculations, the LCM of the two denominators is 36. Therefore, since 12 goes into 36 a total of 3 times, you would multiply the top and bottom of the first fraction by 3. And since 9 goes into 36 a total of 4 times, you would multiply the top and bottom of the second fraction by 4.
Step #2: Now that the denominators are the same, you can simply compare the numerators to determine which fraction is greater. Since 9 is greater than 8, 9/36 is greater than 8/36. Therefore the 1st entry (3/12) is greater than the 2nd entry (2/9).
You borrow $2000 for three years at an annual interest rate of 12% what is the total cost of the loan at the end of the three years
Answer:
2,391 paid altogether. The interest Rate was another 391 dollars.
Step-by-step explanation:
The perimeter of triangle ABC is 138 cm and BC || DE. Is triangle ABC = triangle ADE? Which conjecture supports your conclusion?
please help me it’s due in 30 minutes!!
Answer
yes triangle ABC is equal to triangle ADE
Step-by-step explanation:
x=46 cm, I got this after simplifying the equation of triangle ABC, x+4+x-4+x=138 cm, so this equation simplifies to 3x as +4-4 cancels out and there're 3 x's, so divide 138 by 3 and you get 46 cm, so AB is 50 cm, BC is 42 cm, and AC is 46 cm, this means EA is equal to EC, now here come a property of equality, EC attaches 2 parallel lines, as does DB, this means these 2 lines are transversals, so a number of angles are equal as well, corresponding angles are congruent, a.k.a equal to each other along with alternate interior angles, so since line DB AND line EC are transversals, we can deduce angle ADE is congruent to angle ABC, and angle DEA is equal to ACB, this mean we have 2 congruent angles, and 1 congruent set of sides, this mean that the 2 triangles are congruent due to Angle Angle Side, if your teacher doesn't use these terms, look it up, but the answer in short is yes, they are congruent or equal
We proved that ABC = triangle ADE by the concept of vertically opposite angles and given perimeter.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
We know when a transversal intersects two parallel lines vertically opposite angles are equal hence DE ≅ CB.
Given, (x + 4) + x + (x - 4) = 138.
3x = 138.
x = 46.
Now, BC = ED = (46 - 4) = 42 cm.
Assuming DA to be y.
∴ 46 + 42 + y = 138.
y = 50
And AB = x + 4 = 50 hence proving triangle ABC = triangle ADE.
learn more about congruency here :
https://brainly.com/question/7888063
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Which of the following lines is parallel to x = 4? (2 points)
A.3y = 9
B.y = 4
C.X = 2
D.x=y
Answer:
x = 2
Step-by-step explanation:
x = 4 is the equation of a vertical line parallel to the y- axis
A line parallel to it must also be a vertical line with equation
x = c ( c is a constant )
The only equation of this form is
x = 2 ← parallel to x = 4
If the number of gallons of gas is known, can you find the number of miles driven?
Explain how this value could be calculated.
PLEASE SOMEONE HELP ME!!!!!!
Answer:
It cant
Step-by-step explanation:
car use gas at differnt rates
My son, Garrett, is 11 years old and has a piggy bank that he wants to fill. He started with 5 one dollar bills. Every Saturday he earns 3 more dollar bills for chores he’s completed. How many one dollar bills will he have by the end of 10 weeks?
1. Write a function model, M(x), that represents the total number of one dollar bills garret will have in one dollar bills, x
2. Identify the independent and dependent quantity.
3. The domain and range are represented as discrete or continuous?
4.What is a reasonable domain and range for this scenario?
Thanks for the help!
Answer:
1) M(x) = 5 + 3x
2) Dependent variable; 3 dollar bills
Independent variable: chores
3) Range is continuous
Domain is discrete
4) Range: 0 ≤ x ≤ 10
Domain: 5 ≤ M ≤ 35
Step-by-step explanation:
We are told he started with 5 number of $1 dollar bills and that every Saturday, he earns 3 more $1 dollar bill.
Thus, total number of $1 bills earned after x number of Saturdays(weekly) is;
M(x) = 5 + 3x
After 10 weeks, total number is;
M(10) = 5 + 3(10)
M(10) = 35
The dependent variable is the 3 more dollar bills earned each Saturday because it depends on chores he completed. While the independent variable is the chores because it doesn't depend on anything.
After 10 weeks, the range and domain will be;
Range: 0 ≤ x ≤ 10
For the; Domain:
For x = 1, M(0) = 5 + 3(0) = 5
M(10) = 35
Thus;
Domain: 5 ≤ M ≤ 35
The range could be all numbers in the interval from 0 to 10. Thus, it is continuous.
Whereas, the domain doesn't contain all the numbers in the interval from 5 to 35. Thus it is Discrete.
I really don’t understand this question and I don’t know what to do
What is the equation of the line that passes through the point (-1, -5) and has a
slope of -3?
Answer:
[tex]y=-3x-8[/tex]
Step-by-step explanation:
12. Which of the following numbers is largest?
(a) 1.099
(b) 1.11
©). 1.106
(d) 0.99
(e) 1.009
Please show the work
Susan rides her bicycle 5 miles in 1/4 of an hour. At this rate, how many miles could she ride in 2 hours?
Answer:40 miles
Step-by-step explanation:
5*4=20
20*2=40
Answer:
40 miles
Step by Step Explanation:
Each 1/4 of an hour is 15 minutes. 2 hours is 120 minutes, so you divide 120 by 15, which gives you 8. You multiply 8 times the 5 miles , and you get 40 miles. :)
plz help ill give brainliest In the kite , AK=15 , JK=39 , and AM=77 .
What is JM ?
Answer:
125 i think....
Step-by-step explanation:
NEED HELP PLZ! Will give brainliest, show all your work
Solve for h(x)=x(x+3)(x-2)
Answer:
Your answer is:
If you are solving to find x then your answer would have been: x = 0 , -3 , 2
If you are solving to find the x and y intercepts your answer is: ↓
x-intercept(s): (0,0) (-3,0) (2,0)
y-intercept(s): (0,0)
If you are solving to find roots your answer is: x = 0 , -3 , 2
If you want the graph look below ↓
Step-by-step explanation:
Hope this helped : )
In a figure, such as a triangle or parallelogram, this is used to refer to the
length of one side.
Answer:
The hypotenuse is the side opposite the right angle, or defined as the longest side of a right-angled triangle,
Step-by-step explanation:
convert 8/3 to a mixed number
============================================
Work Shown:
8/3 = (6+2)/3
8/3 = 6/3 + 2/3
8/3 = 2 + 2/3
8/3 = 2 & 2/3
The whole part is 2. The fractional part is 2/3.
-----------
Another way you could do the problem is to use long division as shown in the diagram below.
The result of the long division is
8/3 = 2 remainder 2
The quotient 2 forms the whole part and the remainder is the numerator of the fractional part 2/3.
So that's another way to get 2 & 2/3
an angles measure is 9 degrees more than 2 times the measure of its supplement. Find the measure of the angle
Answer:
The angle would be 123°.
168 stickers for 24 students unit rate
Answer:
89/12
Step-by-step explanation:
Answer: The unit rate is 7 stickers per student!
Step-by-step explanation: This can be found by dividing the amount of stickers by the amount of students.
Hope this helps, if not, comment down below please!!!
−15 ÷ 5 =
A number line going from negative 30 to positive 30. An arrow goes from 5 to 10, from 10 to 15, from 15 to 20.
Emily used the number line to find the quotient for -15 ÷ 5. What errors did she make? Select three correct answers.
The arrows should point in the negative direction.
The small arrows should end in the same place as the large one.
The arrows should end on negative 15.
The arrows should start at zero.
There should be 5 small arrows.
Answer:
-3 is the answer because if we divide 15 by 5 we get 3 . So it is same only the question is -15 divide by 5 so the answer is -3
Answer:
The answer is A,C,D
Step-by-step explanation:
Just had the question :D
Help pls I need help
Answer:
3 3/7
Step-by-step explanation:
8/1 divided by 2 1/3 = 8/1 x 3/7
8/1 x 3/7 = 24/7
24/7 = 3 3/7
PLEASE HELP QUICK!!!!!
Answer:
C.
That is the closest answer since 8 times 10 6 times gets you 8 million.
Step-by-step explanation:
Answer:
C. 8×10⁶
Step-by-step explanation:
8,406,000 to nearest million is 8,000,000
8,406,000 = 8.406 × 10⁶
8,000,000 = 8 × 10⁶
34% x 79% pls help ill give brainliest
Answer:
0.2686
Step-by-step explanation:
It's basically just 34 times 79 lol
Answer:
0.2686
Step-by-step explanation:
(-9) - (-37) =
A -29
B -40
C 28
Answer:c: 28
Step-by-step explanation:
Triangle X Y Z is shown. The length of side X Y is (9 n + 12) feet and the length of side X Z is (15 n minus 6) feet. Angles X Y Z and Y Z X are congruent. Consider isosceles ΔXYZ. What is the value of n? What is the measure of leg XY? ft What is the measure of leg XZ? ft
*the figure is shown in the attachment
Answer/Step-by-step explanation:
Since <XYZ and <YZX are said to be congruent, therefore, the side opposite to each of the angle are also equal. Therefore, ∆XYZ is an isosceles ∆.
Find the value of n by creating an equation to solve for n:
XY = (9n + 12) ft
XZ = (15n - 6) ft
XY = XZ (2 equal lengths of isosceles ∆)
9n + 12 = 15n - 6 (substitution)
Combine like terms
9n - 15n = - 12 - 6
-6n = -18
Divide both sides by -6
-6n/-6 = -18/-6
n = 3
Find the length of leg XY by substituting n = 3 into XY = (9n + 12) ft.
XY = (9(3) + 12) ft
XY = (27 + 12) ft
XY = 39 ft
Find the length of leg XZ by substituting n = 3 into XZ = (15n - 6) ft.
XZ = (15(3) - 6) ft
XZ = (45 - 6) ft
XZ = 39 ft
Answer:
1st box: 3
2nd box: 39
3rd box: 39
Have a great day, remember to wear a mask! :)
Solve for x. 0 = 2x² + 3x + 5
Answer: No real solutions.
Step-by-step explanation:
Pls help question is in the pic. Please give a right answer thx :D
Answer:
61.2
Step-by-step explanation: