A bicycle wheel has diameter 66 cm. Find how many turns the wheel makes when the bicycle travels 400 metres.​

E and M are shown as congruent. This could be an Isosceles Triangle, so let's check. In an isosceles triangle, there are two congruent angles adjacent to the non-congruent side, and two congruent sides to the non-congruent angle. This angle is the apex. The apex of this triangle is adjacent to two congruent sides, however it is congruent to angle M, and thus this cannot be an isosceles triangle. That means this is an equilateral triangle, so all sides are congruent. So: LM = 16

Answer:

11.0 cm

Step-by-step explanation:

Answer:

11.8 cm

Step-by-step explanation:

2.5 + 5 + 2.5√3 = 7.5 + 2.5√3 = 11.8 cm

The rocket reaches its maximum height at 2.25 second(s) after launch

The maximum height reached by the object is 88 feet.

The function is given as

h(t) = -16t² + 72t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 72

Set to 0

-32t + 72 = 0

So, we have

32t = 72

Divide by 32

t = 2.25

Hence, the time is 2.25 seconds

In (a), we have

t = 2.25

Substitute t = 2.25 in h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

Evaluate

h(2.25) = 88

Hence, the maximum height is 88 feet

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Answer:

11/56 i think

Step-by-step explanation:

The slope of the line is m = - 11/7

And the y-intercept is b = 8

Find the slope and the y-intercept.

Step 1 – Transform the equation.

-11x - 7y = -56

To get a slope-intercept form, we need to isolate the variable y on the left-hand side of the equation.

First, we need to eliminate variable x from the left-hand side.

To eliminate the term with x, we'll add it to both sides of the equation. Remember to always perform the same operation on both sides to keep the equality true!

-11x – 7y + 11x = -56 + 11x

Now, let's add terms on the left-hand side. Keep in mind that two opposites add up to zero, so we can just remove it.

-7y = -56 + 11x

Since the variable x should be the firs on the righ-hand side in slope-intercept form, let's make it that way. Use the commutative property to reorder the terms.

-7y = 11x – 56

We're almost there! We just have to eliminate -7 from the left-hand side. To do that, let's divide both sides of the equation by -7.

(-7y)/(-7) = (11x - 56)/(-7)

Simplify the left-hand side. Each number divided by itself equals 1, so we are left with y.

y = (11x - 56)/(-7)

Next, separate the fraction on the righ-hand side into two fractions.

y = 11x/(-7) - 56/(-7)

Simplify the fraction on the right-hand side of the equation.

y = - 11x/7 + 56/7

y = - 11x/7 + 8

Finally, write the expression with x as a product.

y = - 11/7 x + 8

That's it! We've got the slope-intercept form of the equation.

Step 2 – Identify the slope.

Since the equation is written in slope-intercept form, y = m x + b, identify the slope of the lines as the coefficient next to the variable x.

y = - 11/7 x + 8

m = - 11/7

Step 3 – Identify the y-intercept.

Identify the y-intercept of the line as the constant term.

y = - 11/7 x + 8

m = - 11/7

b = 8

The slope of the line is m = - 11/7

And the y-intercept is b = 8

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A) Y = [tex]-2^{x}+4[/tex] is the equation which have real zero(s) corresponding to the x-intercept(s) of the graph below

What does a mathematical coordinate mean?

a set of numbers used to represent the horizontal and vertical divisions of the positions of two reference axes in a coordinate plane. often shown as the combination of x-values and y-values (x,y).

What is the Slope Intercept Form Equation?

The slope intercept equation can be used to find the general equation of a straight line using its slope and the point of its y-axis junction. The equation in slope intercept form is Y = mx + b.

You must enter y=0 for the x intercept.

in equation A we can see that at x=2 , y=0

so hence answer is option A) Y =[tex]-2^{x}+4\\[/tex]

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If we make r the subject formula, then the formula would be r = log_h(V/π) + (h/3)

In this question, we have been given a formula V=πh^(r-h/3)

We need to make r the subject formula

This means we need to rewrite formula for r.

V = πh^(r-h/3)

h^(r-h/3) = V/ π

r - h/3 = log_h(V/π)

r = log_h(V/π) + (h/3)

Therefore, if we make r the subject formula, then the formula would be r = log_h(V/π) + (h/3)

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( 3,7 ) will be point when its moved 5 units down on coordinate plane .

What is the short definition of a coordinate plane?

( 3,2) is the point .

when the point is moved 5 units down

then the point will be  = ( 3, 7 )

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Answer:

x ≥ 1

Step-by-step explanation:

Solving inequalities are essentially like solving equations where the main focus is getting the variable, x in this case, on one side and a constant on the other using inverse operations.

10x+16 ≥ 6x+20

==> subtract 16 from both sides

10x ≥ 6x + 4

==> subtract 6x from both sides

4x ≥ 4

==> divide both sides by 4

x ≥ 1

So the answer would be A

Also an important note for future references is when you divide one of the sides by a negative number you must flip the inequality sign.

E.g. -4x>8

We would divide both sides by -4 and because we divide by a negative number we must flip the inequality signs

This would result to x<-2

Answer:

t = (x - μ) / SE. where x is the sample mean, μ is the hypothesized population mean in the null hypothesis, and SE is the standard error. P-value. The P-value is the probability of observing a sample statistic as extreme as the test statistic.

Step-by-step explanation:

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The mean in hypothesis testing is the parent population from which the samples are drawn.

In statistics, hypothesis testing is the process by which an analyst tests an assumption about a population parameter. The analyst's methodology is determined by the nature of the data and the purpose of the analysis. Using sample data, hypothesis testing is used to assess the plausibility of a hypothesis.

Hypothesis testing is a type of statistical inference that employs sample data to draw conclusions about a population parameter or probability distribution. First, an educated guess is made about the parameter or distribution.

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Answer:

XY - YT = 2

Step-by-step explanation:

substitute the given values into the expression

XY - YT

= (12 × [tex]\frac{1}{3}[/tex] ) - ([tex]\frac{1}{3}[/tex] × 6 )

= 4 - 2

= 2

The function rule for the line is f(x) = [tex]\frac{2}{3}x[/tex] - 2

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

The line cuts the x and y axis at (3,0) and (0, -2)

standard form of equation of line: y = mx + c

when x =3, y = 0

substitute these values into the equation

0 = 3m + c

c = -3m----------------1

when x = 0, y = -2

substitute these values into the equation, we have

-2 = 0(m) + c

c = -2

substitute the value of c in equation 1 to find m

-2 = -3m

m = 2/3

Substitute the values of m and c into the standard equation,

y =  [tex]\frac{2}{3}x[/tex] - 2

In conclusion, the function rule for the given line is y =  [tex]\frac{2}{3}x[/tex] - 2

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Answer:23000

Step-by-step explanation:

The principal amount​ is ₹20000.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]

Let the money at beginning of the year 2005, a person invests in a bank be x.

At the beginning of 2010, the accumulated interest was ₹10000.

Now, x(1+r/100)⁵=x+10000 ------(I)

Let x(1+r/100)⁵=A

At the beginning of 2015, the accumulated interest became ₹25000.

So, x(1+r/100)¹⁰=x+25000 ------(II)

From the equation (I),

x(A-1)=10000 ------(III)

From equation (II), we get

x×A²=x+25000

x(A²-1)=25000 ------(IV)

From equation (III) and (IV), we get

10000(A+1)=25000

A=1.5

Put A=1.5 in equation (III), we get

0.5x=10000

x=10000/0.5

x=₹20000

Therefore, the principal amount​ is ₹20000.

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An open circle at 5 and a bold line starting at 5 and pointing to the right (>) is the correct representations of the inequality

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given: the inequality –3(2x – 5) < 5(2 – x)

First, we have to solve for x in the inequality

–3(2x – 5) < 5(2 – x)

Clear the parenthesis:

-6x + 15 < 10 - 5x

Collect like terms:

-6x + 5x < 10 - 15

-x < -5

Divide both sides by -1:

x > 5              ( Note:  Dividing both sides by -1 will change the < to > )

This is what will determine our answer

Since our answer is x > 5.  An open circle will be at 5 and a bold line starts at 5 and is pointing to the right (>)

Therefore,  the correct representations of the inequality is  an open circle is at 5 and a bold line starts at 5 and is pointing to the right

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Answer:

3000/17281 mm

Step-by-step explanation:

We can model this as a cylinder with a volume of 66 mm³, a radius of 11 mm, and an unknown height [tex]h[/tex] mm.

Using the formula for the volume of a cylinder,

[tex]V=\pi r^2 h \\ \\ 66=11^2 \pi h \\ \\ h=\frac{66}{121\pi} \\ \\ h=\frac{6}{11\pi} \\ \\ h \approx \frac{6}{11(3.142)} \\ \\ h \approx 3000/17281[/tex]

Answer:

0.17 (2d.p)

Step-by-step explanation:

volume of cylinder= πr^2Xh

22/2=11 which is radius

11^2=121

121X3.142=380.182

380.182Xh=66

h=66/380.182=0.1736010648

Answer:

  3 -n/2 ≤ 5

Step-by-step explanation:

You want a math expression that means "half a number less than 3 is at most 5."

We can let "n" represent "a number." Then "half a number" is (1/2)n or n/2.

That amount "less than 3" means it is subtracted from 3:

  3 -n/2 . . . . . . half a number less than 3

The wording "is at most" means "is less than or equal to." In symbols, the words mean ...

  3 -n/2 ≤ 5

__

Additional comment

Often 'x' is used to represent an unknown quantity. We like 'n' for "a number" because it is mnemonic, and because the numbers of interest are often integers or natural numbers from the set represented by ℕ.

English expressions of math relations are often ambiguous. In this case, we're not completely sure that the intention is not "half (a number less than 3)", which would be (3 -n)/2. Usually, we fall back on the Order of Operations, which requires that multiplication be done before addition. That is "half a number" must be computed before "less than 3" is evaluated, hence 3 -n/2.

If she gave two to each of her friends. She only has 8 remaining balls. so she has a total of 16 friends.

What is division in mathematics?

In mathematics, division is the process of dividing a number into equal parts and determining how many equal parts can be made. For instance, dividing 15 by 3 means dividing 15 into three equal groups of five. The symbol " or sometimes '/' represents division.

Sumalee won a total of 40 super bouncy balls.

then she gave two balls to each of her friends.

So she can distribute the balls to = 40/2

                                                       = 20 friends.

But after the distribution, she remained with 8 balls.

Now the number of balls will be = 40 - 8 = 32 balls.

and she can distribute 32 balls to = 32/2

                                                        = 16 friends.

Hence, If she gave two to each of her friends. She only has 8 remaining balls. so she has a total of 16 friends.

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Answer: 2z+2

Step-by-step explanation:

The height of the two trees will be same after 13 years and the height of the trees will be 24 feet.

According to the question,

We have the following information:

One tree, a ficus, was 6 feet tall when it. was planted and has grown 1.5 feet per year. The other tree, an oak, was grown from an acorn on the ground and has grown 2 feet per year.

So, for first tree, we have:

6, 7.5, 9, ...

Now, this is an arithmetic progression.

So, for the second tree, we have:

0,2,4, ...

Now, this is again an arithmetic progression.

Formula to find nth term of an A.P.:

an = a+(n-1)d where a is the first term and d is the common difference

6+(n-1)1.5 = 0+(n-1)2

6+1.5n-1.5 = 0+2n-2

4.5 = 2n-1.5n-2

6.5 = 0.5n

n = 13 years

Now, we have the height of the trees after 13 years:

an = 0+(13-1)2

an = 12*2

an = 24 feet

Hence, the height of the two trees will be same after 13 years and the height of the trees will be 24 feet.

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The angles of the given figure are:

∠1 = 128°

∠2 = 52°

∠3 = 47°

∠4 = ∠5  = 81°

What are corresponding angles?

The angle is supplementary(∠5)

52° + ∠5 + 47° = 180°

∠5 + 99° = 180°°

∠5  = 180° - 99°

∠5  = 81°

Then the  ∠1 and 52° are supplementary (Interior adjacent angles)

∠1 + 52° = 180°

∠1 = 180° - 52°

∠1 = 128°

Now,  ∠2

∠2 +  ∠5  + 47° = 180°

∠2 + 81° + 47° = 180°

∠2 = 180° - 128°

∠2 = 52°

Based on interior opposite angles are equal. Then

∠5 =  ∠4 and ∠3 = 47°

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Answer:

The number is 5

Step-by-step explanation:

Let us use an equation ( X is the unknown number)

2(x-3)=4

2x-6=4

2x-6+6=4+6

2x/2=10/2

x=5

Two planes that are orthogonal to one another are parallel. This is untrue. Although they might not be parallel, two planes can be orthogonal to a third plane.

Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same 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.

Given,

Two planes intersected by a third plane are parallel.

Two planes that are orthogonal to one another are parallel. This is untrue. Although they might not be parallel, two planes can be orthogonal to a third plane.

A line is formed by the intersection of two planes. The planes are parallel if they do not intersect. Due to the endless nature of planes, they cannot meet at a single place. Stack a hardcover book on your desk and open the two hard covers at any random angle. The coverings' planes are not parallel to one another but are individually perpendicular to the desk top (or necessarily perpendicular to each other).

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Answer:

It costs 32.75 for five pounds. and the expression would be p7.25-3.50

Step-by-step explanation:

5*7.25 = 36. 25. 36.25-3.50=32.75

c=p7.25-3.50 would be the expression. :)

The ratio 5 to 2 is written in other notations as

Mathematicians use the term "ratio" to compare two or more numbers.

It serves as a comparison tool to show how big or small an amount is in relation to another.

In a ratio, division is used to compare two amounts.

The ratio 5 is to 2 can be represented as a fraction to 5 / 2

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Moloch have $133,737.75 after 2 years at the interest of 1.02% per month.

Interest accrued on both the principal sum of money and the interest already earned.

The formula for compound interest is A= p(1+r/100)ⁿ

Where A is amount, p is principal, r is rate and n is time.

Given that,

The amount Moloch placed in account = $104,828

The rate of interest = 1.02% per month

time = 2 years,

To find total amount Moloch has after 2 year,

Use formula

Amount = [tex]p(1+r/100)^{nt}[/tex]

             = 104,828 (1+1.02/100)²ˣ¹²

              = 104,828 (1+0.0102)²⁴

              = 104,828 (1.0102)²⁴

               = 104,828×1.27578

               = 133,737.75

After 2 years, Moloch have $133,737.75 in account.

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Answer:

Step-by-step explanation:

You want the complete factorization of x³ +4x² -4x -16.

Pairing terms of the given polynomial, we have ...

  (x³ +4x²) -(4x +16)

Factoring each pair gives ...

  x²(x +4) -4(x +4)

  = (x² -4)(x +4)

The factorization of x² -4 is found using the form for factoring the difference of squares:

  a² -b² = (a +b)(a -b)

  x² -4 = (x +2)(x -2)

Note that x+2 is a factor here.

The complete factorization of the given polynomial is ...

  x³ +4x² -4x -16 = (x +4)(x +2)(x -2)

This is confirmed by the graph, which shows zeros at x = -4, -2, 2.

Answer:

yes, The result is the same

Step-by-step explanation:

-3(5)=-15

5(-3)=-15

Answer:

They are same (equal)

Step-by-step explanation:

-3 multiplied with 5 is equal to -15.

5 multiplied with -3 is also equal to -15

so these two expressions are same when multiplied because the products are equal to one another.

Answer: p = -2/3, sum = 0

Step-by-step explanation:

Additive inverse has the name numerical value as the given number but has the opposite sign so when they are added together they equal zero. The sum of any number and its additive inverse equal 0.

EX: 1 and -1      

1+ (-1) = 0

EX: -4.5 and 4.5

-4.5 + 4.5 = 0

1) Saleena worked for 20 hours in total.

2) She earned $220 during the week.

Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present, and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.

Given,

Saleena has a part time job.

a) On Monday

Start time = 4: 30 pm

End time = 9:00 pm

Hours worked = 4 : 30 hours

b) On Tuesday

Start time = 3: 00 pm

End time = 9 : 00 pm

Hours worked = 6 hours

c) On Thursday

Start time = 4: 30 pm

End time = 9: 00 pm

Hours worked = 4 hours 30 minutes

d) On Saturday

Start time = 10:30 pm

End time = 3 : 30 pm

Hours worked = 5 hours

Total hours worked = 4:30 + 6 + 4: 30 + 5

1) Saleena worked for 20 hours in total.

2) She earns $11/h

Saleena worked for 20 hours in total.

Multiplying by $11 for per hour

20 × 11

220

2) She earned $220 during the week.

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