A kangaroo hops 2 km in 5 minutes at this rate how far does the kangaroo travel in 3 minutes?

[tex]\displaystyle \lim_{x\to 0}~\cfrac{1-cos^2(7x)}{8x^2(~~1-sin^2(7x)~~)}~\hfill \boxed{u=7x\implies \cfrac{u}{7}=x\implies \cfrac{u^2}{49}=x^2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1-cos^2(u)}{8\left(\frac{u^2}{49} \right)(~~1-sin^2(u)~~)}\implies \cfrac{1-cos^2(u)}{ ~~ \frac{8u^2(~~1-sin^2(u)~~)}{49} ~~ }\implies \cfrac{[1-cos^2(u)]49}{8u^2(~~1-sin^2(u)~~)} \\\\\\ \cfrac{[1-cos(u)][1-cos(u)]49}{8u^2(~~1-sin^2(u)~~)}\implies \cfrac{1-cos(u)}{u}\cdot \cfrac{49[1-cos(u)]}{8u[1-sin^2(u)]} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\displaystyle \lim_{x\to 0}~\cfrac{1-cos(u)}{u}\cdot \cfrac{49[1-cos(u)]}{8u[1-sin^2(u)]}\implies \lim_{x\to 0}~\cfrac{1-cos(u)}{u}\cdot \lim_{x\to 0}~\cfrac{49[1-cos(u)]}{8u[1-sin^2(u)]} \\\\\\ \displaystyle \lim_{x\to 0}~\cfrac{1-cos(7x)}{7x}\cdot \lim_{x\to 0}~\cfrac{49[1-cos(7x)]}{8(7x)[1-sin^2(7x)]} \\\\\\ \displaystyle \text{\LARGE 0}\cdot \lim_{x\to 0}~\cfrac{49[1-cos(7x)]}{8(7x)[1-sin^2(7x)]}\implies \text{\LARGE 0}[/tex]

The two ways of forming isosceles triangle by bending the metal strip using length by length by base are

A triangle that have the two sides equal is referred to as an isosceles triangle.

Using a strip of 20 inches long to construct an isosceles triangle means that the perimeter of the triangle is 20 inches

the perimeter is equal to base + length + length

bending 6 inches already means one of the dimensions is gotten then fo the other is based on if

if the 6 is base then minus the 6 from 20 and divide the rest for the length

20 - 6 = 14

the two lengths is 14 one length is 7. so we have 6 + 7 + 7 = 20

If the 6 is length then get another 6 and the rest is base

20 - 6 = 14

14 - 6 = 8

therefore we have 6 + 6 +8 = 20 inches

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The value of x is=-1

acc to our question-

hence,The value of x is=-1

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Answer:

[tex]\large\begin{array}{c|c|c|}\cline{2-3}&x&y\\\cline{2-3}\phantom{\dfrac12}&0&\boxed{9}\\\cline{2-3}\phantom{\dfrac12}&\boxed{2}&0\\\cline{2-3}\phantom{\dfrac12}&4&\boxed{-9}\\\cline{2-3}\end{array}[/tex]

Step-by-step explanation:

Given equation:

[tex]9x+2y=18[/tex]

Substitute x = 0 into the given equation and solve for y:

[tex]\begin{aligned}x=0 \implies 9(0)+2y&=18\\2y&=18\\\dfrac{2y}{2}&=\dfrac{18}{2}\\y&=9\end{aligned}[/tex]

Substitute y = 0 into the given equation and solve for x:

[tex]\begin{aligned}y=0 \implies 9x+2(0)&=18\\9x&=18\\\dfrac{9x}{9}&=\dfrac{18}{9}\\x&=2\end{aligned}[/tex]

Substitute x = 4 into the given equation and solve for y:

[tex]\begin{aligned}x=4 \implies 9(4)+2y&=18\\36+2y&=18\\36+2y-36&=18-36\\2y&=-18\\\dfrac{2y}{2}&=\dfrac{-18}{2}\\y&=-9\end{aligned}[/tex]

Therefore:

[tex]\large\begin{array}{c|c|c|}\cline{2-3}&x&y\\\cline{2-3}\phantom{\dfrac12}&0&\boxed{9}\\\cline{2-3}\phantom{\dfrac12}&\boxed{2}&0\\\cline{2-3}\phantom{\dfrac12}&4&\boxed{-9}\\\cline{2-3}\end{array}[/tex]

Step-by-step explanation:

the expression is

45 × 12 + 45 × 32

this is the same as

45 × (12 + 32)

you can extract a common factor from a sum and make it the central factor for the sum.

it is the opposite operation of simplifying this central multiplication, where you have to multiply every part of the left factor with every part of the right factor and sin things up according to the resulting signs.

so, the 4th answer is correct.

Answer:

12.5 72

Step-by-step explanation:

Because shows that the basketball player wear size 11.5 73 inches tall so basically the answer would be 12.5 72

The equation of the regression line is y = 0.77x + 61.95. The residual is 2.2 inches. The residual means that the gap between the estimated and anticipated values is 2.2 inches.

A regression line shows a linear connection between the y-dependent axis's variables and the x-independent axis's variables. The connection is determined by examining the data pattern created by the variables.

From the table, the points are given as follows:

(7, 64.5), (10, 70), (12.5, 72), (8.5, 71), (9, 69), (10, 70), (11, 75), (12.5, 69), (13, 71), (10.5, 68).

Inserting these points into the linear regression calculator, the equation is given as follows:

y = 0.77x + 61.95 ...(i)

For a shoe size of 11.5 inches, the predicted height is given as below:

y = 0.77(11.5) + 61.95 = 70.8 inches.

The residual is the gap between the estimated and anticipated values, hence:

Residual = 73 inches - 70.8 inches = 2.2 inches.

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Answer: ima say something so hopefully this gets more noticed

Step-by-step explanation:

Answer:

Step-by-step explanation 43 453 645

The inequality that compares the given numbers -4;-1 is -4 < -1.

Inequalities are created through the connection of two expressions.

It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, it should be noted -4 is less than -1. Therefore, the inequality will be -4 < -1.

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The value of the expression, (-3x)(-6)*(-10)/(-9), after simplification is 20x.

According to the question,

We have the following expression:

(-3x)(-6)*(-10)/(-9)

Now, we will first solve the numerator of this expression.

We know that the multiplication of two negative integers always gives us the positive results.

So, the multiplication of -6 and -3x will give us the positive results.

18x*(-10)/(-9)

When two negative integers are in division then their results is also positive.

18x*10/9

Dividing 18 in the numerator by 9 in the denominator, we will get 2as the result:

2x*10

20x

Hence, the value of the expression, (-3x)(-6)*(-10)/(-9), after simplification is 20x.

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Answer:

82 miles

Step-by-step explanation:

75-29.50 = 45.50

45.50/0.55 = 82.7272727273

82 x 0.55 = 45.10

45.10+29.50 = 74.60

Here in the rhombus ABCD the value of y is 7.5.

A rhombus is a unique kind of quadrilateral with four equal sides and perpendicular diagonals that cut the angles and one another in half.

So here 4x+15 = 7x+2 and

12y = 90.

To find the remaining values by first solving for each variable, then substituting as necessary.

4x+15=7x+2

15=3x+2

13=3x

13/3 = x

BC is 4x+15

= 4(13/3)+15

= 52/3 + 45/3

= 97/3

CD is 7x+2

= 7(13/3)+2

= 91/3 + 6/3 = 97/3

Then, find 12y=90 and y=7.5.

AFB is a 90° angle (12(7.5)).

BCF is a 4y-1 = 4(7.5)-1 = 29 angle.

Because the diagonal cuts the angle in half, angle BCD is equal to 58. Angle ABC thus becomes 180-58 = 122.

Therefore the value  of  y  is 7.5 .

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The relative percentages of the column-wise frequencies are different, indicating that there is indeed an association between the variables.

A user-defined collection of related groups and items is referred to as a data association. It may include one or more groupings, as well as some, all, or neither of the items found inside those groups. It is helpful to initially identify various groups and components that you believe to be connected in some way before establishing Rules of Visibility.

Because of the differences in the relative percentages of the column-wise frequencies, there is a link between the variables. The animal mascot in the first column has 74% victories and 26% defeats. These percentages fluctuate greatly from one another. The other type of mascot, which similarly has a significant disparity between them, has 49% victories and 51% losses. The association between the variables is stronger the larger the difference.

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In the fractions given 2/3 + 7/3 * -9/4 and (4/5 - 2) * (3/4 - 2/3) the results of the expressions are -55/12 and -1/10 respectively

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.

In the first expression;

2/3 + 7/3 * -9/4

Applying PEDMAS

2/3 + 7/3 * -9/4 = -55/12

In the second expression;

(4/5 - 2) * (3/4 - 2/3) = - 1/10

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The equation of line h that passes through (2,6) and is parallel to a line passing through (-3, 4) and (1, 1) is 4y + 3x = 30

Slope is the ratio of the change in the y-coordinates to the change in the x-coordintes of any two given points.

It is a measure of the steepness of a line.

Slope may be positive or negative

slope of the line joining the the points (-3,4) and (1,1)

slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

[tex]x_{1}[/tex] = -3, [tex]x_{2}[/tex] = 1, [tex]y_{1}[/tex] = 4, [tex]y_{2}[/tex] = 1

slope = 1-4 / 1 - -3

slope = -3/4

since the two lines are parallel their slopes are equal.

equation of first line

y = mx + c

where y = 6, x = 2, m = -3/4

6 = -3/4(2) + c

6 = -3/2 + c

c = 6 + 3/2

c = 15/2

Equation, y = -3/4x + 15/2

multiply through by 4

2y = -3x +30

2y + 3x = 30

In conclusion the equation of the line passing through the given point is 2y + 3x = 30

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Answer:

The 5 consecutive odd integers are 11 , 13 , 15 , 17 , 19

Step-by-step explanation:

The Difference between any odd Integer and its consecutive Integer = 2

So let the 3rd Odd Integer be x

Then the 1st Odd Integer is x - 2

and the 2nd Odd Integer is x - 4

and the 4th Odd Integer is x + 2

and the 5th Odd Integer is x + 4

Since the Sum of the 1st three integers is 3 more than the sum of the last two

Then 1st + 2nd + 3rd = 4th +5th +3

Then (x) + (x - 2) + (x - 4) = (x + 2) + ( x + 4) +3

Then 3x - 6 = 2x + 9

subtract 2x from both sides

3x - 2x -6 = 9

x - 6 = 9

Add 6 for both sides

Then x = 9 + 6 = 15

So the 3rd odd Integer is 15

So the five consecutive odd integers are 11 , 13 , 15 , 17 , 19

Answer:

11 x 6

Step-by-step explanation:

The Scale factor of ΔADC to ΔCDB is 2  .

In the question ,

a right triangle ABC is given (the figure is shown below )

h is the length of the altitude , AD = 12 , DB = 3 ,

to find the scale factor , we first need to find the value of h ,

since triangles ADC is similar to triangle CDB ,

we have , CD / AD = DB / CD

on cross multiplication , we get

CD² = AD × DB

CD² = 12 × 3 = 36

CD = 6

For the scale factor we divide the length of the original triangle ADC with the length of the image triangle CDB .

we get

Scale factor = AD / CD

= 12/6

= 2

Therefore , The Scale factor of triangle ADC to triangle CDB is 2  .

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Answer:

Step-by-step explanation:

We are told that P(dark) = 5/12 and Nd = 25. Plugging these numbers in we get:

5/12 = 25 / (25 + Nw)

Solving this equation for Nw yields Nw = 35.

Therefore, there must be 35 milk chocolates in the bag.

The required value of n is [tex]\frac{1}{2}[/tex] .

What is an algebraic equation?

The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.

Given, [tex]\frac{3}{8} +n=\frac{7}{8}[/tex]

or, [tex]n=\frac{7}{8}- \frac{3}{8}[/tex]

or, [tex]n=\frac{7-3}{8}[/tex]

or, [tex]n=\frac{4}{8} = \frac{1}{2}[/tex]

Hence, the value of n is [tex]\frac{1}{2}[/tex] .

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The area of the rectangle can be expressed as [tex](\frac{6x}{5})^2[/tex].

What is the area of the rectangle?

If the length of the rectangle is 'l' and the breadth of the rectangle is 'b', then the area of the rectangle can be computed as

                   Area = l * b

Given data:

        The width of the rectangle is 3x/5 cm.

   And its length is four times its width so length = 4 * 3x/5

                                                                                 = 12x/5 cm.

Then the area will be

              Area = length * breadth

                       = 12x/5 * 3x/5

                       = 36x²/25

                       [tex]=(\frac{6x}{5})^2[/tex]

Hence, the area of the rectangle can be expressed as [tex](\frac{6x}{5})^2[/tex].

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Answer:

x = -4

Step-by-step explanation:

[tex] \frac{ \sqrt[3]{6x} }{ \sqrt[3]{2x + 5} } = 2[/tex]

[tex] {( \frac{ \sqrt[3]{6x} }{ \sqrt[3]{2x + 5} } )}^{3} = {2}^{3} [/tex]

[tex] \frac{6x}{2x + 5} = 8[/tex]

[tex]6x = 8(2x + 5)[/tex]

[tex]6x = 16x + 40[/tex]

[tex] - 10x = 40[/tex]

[tex]x = - 4[/tex]

[tex] \frac{ \sqrt[3]{6( - 4)} }{ \sqrt[3]{2( - 4) + 5} } = 2[/tex]

[tex] \frac{ \sqrt[3]{ - 24} }{ \sqrt[3]{ - 3} } = 2[/tex]

[tex] \sqrt[3]{ \frac{ - 24}{ - 3} } = 2[/tex]

[tex] \sqrt[3]{8} = 2[/tex]

The meaning of the c-value when T=65 is:  The number of times the cricket could be expected to chirp in one minute if it's 65 degrees F

The correct answer is an option (D)

In this question, we have been given a linear relationship.

For a certain type of cricket, this relationship can be expressed using the formula T=34+0.3c,

where T represents the temperature in degrees Fahrenheit and

c represents the number of times the cricket chirps in one minute.

We need to interpret the value of c when T = 65.

T = 34 + 0.3c

65 = 34 + 0.3c

c = 103.33

c = 103.33 represents the number of times the cricket could be expected to chirp in one minute if it's 65 degrees F

Therefore, the meaning of the c-value when T=65 is:  The number of times the cricket could be expected to chirp in one minute if it's 65 degrees F

The correct answer is an option (D)

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The equation of the line in slope - intercept form is [tex]y=\frac{-7}{4}x-5[/tex]


Explain what the slope-intercept form is?

Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This expression is sometimes referred to as y = mx + b form

Given: x = -4 , y = 2 and b = -5

y = mx + b

2 = m (-4) + (-5)

m = [tex]\frac{-7}{4}[/tex]
By putting the value of m we get equation of line
[tex]y=\frac{-7}{4}x-5[/tex]

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S= 0.0625t² is the composition of a function to represent the area of the puddle as a function of time.

The defined region represents the extent of the area on a plane or curved surface. The area of ​​a planar region refers to the area of ​​a shape or planar layer, while surface area refers to the area of ​​an open surface or boundary of a three-dimensional object. Area can be defined as the amount of material of a certain thickness required to model the mold, or the amount of paint required to cover the surface in a single layer. This is a two-dimensional equivalent of the length of a curve or the volume of a solid..

We obtain the data from the equation.

The radius is increased by 0.25 Cm for each t min.

Assume that the puddle's area is S.

We all know that.

Circle area =  πr²

So, S= πr²

S= π(0.25t)²

S= π0.0625t²

S= 0.0625πt²

Therefore, the area of the puddle is S= 0.0625πt²

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The opposite of |3| = - |3|

What is Modulus Function?

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

Given data ,

Let the number be x

x = |3|

Now , the opposite of the number x = -x

So ,

The opposite of |x| = -|x|

And ,

The opposite of |3| = - |3|

Hence , The opposite of |3| = - |3|

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The coordinates of the other 3​ vertice s are; Vertex 2 =  (0.5​, 2.5)

Vertex 3 =  (2, 1), Vertex 4 =(2, 2.5 )

Its the sum of length of the sides used to made the given figure.

Given that the Perimeter, P = 6 units

The Perimeter of a square = 4s ; s = side length

6 = 4s

s = 6/4

s = 1.5 units

If Vertex 1 =(0.5​,1​) and all vertexes are located in Quadrant​ I

Vertex 2 = (0.5​,1 + 1.5​) =(0.5​, 2.5)

Vertex 3 = (0.5 + 1.5 ​,1​) = (2, 1)

Vertex 4 = (2, 1 + 1.5) = (2, 2.5 )

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Answer:

9/64

Step-by-step explanation:

it is just 3/8 x 3/8

Answer:

Yes they are equal

Step-by-step explanation:

First we simplify the left side of the equation

7 x 3,012 = 21084

Next we simplify the right side of the equation. Using PEMDAS we know that we must add whatever is inside the parentheses first.

7 x (3,012)

We then multiply 7 x (3,012) = 21084

21084 = 21084

They are equal.