6 children were jumping rope.
5 children joined them.
2 children left because the line was too long.
How many children were jumping rope then

We conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.

In an arithmetic sequence, the difference between any two consecutive terms is a constant.

Here we know that:

[tex]a_1 = 3/5\\a_8 = 1/4[/tex]

There are 7 times the common difference between these two values, so if d is the common difference:

[tex]a_1 + 7*d = a_8\\\\3/5 + 7*d = 1/4\\\\7*d = 1/4 - 3/5 = (5 - 12)/20 = -7/20\\\\d = -1/20[/tex]

Then the sum of the first 8 terms is given by:

[tex]3/5 + (3/5 - 1/20) + (3/5 - 2/20) + ... + (3/5 - 7/20)\\\\8*(3/5) - (1/20)*(1 + 2 + 3+ 4 + 5 + 6 + 7) = 3.4 = 34/10 = 17/5[/tex]

So we conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.

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Answer:

12 is 50% of 24

7 is 20% of 35

9 is 10% of 90

20/60 is 33.33%

Answer:

[tex]4*6^\frac{5}{2}[/tex]

Step-by-step explanation:

Use [tex]\sqrt[n]{a^x}=a^{\frac{x}{n} }[/tex] to rewrite [tex]\sqrt{6^5}[/tex] as [tex]6^\frac{5}{2}[/tex].

[tex]4*6^\frac{5}{2}[/tex]

Answer:

18

Step-by-step explanation:

my answer is correct,try to read the question,

if the length of larger triangle is 6 times so it means 6 ×5= 30 and you will times 3 to 6=18

so that's why it has lenght of 30

because the. larger triangle is 6 times bigger than smaller rectangle

100%✓sure answer

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The domain is  All real numbers except odd integer multiples of 2π/3 , Option B is the correct answer.

A function is defined as a mathematical statement that identifies the relation between a dependent and an independent variable.

A function has a defined range and domain.

In the given function

y = (5/3)tan(3x/4)

Domain is the all the value at which the function is defined .

Tan x is defined for every value except at

x = (2n+1)π/2

The domain of the function y = (5/3)tan(3x/4) is

3x/4 = (2n+1)π/2

x = (2n+1)2π/3

Therefore the domain is  All real numbers except odd integer multiples of 2π/3 , Option B is the correct answer.

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2x - 3y = 7 can be rewritten as y = 2/3x - 7/3, therefore, the equation that is a linear equation is: C. 2x - 3y = 7.

A linear equation is expressed in the slope-intercept form as y = mx + b.

2x - 3y = 7, rewritten in slope-intercept form would be:

-3y = -2x + 7

y = -2x/-3 + 7/-3

y = 2/3x - 7/3

m = 2/3 and b = -7/3

Therefore, the equation that is a linear equation is: C. 2x - 3y = 7.

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Answer:

(-21, 54.5)

Step-by-step explanation:

Hello there!

We have two methods to solve this problem.

We will limit ourself to Substitution method.

3x – 2y = -4.................... 1.

4x + 2y = 25................... 2.

First lets manipulate eq.2 in terms of y.

4x + 2y = 25

2y = 25 - 4x

y = 25/2 - 2x .............. eq.3

Substitute eq.3 into eq.1

3x – 2(25/2 -2x) = -4

Solve for x.

Opening the brackets

3x - 25 - 4x = -4

-x = 21

x = -21

Substitute x into equation 3

y = 25/2 - 2x

=> y = 25/2 - 2(-21)

= 54.5

In terms of x and y; (x,y)

= (-21, 54.5)

I hope this helps.

Have a nice studies.

Answer:

length: 9 units width: 2 units

Step-by-step explanation:

The formula to find the area of a rectangle is length*width (LW)

x+3 is the length and x-4 is the width; together they multiply up to 18

(x+3)(x-4) = 18

x^2 - 4x + 3x - 12 = 18 (multiply it out using FOIL)

x^2 - x - 12 = 18 (combine like terms on the left side)

x^2 - x -30 = 0 (subtract 18 from both sides so that the right side is 0)

Think what two numbers multiply up -30 and add up to -1 (5 and -6)

(x+5)(x-6) = 0 (factor it)

x+5 = 0 and x-6 = 0 (solve using zero-product property)

x = -5 and x = 6 (solve)

x = 6 (only this one works since you cannot have a negative side length)

(6+3)(6-4) = 18 ? (plug in to find side lengths and check)

9 * 2 = 18 (Correct!)

Answer:

  length: 9 ft

  width: 2 ft

Step-by-step explanation:

This can be worked using a quadratic equation, or it can be worked by considering factors of the area value.

__

The difference in length between the long side (x+3) and the short side (x-4) is ...

  (x +3) -(x -4) = 3+4 = 7 . . . . feet

The area formula is ...

  A = LW

The given area is 18 square feet, so we want to find numbers that multiply to give 18 and that differ by 7 in their values. Here are the integer factors of 18:

  18 = 1×18 = 2×9 = 3×6

Of these factor pairs, the values 2 and 9 differ by 7.

The garden is 9 feet long and 2 feet wide.

_____

Additional comment

We can check to see if these numbers are consistent with the given expressions:

  x+3 = 9  ⇒  x = 6

  x -4 = 6 -4 = 2 . . . . the other dimension we found

__

If you solve this using a quadratic equation, you will find that dimensions -2 ft and -9 ft also pop out. That is x +3 = -2, or x = -5 is also a solution to the quadratic. Of course, that is an extraneous solution, which we avoid by considering only positive factors of 18.

The quadratic equation we're referring to is A=18 ⇒ (x+3)(x-4) = 18.

[tex]~~~~~~~4x^2-12x+9=0\\\\\implies (2x)^2-2 \cdot 2x \cdot 3+3^2 = 0\\\\\implies (2x-3)^2 = 0\\\\\implies 2x -3 = 0\\\\\implies x =\dfrac 32[/tex]

Nani wait what I don't know

The formula for calculating the volume of a cube is expressed as V = L³. The volume of the cube is 1/27 cubic meters

The formula for calculating the volume of a cube is expressed as:

V = L³

where:

L = 1/3cm

Substitute

V = (1/3)³
V = 1/3³

V = 1/27 cubic meters

Hence the volume of the cube is 1/27 cubic meters

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The figure is the combination of the rectangle and square. Then the area of the figure will be 13 square units.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Then the area of the geometry will be

The figure is the combination of the rectangle and square.

Then we have

Area = 3 x 3 + 4 x 1

Area = 9 + 4

Area = 13 square units

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The area of the park is 1640 square meters.

A quadrilateral is a plane shape with four sides and four angles.

The above figure is made up of two quadrilateral; a square and a trapezium.

Analysis:

Area of park = area of square + area of trapezium

Area of park = 1/2(a + b)h + s x s

where a = length of smaller parallel side of the trapezium = 40m

           b = length of the larger parallel side = 48m

           h = height of trapezium = 35m

           s = length of side of square = 10m

Area of park = 1/2(40 + 48)x35 + 10 x 10 = 1640 square meters

In conclusion, the area of the park is 1640 square meters

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The attached number line represents points of the lowest recorded temperatures

The table is given as:

City                 Lowest Recorded Temperature

Morgantown       7°F below 0

Charlotte            6°F above 0

Huntsville           4°F above 0

Bluefield            8°F below 0

To rewrite the table, we use the following representations:

So, we have:

City                 Lowest Recorded Temperature

Morgantown       -7

Charlotte            6

Huntsville           4

Bluefield            -8

See attachment for the number line that represents the above points

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The equation represented by the graph will be y = eˣ. Then the correct option is A.

The missing graph is given below.

Functions are found all across mathematics and are required for the creation of complex relationships.

The graph is given below.

The exponential graph is always positive and the graph is also positive of the Real value of x.

The equation represented by the graph will be y = eˣ.

Then the correct option is A.

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Step-by-step explanation:

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The measure of the remote exterior angle is 128°.

From the information given, x = y + z. Therefore, .(198 - 5n) = (5n + 37( + (n + 7)

198 - 5n = 6n + 44

Collect like terms

154 = 6n + 5n

154 = 11n

n = 154/11

n = 14

The value of angle x will be:

= 198 - 5n

= 198 - 5(14)

= 198 - 70

= 128

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Step-by-step explanation:

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Answer:

  (b)  -7.275i -4.244j

Step-by-step explanation:

The projection of vector u onto vector v is the product of the unit vector v, the magnitude of vector u, and the cosine of the angle between them.

__

The dot product gives the product of the magnitudes of the two vectors and the cosine of the angle between them. To find the projection, we must divide the dot product by the magnitude of v and multiply by the unit vector in the direction of v.

  [tex]proj(u,v)=(\vec{u}\cdot\vec{v})\cdot\dfrac{\vec{v}}{|\vec{v}|^2}=\dfrac{((-8)(-12)+(-3)(-7))(-12\vec{i}-7\vec{j})}{(-12)^2+(-7)^2}\\\\=\dfrac{-(96+21)(12\vec{i}+7\vec{j})}{144+49}=-\dfrac{117}{193}(12\vec{i}+7\vec{j})\approx\boxed{-7.275\vec{i}-4.244\vec{j}}[/tex]

An x-intercept of the continuous function in the table is (-1, 0)

The x-intercept of a line is the point where the line crossed the x-axis or the  point where the value of y is zero.

From the table, the x-intercept are all the point where the value of f(x) is zero. Hence the Which is an x-intercept of the continuous function in the table is (-1, 0)

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Option third "words per minute, because the independent quantity is the minutes" is the correct choice.

It is defined as the change in values of a dependent variable with respect to the independent variables.

We have a statement:

Which of the following is the most appropriate unit to describe the rate at which a person reads?

As we know the rate of change is the ratio of change in y to change in x.

y is the dependent quantity and x is the independent quantity.

Rate of change = change in y/change in x

Rate at which a person reads = words/minute

Word is the dependent quantity and minute is the independent quantity.

Thus, option third "words per minute, because the independent quantity is the minutes" is the correct choice.

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The equation for the sinusoidal function described is given as follows:

[tex]y = 4\cos{\left(\frac{1}{2}x\right)} + 2[/tex]

We want a function with a y-intercept at it's maximum value, hence we use the cosine equation, given by:

[tex]y = A\cos{\left(\frac{2\pi}{B}x\right)} + C[/tex]

In which:

The amplitude is of 8, hence 2A = 8 -> A = 4. This would represent a function between -4 and 4, but we want between -2 and 6, hence the vertical shift is of C = 2.

As for the period, we have that:

[tex]B = 4\pi[/tex]

Then, the equation is given by:

[tex]y = 4\cos{\left(\frac{1}{2}x\right)} + 2[/tex]

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Answer:

Step-by-step explanation:

Let the number of people were surveyed is x.

We have 60% of x is 48 people.

Set this as equation and solve:

Correct choice is C.

Answer:

C.  80

Step-by-step explanation:

Given:

Let x be the total number of people surveyed.

Set up a ratio of people to percentage and solve for x:

[tex]\implies \sf 48 : 60 = x : 100[/tex]

[tex]\implies \sf \dfrac{48}{60}=\dfrac{x}{100}[/tex]

[tex]\implies \sf x=100 \cdot \dfrac{48}{60}[/tex]

[tex]\implies \sf x=\dfrac{4800}{60}[/tex]

[tex]\implies \sf x=\dfrac{480}{6}[/tex]

[tex]\implies \sf x=80[/tex]

Therefore, the total number of people who were surveyed was 80.

Answer:

False

Step-by-step explanation:

9(k-2)=-6 and k=1

9(1-2)=-6

9(-1)=-6

-9=-6

No, -9 doesn't equal -6.

So this system of equations is false.

Hope this helped! :)

Answer:
10

Step-by-step explanation:

-3x+7x-8=34+9x-2

(Combine like terms)

4x-8=32

(Add 8 to each side)

4x=40

(Divide by 4)

X=10

Step-by-step explanation:

Use the product rule for finding the derivative of a product of functions. Use the quotient rule for finding the derivative of a quotient of functions.