Let ​ f(x)=x2−3x−4​ .

What is the average rate of change from x = 7 to x = 10?

Answer:

60

Step-by-step explanation:

124−4(3−5(17−14)+2(9+5))

=124−4(3−(5)(3)+2(9+5))

=124−4(3−15+2(9+5))

=124−4(−12+2(9+5))

=124−4(−12+(2)(14))

=124−4(−12+28)

=124−(4)(16)

=124−64

=60

[tex]\bf \begin{array}{llll} term&value\\ \cline{1-2} a_5&36\\ a_6&36\left( \frac{1}{3} \right)\\ a_7&36\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\\ a_8&36\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\\ a_9&36\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\\ a_{10}&36\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right) \end{array}[/tex]

[tex]\bf a_{10}=36\left( \frac{1}{3} \right)^5\implies a_{10}=36\cdot \cfrac{1^5}{3^5}\implies a_{10}=\cfrac{36}{243}\implies a_{10}=\cfrac{4}{27}[/tex]

Answer:

410.5 yards cubed

Step-by-step explanation:

Volume of a cone is 1/3Bh

h is the height of the cone

B is the area of the base, which is a circle, so use πr^2 to find area of the circle

The radius is 7, so:

π7^2

π49(8)(1/3) = 410.5

Answer:

Step-by-step explanation:

Equation

Volume = (1/3) * pi * r^2 * h

Givens

pi = 3.14

r = 7 yd

h = 8 yd

Solution

V = (1/3) * 3.14 * 7^2 * 8

V = (1/3) * 3.14 * 49 * 8

V = (1/3) *  1231.5

V = 410.5 cubic yds.

Separate the kite into two triangles.

The base of the triangles would be 6 ( half the width is given as 3, so the full width would be 3 x 2 = 6).

The height of the bottom triangle is given as 10.

The area of a triangle is 1/2 x base x height.

Bottom triangle = 1/2 x 10 x 6 = 30 square units.

For the top triangle you need to find the height using the Pythagorean theorem.

Height = √(5^2 - 3^2) = √(25-9) = √16 = 4

Now the area of the top triangle is 1/2 x 4 x 6 = 12 square units.

Total area = Bottom + top = 30 + 12 = 42 square units.

Answer:

500000x4000000000000 = 2 x 10^18

Answer: [tex]2*10^{18}[/tex]  or  [tex]2,000,000,000,000,000,000[/tex]

Step-by-step explanation:

You can just make the multiplication indicated:

[tex]500,000*4,000,000,000,000=2,000,000,000,000,000,000[/tex]

You can rewrite the product in scientific notation form. This form is:

[tex]a*10^n[/tex]

Where "a" is a number between 1 and 10 but lesss than 10, and "n" is an integer.

In scientific notation, the decimal point must be after the first digit.

So, for the product [tex]2,000,000,000,000,000,000[/tex] the decimal point must be moved 18 places to the left.

Then, you get:

[tex]=2*10^{18}[/tex]

Answer:

0.2

Step-by-step explanation:

2 divided by 10 gives you the decimal.

Answer:

36 watts.

Step-by-step explanation:

Power is calculated from

W = E^2/R

E = 24 volts.

R = 16 ohms

W = 24^2 / 16

W = 576 / 16

W = 36 watts.

Answer:

The area of the biggest possible square that fit into the circle is 18 cm²

Step-by-step explanation:

* Lets talk about the square inscribed in a circle

- The square is fit into the circle if its four vertices lie on the

  circumference of the circle

- The diagonal of the square is the diameter of the circle

- The vertices of the square divide the circle into 4 equal arcs

* Look to the attached figure

- The square ABCD fit into the circle M

- A , B , C , D lie on the circumference of the circle M

- The four arcs AB , BC , CD , AD are equal in measure and length

- The diagonal of the square is DB

- The diameter of the circle M is DB

∵ The radius of the circle is 3 cm

∵ The diameter = twice the radius

∴ The diameter of the circle = 2 × 3 = 6 cm

∴ DB = 6 cm

- The rule of the area of the square = (diagonal)²/2

∵ The length of the diagonal is 6 cm

∴ The Area of the square = (6)²/2 = 36/2 = 18 cm²

* The area of the biggest possible square that fit into the circle is 18 cm²

Answer:

The area of the biggest possible square = 36 cm²

Step-by-step explanation:

From the figure attached with this answer shows that, the biggest possible square that would fit into a circle having a radius of 3 cm.

To find the area of square

Side of square  = 2 * radius of circle = 2 * 3 = 6 cm

Area of square = side * side = 6 * 6 = 36 cm²

Answer: [tex]x=-5[/tex]

Step-by-step explanation:

You need to find the value of the variable "x".

Solve for "x":

Subtract [tex]\frac{5}{6}x[/tex] from both sides of the equation:

[tex]\frac{2}{3}x-\frac{1}{2}-\frac{5}{6}x}=\frac{1}{3}+\frac{5}{6}x\\\\-\frac{1}{6}x-\frac{1}{2} =\frac{1}{3}[/tex]

Add  [tex]\frac{1}{2}[/tex]  to both sides of the equation:

[tex]-\frac{1}{6}x-\frac{1}{2}+\frac{1}{2} =\frac{1}{3}+\frac{1}{2}\\\\-\frac{1}{6}x=\frac{5}{6}[/tex]

Multiply both sides of the equation by -6:

[tex](-\frac{1}{6}x)(-6)=(\frac{5}{6})(-6)\\\\x=-5[/tex]

Answer:

I may not be completely sure but I am 85% confident the answer is B

For line A,

if we increase x by 1 unit then y increases by 4 units i.e. (1,3) and similarly another point becomes

(2,7).

For line B,

if we increase x by 1 uni then y also increases by 1 unit i.e ( 1,1) and similarly another points becomes (2,2),(3,3),(4,4), etc.

For line C,

if we increase x by 3 units then y increases by 1 units i.e.(3,1) and similarly another points becomes

(7,2) and so on.

In above lines, the value of x is exactly equal to that of y in line B.

therefore, line B has constant proportionality between x and y.

To find the line with a constant of proportionality of 111 between y and x, we calculate the slope for each line. Line A has a slope of 111, making it the correct answer.

To determine which line has a constant of proportionality of 111, we need to examine the slope of each line. The slope represents the ratio of the change in the y-values to the change in the x-values for any two points on the line. If the slope is the same for all points on the line, then it has a constant of proportionality. Let's calculate the slopes for lines A, B, and C:

Line A: Let's choose two points: (0, 0) and (1, 111). The slope is (111 - 0) / (1 - 0) = 111 / 1 = 111.

Line B: Let's choose two points: (0, 0) and (1, 1110). The slope is (1110 - 0) / (1 - 0) = 1110 / 1 = 1110.

Line C: Let's choose two points: (0, 0) and (1, 11100). The slope is (11100 - 0) / (1 - 0) = 11100 / 1 = 11100.

Therefore, the line with a constant of proportionality of 111 is Line A.

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Answer:

15

Step-by-step explanation:

if you have 2/5 lengths each time, if you divide that by 6 it gives 15.

Or if you go 2/5 to 4/5 to 6/5 until you have 30/5 because that is how long 6 feet is.

Answer:

The length of side AB is 5 units

Step-by-step explanation:

* Lets revise how to find the distance between two points

- If there are two points their coordinates are (x1 , y1) and (x2 , y2),

 then we can find the distance between them by this rule:

 d = √[(x2 - x1)² + (y2 - y1)²]

- Now lets solve the problem

∵ A = (4 , -5)

∵ B = (7 , -9)

- To find the length of AB use the rule of the distance above

- Let point A is (x1 , y1) and point B is (x2 , y2)

∵ x1 = 4 and x2 = 7

∵ y1 = -5 and y2 = -9

∴ AB = √[(7 - 4)² + (-9 - -5)²]

∴ AB = √[(3)² + (-4)²]

∴ AB = √[9 + 16] = √25 = 5

* The length of side AB is 5 units

You are basically just working this problem backwards; the way you would find the zeros of the function.

Therefore, to start, make each equal to zero and do the opposite (+ or -) to each side.

-2=x and 2/3=x

0=x+2 and 0=x-2/3

In a function like this, we are usually given an equation like (x+#)(x+#) then we would set these to zero. However, since we are working backwards we are trying to get it in that (x+#)(x+#) form.

(x+2)(x-2/3)

2+2/3 = 2 2/3 or 2.667

2 x 2/3 = 4/3 or 1.334

Your quadratic function is now x^2+2.67x+1.334

or x^2+2 2/3x+4/3.

Hope I helped!

Answer:

1/5 *3 = 15

You have to do Keep, Change, Flip. When you do that it becomes 1/5*3/1.

That equals 15.

Answer:

1 out of 5

Step-by-step explanation:

There are 5 answer choices total and you're supposed to choose 1 answer so 1 outta 5.

The probability that Peter will choose the correct answer by chance is 1/5 or 0.2 (or 20%).

If Peter has no knowledge about the correct answer to question number 4 on a multiple-choice test with 5 answer choices, the probability of him randomly selecting the correct answer is 1 out of 5.

This probability can be calculated by dividing the number of favorable outcomes (1, since there is only one correct answer) by the total number of possible outcomes (5, since there are 5 answer choices).

Mathematically, it can be represented as 1/5. Thus, the probability that Peter will choose the correct answer by chance is 1/5 or 0.2 (or 20%). This means that, on average, he would be expected to choose the correct answer 20% of the time if he were to guess without any knowledge or information.

To know more about probability:

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Answer:

(9,-6)

Step-by-step explanation:

4x+3y=18

3x+4y=3

Multiply the first equation by 3

3(4x+3y)=18*3

12x+9y = 54

Multiply the second equation by -4

-4(3x+4y)=3*-4

-12x -16y = -12

Add these two new equations together to eliminate x

12x+9y = 54

-12x -16y = -12

-----------------------

    -7y = 42

Divide each side by -7

-7y/-7 = 42/-7

y = -6

Now we can find x

3x+4y =3

3x +4(-6) = 3

3x -24 =3

Add 24 to each side

3x-24+24 = 3+24

3x = 27

3x/3 = 27/3

x = 9

(9,-6)

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}4x+3y=18&(1)\\3x+4y=3&(2)\end{array}\right\\\\(1)\\4x+3y=18\qquad\text{subtract}\ 4x\ \text{from both sides}\\3y=-4x+18\qquad\text{divide both sides by 3}\\y=-\dfrac{4}{3}x+6\qquad\text{substitute it in (2):}\\\\3x+4\left(-\dfrac{4}{3}x+6\right)=3\qquad\text{use the distributive property}\\\\3x+(4)\left(-\dfrac{4}{3}x\right)+(4)(6)=3\\\\3x-\dfrac{16}{3}x+24=3\qquad\text{multiply both sides by 3}\\\\9x-16x+72=9\qquad\text{subtract 72 from both sides}\\\\-7x=-63\qquad\text{divide both sides by (-7)}\\\\\boxed{x=9}[/tex]

[tex]\text{Put the value of x to (1):}\\\\y=-\dfrac{4}{3}(9)+6\\\\y=(-4)(3)+6\\\\y=-12+6\\\\\boxed{y=-6}[/tex]

11 • 55 = 55

The starfish had 55 arms all together.

Hope this helps!

Answer:

option D is correct.

Step-by-step explanation:

We need to find the value of

[tex]\sum_{n=1}^{6} 4(3)^{n-1}[/tex]

Here value of n starts from 1 and goes on till 6

And we need to add the values of all the terms by putting value of n from 1 to 6

This can be written as:

[tex]=4(3)^{1-1}+4(3)^{2-1}+4(3)^{3-1}+4(3)^{4-1}+4(3)^{5-1}+4(3)^{6-1} \\    Solving\\=4(3)^0+4(3)^1+4(3)^2+4(3)^3+4(3)^4+4(3)^5\\=4(1)+4(3)+4(9)+4(27)+4(81)+4(243)\\=4+12+36+108+324+972\\=1456[/tex]

So, option D is correct.

Answer:

1456

Step-by-step explanation:

This is the sum of a geometric sequence

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

4[tex](3)^{n-1}[/tex] ← is in this form

with a = 4 and r = 3

The sum to n terms of a geometric sequence is

[tex]S_{n}[/tex] = [tex]\frac{a(r^n-1)}{r-1}[/tex], hence

[tex]S_{6}[/tex] = [tex]\frac{4(3^6-1)}{3-1}[/tex] = [tex]\frac{4(729-1)}{2}[/tex] = 2 × 728 = 1456

Answer:

-69.19x + 38.2

Step-by-step explanation:

–9.2(8x – 4) + 0.7(2 + 6.3x)

= -73.6x + 36.8 + 1.4 + 4.41x

= -69.19x + 38.2

Answer:

53:2 Im sure.

Ratio is a comparison of two quantities. Online Simplifying ratios calculator is a ratio simplifier that simplify ratios in to its simplest form. For that ones should know the greatest common factor of both numerator and denominator. And then divide these two by the common factor. By using ratio in simplest form calculator one can simplify ratio from the high value to lower value in an easy way.

Answer:

Change values to whole numbers.

Convert any mixed numbers to fractions.

Convert 3 1/8

3 1/8 = 25/8

We now have:

5 : 3 1/8 = 5 : 25/8

Convert the whole number 5 to a fraction with 1 in the denominator.

We then have:

5 : 3 1/8 = 5/1 : 25/8

Convert fractions to integers by eliminating the denominators.

Our two fractions have unlike denominators so we find the Least Common Denominator and rewrite our fractions as necessary with the common denominator

LCD(5/1, 25/8) = 8

We now have:

5 : 3 1/8 = 40/8 : 25/8

Our two fractions now have like denominators so we can multiply both by 8 to eliminate the denominators.

We then have:

5 : 3 1/8 = 40 : 25

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 40 and 25 is 5

Divide both terms by the GCF, 5:

40 ÷ 5 = 8

25 ÷ 5 = 5

The ratio 40 : 25 can be reduced to lowest terms by dividing both terms by the GCF = 5 :

40 : 25 = 8 : 5

Therefore:

5 : 3 1/8 = 8 : 5

Step-by-step explanation:

Answer: 42.5

Step-by-step explanation:

The answer is 42.5

Answer: 42.5 cm

Step-by-step explanation: Its really simple. You multiply 8.5 cm and 5 cm to get 42.5 cm.

First you must distribute the 3 to the numbers in the parentheses

(3*m) + (3 * -5) + m

3m + (-15) + m

3m - 15 + m

Combine like terms (3m and m)

4m - 15

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

3m - 15 + m

Step-by-step explanation:

Multiply (m - 5) by 3.

m * 3 = 3m

-5 * 3 = -15

This doesn't apply with +m.

So this leaves it as 3m - 15 + m.

Hope this helps! :)

Answer:

C=175-35t

Step-by-step explanation:

Each week - $35

After the 1st week - has $140 left

So, at the beginning of the first week he has $140+$35=$175 on the card.

Now,

Initial amount of monay = $175

Spent each week= $35

Number of weeks = t

Spent in t weeks =$35t

The cash balance C on his card after t weeks =$175-$35t (left)

So, the equation is

[tex]C=175-35t[/tex]

The equation that represents the cash balance on Rodolpho's prepaid gas card after t weeks is Balance = 175 - 35t, where t is the number of weeks.

The equation that represents the cash balance on Rodolpho's prepaid gas card after t weeks can be derived from the information given. We know that every week, he spends $35 on gas, which decreases the balance on his card by that amount. If he starts with $140 after the first week, we can establish the initial balance (before any purchase) as $175. Thus, the formula to calculate the remaining balance after t weeks would be:

Balance = Initial balance - (Weekly spending × Number of weeks)

Balance = 175 - (35 × t)

So, the equation that represents the balance on the card after t weeks is:

Balance = 175 - 35t

Answer:

The paths between the three cities DO NOT form a right triangle.

Step-by-step explanation:

For a right triangle to be formed, the Pythagorean Theorem (a2+b2=c2, with a and b being the legs that form the right angle, and c being the hypotenuse) needs to apply correctly to the distances. In a right triangle, the longest distance is always the hypotenuse, or the slanted side that doesn't touch the right angle. The question is to suggest that the hypotenuse is 400 km. long and the legs being 200 km. and 300 km. long respectively. So, to solve this, all we have to do is plug these distances into the Pythagorean Theorem and see if it comes out correct. When plugged in, the equation should be 2002+3002=4002. Then, you solve! It should go like this: 2002+3002=4002, then 40,000+90,000=160000, then add the numbers on the left side to get 130,000=160,000, but, hang on a second. 130,000 does not equal 160,000. This means that the Pythagorean Theorem does not work with the proposed right triangle, which means that the paths between the three cities do NOT form a right triangle!

  Paths between the three cities do not form a right triangle.

"In a right angle triangle, square of the hypotenuse is equal to the sum of squares of the other two sides"

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

Given in the question,

If ABC is a right triangle, sides of the triangle will follow Pythagoras theorem.

AC² = AB² + BC²  [By Pythagoras theorem]

(400)² = (200)² + (300)²

160000 = 40000 + 90000

160000 = 130000

But 160000 ≠ 130000.

Therefore, ΔABC is not a right angle triangle.

Learn more about the use of Pythagoras theorem here,

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Answer:

Add 8 to both sides of the equation

Step-by-step explanation:

We have been given the quadratic equation;

x^2 - 14x +41 = 0

we are required to complete the square in order to express it in the form;

(x - p)^2 = q

In order to do this we need to find a constant c, such that;

[tex]c=(\frac{b}{2})^{2}[/tex]

where b is the coefficient of x in the quadratic equation. In our case b = -14. Therefore,

[tex]c=(\frac{-14}{2})^{2}=49[/tex]

Therefore, for us to complete the square, the left hand side of the quadratic equation should be;

x^2 - 14x +49

Since we already have 41, we can simply add 8 to make it 49. Thus, the first correct step to write the above equation in the form (x - p)2 = 9, where p and q are integers is to Add 8 to both sides of the equation

The distribution is very simple. Using FOIL.

It states that [tex](a+b)(c+d)=ac+ad+bc+bd[/tex].

Also note that when multiplying expressions we multiply variables and values differently. If we have variables like [tex]x[/tex] their exponents will add. If we have values like 3 we multiply them normally.

For example your practise 3.

[tex](x+3)(2x^2+4)=2x^2\cdot x+4x+3\cdot2x^2+3\cdot4 \\

\underline{2x^3+4x+6x^2+12}

[/tex]

Now just order the expressions from bigger exponent to smaller and than values. (Usual notation although no need).

And solution is:

[tex]\boxed{2x^3+6x^2+4x+12}[/tex]

Hope this helps.

r3t40

Answer:

See below

Step-by-step explanation:

[tex]a\cdot(b + c) = a\cdot b + a\cdot c[/tex]

3) Practice: Organizing information

[tex]\begin{array}{lll}\qquad \textbf{Steps} & \textbf{Problem: }(x + 3)(2x^{2} + 4) & \\\textbf{1. List variables} & a = x + 3 & \\ & b = 2x^{2} & \\ & c = 4 &\\\\\textbf{2. Distribute} & (x + 3)(2x^{2} + 4)& = (x + 3)(2x^{2}) + (x + 3)(4)\\\\\textbf{3. Redistribute} & (x + 3)(2x^{2})& (x + 3)(4)\\& a = 2x^{2} & a = 4\\& b = x & b = x\\& c = 3 & c = 3\\& 2x^{3} + 6x^{2} & 4x + 12\\\textbf{4. Combine}& & \\\qquad\textbf{terms} & 2x^{3} + 6x^{2}+ 4x + 12 & \\\end{array}[/tex]

4. Practice: Summarizing

[tex]\text{You can use the FOIL method to multiply two }\underline{\text{binomials}}.\\\text{The letters in FOIL stand for }\underline{\text{First, Outer, Inner, Last}}.\\\text{The FOIL method helps you to remember how to multiply each term in one }\\\underline{\text{binomial}} \text{ by each term in the other }\underline{\text{binomial}}.[/tex]

When r varies inversely with x and r = -2 when x = 6, the value of r when x = -3 is 4.

r varies inversely with x, meaning that as one increases, the other decreases. Given r = -2 when x = 6, we can find the constant of variation by using the formula for inverse variation: r₁ * x₁ = r₂ * x₂. Plugging in the values, we have (-2) * 6 = r₂ * -3, which simplifies to r₂ = 4. Therefore, when x = -3, the value of r is 4. This demonstrates the relationship between variables in an inversely proportional scenario, elucidating the concept of variation in algebraic contexts.

Answer:

Step-by-step explanation:

6+2 = 8 your welcome or 4 x 2 = 8 :)

I have no idea about the part A, but part b, all you have to do is get all the numbers of the fans, and put them in least to greatest. Then you count how fans are from 0-9, then you count how much fans are from 10 - 19, and so on. Im sorry that i couldn't answer it completely but i hope this helps.

Answer:

Step-by-step explanation:

First we will arrange the ages of fans of the basketball game in the increasing order.

9, 11, 14, 14, 16, 25, 25, 27, 28 30, 33, 35, 35, 37, 38, 39, 42, 46, 47, 60

Part A. Now we will make stem-and-leaf plot

0  |  9

1   |  1, 4, 4, 6

2  |  5, 5, 7, 8

3  |  0, 3, 5, 5, 7, 8, 9

4  |  2, 6, 7

5  |

6  |  0

Part B.

Frequency table

Age           Number of Fans

0 - 9                  1

10 - 19               4

20 - 29             4

30 - 39             7

40 - 49             3

50 - 59             0

60 - 69             1