Points scored: 9, 4, 13, 11, 12, 5

What is the median of the points scored?

The equation of the line that is perpendicular to y = 4x + 5, in slope-intercept form is: y = -1/4x - 2.

Lines that are perpendicular to each other have slope that are negative reciprocal to each other.

Slope of y = 4x + 5 is 4.

Negative reciprocal of 4 is -1/4.

Substitute m = -1/4 and (a, b) = (8, -4) into y - b = m(x - a):

y - (-4) = -1/4(x - 8)

y + 4 = -1/4x + 2

y = -1/4x + 2 - 4

y = -1/4x - 2

Equation of the perpendicular line is: y = -1/4x - 2.

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We're given a point that the line intersects and its slope.

Let's use Point-slope:-

[tex]\boxed{y-y1=m(x-x1)}[/tex]

y1 = -5

m=-5

x1=-1

[tex]\boxed{y-(-5)=-5(x-(-1)}[/tex]

[tex]\boxed{y+5=-5(x+1)}[/tex]

Convert to slope-intercept:-

[tex]\boxed{y+5=-5x-5}[/tex]

[tex]\boxed{y=-5x-5-5}[/tex]

Finally,

[tex]\bigstar{\boxed{\pmb{y=-5x-10}}[/tex]

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Answer:

x= -1/3

x = -7

Step-by-step explanation:

9x^2 +66x+21 = 0​

a=9 b=66 c=21

quadratic formula

x=(-b +/- square root of (b^2 – 4ac))/(2a)

x = (-66 +/- square root of (66^2 -4*9*21))/(2*9)

x = (-66 +/- square root of (4356 -756))/(18)

x = (-66 +/- square root of (3600))/(18)

x = (-66 +/- 60)/18

split the fraction

(-66 +/- 60)/18 = -6/18 and -126/18 because of the +/-

x = -6/18  x = -126/18

x = -1/3   x = -7

[tex]~~~~~~9x^2+66x+21 = 0\\\\\implies 3(3x^2+22x+7)=0\\\\\implies 3x^2+22x+7=0\\\\\implies 3x^2 +21x +x +7=0\\\\\implies 3x(x+7) +(x+7)=0\\\\\implies (x+7)(3x+1)=0\\\\\implies x = -7~~ \text{or}~~ x =-\dfrac 13[/tex]

The following solution is arrived at by using the formula for the area of a regular octagon in relation to its Apotem which in this case is 18. Hence the area of the Octagon given is 1,446.

An apothem is defined as a line from the center of a regular polygon at right angles to any of its sides.

The calculation for this shape using only it's apothem has some curved bends. In order to derive the area, we have to divide the octagon into triangles.

When we find the area of the triangles we can then multiply by the total number to get the area of the Octagon.

Hence we can say that the area of the Octagon (A) = (1/2b*h)n

Where b = base

           h = height

           n = number of triangles.

Recall that the total angle in a circle is 360°, hence given that all the triangles are equal, we must divide 360° by  8 triangles to get the angle in the vertex of each triangle.

Thus, 360°/8 = 45°

So we have The angle of our triangle which is opposite the base.

Recall that the triangle is split in two so that each of the triangles are right-angled triangle,

Hence, the angle opposite the base for each right angle triangle is given as:

45°/2 = 22.5°

So to get the length of the opposite side (x), we use the law of tangents:

Which means:

x = 18 Tan 22.5°

= 18 * 0.55785173935

≈ 10.04

So if x is ≈ 10.04, then area of that triangle is

= 1/2 * 10.04 * 18 (that is 1/2bh)

= 90.3792

From the above, we can state that the Area of the triangle with the Apothem is

= 90.3792 * 2

= 180.74

Recall our formula for finding the area of the octagon:

A = (1/2bh)n

A = (108.74) *8

A = 1,445.95

≈ 1,446

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Answer:

C. 11

Step-by-step explanation:

Calculating range is subtracting the highest data value(11) from the lowest data value(0)

11 - 0 = 11

Answer:

₹9900

Explanation:

Total sold : (41 + 59) = 100 watermelons

Amount earned : 100 * 99 = ₹9900

#Thursday

Money earned=41(99)

#Friday

Money earned

Total:-

5841+4059=$9900

Answer:

A) x = 2.5

B) x = 7/3

Step-by-step explanation:

A) 4x - 1/2 = x + 7

4x - x = 7 + 1/2

3x = 7.5

x = 7.5/3

x = 2.5

B) 3x + 2 = 2x + 13/3

x +2 = 13/3

x = 13/3 - 6/3

x = 7/3

I hope this helps!

The equivalent expression of 3 to the power of 4. is 9 to the power of 2.

The expression is given as:

3 to the power of 4.

Mathematically the expression is

[tex]3^4[/tex]

Express 4 as 2 * 2

[tex]3^{2*2}[/tex]

Evaluate 3^2

[tex]9^2[/tex]

This means that:

9 to the power of 2.

Hence, the equivalent expression of 3 to the power of 4. is 9 to the power of 2.

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The volume of a sphere with a radius of 4 feet, to the nearest hundredth is: 268.08 cubic feet.

Volume of a sphere, where r is the radius of the sphere, is determined using the formula, V = 4/3 × π × r³.

Given the radius of the sphere is 4 feet

Volume of the sphere = 4/3 × π × r³ = 4/3 × 3.14 × 4³

Volume of the sphere = 268.08 ft³

Therefore, the volume of a sphere with a radius of 4 feet, to the nearest hundredth is: 268.08 cubic feet.

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[tex]3x^2y+6xy-9xy^2\\\\=3xy(x+2-3y)[/tex]

Answer:

I think one is 5 and another is 6 because 5+6=11

Answer:

a=5

a=6

add the exponents and keep the base the same

Answer:

4 1/4 cups were served

Step-by-step explanation:

Just multiply 5 2/3 cups by 3/4:  

17      3

---- * ---- = 4 1/4 cups were served.

 3      4

An equation shows the amount of juice that Jose served is x= 3/4 × 17/3.

The product of two fractions is the product of the numerators and the product of the denominators.

Product of two fractions = Product of their numerators / Product of their denominators.

Given that, Jose made [tex]5\frac{2}{3}[/tex] cups of juice. He served 3/4 of it at dinner.

Here, [tex]5\frac{2}{3}[/tex] cups can be written as 17/3

Let the amount of juice that Jose served be x

Now, x= 3/4 × 17/3

x= 17/4

x= [tex]4\frac{1}{4}[/tex] cups

Therefore, an equation shows the amount of juice that Jose served is x= 3/4 × 17/3.

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Answer: about 0.0202161

Step-by-step explanation:

This is a transcendental equation, so graph the two equations and find the x coordinate where they intersect.

Answer:

16

Step-by-step explanation:

2 pounds = 32 ounces

32 ounces / 2 ounces = 16 ounces

Answer:

x+3y=15

idrk how to explain but thats the answer

Answer:

131 here is the answer and your welcome

Answer:

  19

Step-by-step explanation:

The triangle inequality tells you the possible values of x are ...

  24 -10 < x < 24 +10

  14 < x < 34

There are 19 integer values of x in this range.

Answer:

y = 3x - 5

Step-by-step explanation:

To find the equation of the line, you can use y = m x + c.

Here,

m ⇒ slope

c ⇒ y-intercept

Given that,

slope = 3

y-intercept = -5

So, to find the equation of the line you have to simply replace m and c in the formula, (y = m x + c )with the given slope and y-intercept.

Let us solve it now.

y = m x + c

y = 3x - 5

Answer:

y = 3x - 5

Step-by-step explanation:

Slope-intercept form of an equation

Given that m = 3 and b = -5

[tex]5 {}^{ \frac{1}{8} } \times 5 {}^{ \frac{3}{8} } [/tex]

[tex] = 5 {}^{ \frac{1 + 3}{8} } = 5 {}^{ \frac{4}{8} } = 5 {}^{ \frac{1}{2} } = \sqrt{5} [/tex]

The equation that represents the amount saved by Alyssa after tt weeks is AA = 100 + $7tt

The equation that represents the amount saved by Colton after tt weeks is CC = $55 + $10tt

The amount they would have when they have same amount of money is $205.

The total amount saved: inital amount + (amount saved per week x total number of weeks

AA = 100 + $7tt

CC = $55 + $10tt

$55 + $10tt = 100 + $7tt

Combine similar terms and solve for tt

100 - 55 = 10tt - 7tt

45 = 3tt

tt = 15 weeks

100 + $7(15) = $205

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The answers are presented below:

The quadratic function can be represented by a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

The vertex of an up-down facing parabola of the form ax²+bx+c is [tex]x_v=\frac{-b}{2a}[/tex]  . Knowing the x-coordinate of vertex, you can find the y-coordinate of vertex. When a vertical line passes through the vertex of the parabola, it  is called the axis of symmetry.

The y-intercept is the point where the function crosses the y-axis. And, the x-intercept is the point where the function crosses the x-axis, in other words, when y=0.

First, you should convert the given equation to Standard form.

f(x) = -(c+7)² + 4

f(x)= - (c²+14c+49)+4

f(x)= -c²-14c-49+4

f(x)= -c²-14c-49+4

f(x)= -c²-14c-45

After that, you should check each option of the question.

Correct because present a degree 2 -- f(x)= -c²-14c-45

Incorrect because it is a quadratic function and this function is represented by a parabola.

The coefficients are: a=-1, b=-14, c=-45. Therefore,

[tex]c_v=\frac{-b}{2a}=-\frac{-14}{2*(-1)} =-\frac{-14}{-2}=-(7)=-7[/tex]

Incorrect because x-coordinate of vertex is -7

Correct because  [tex]c_v=\frac{-b}{2a}=-\frac{-14}{2*(-1)} =-\frac{-14}{-2}=-(7)=-7[/tex]

You can find the y-intercept using c=0, then f(x)= -c²-14c-45 will be:

f(x)=-45.

Incorrect because the y-intercept is (0,-45).

The coefficient a of a quadratic function is negative, thus the function has a point maximum. A relative maximum point is defined as the point where the function changes your direction. In other words, the values of the function increase before the relative maximum and the values decrease after the relative maximum.

Correct, see the attached image.

It is possible to find the number of roots or solutions from discriminant.

For quadratic equation the discriminant is determined by D=b²-4ac, where: a, b and c are coefficients.

If D > 0 - the function will have two real solutions;

If D = 0 - the function will have one real solution;

If D < 0 - the function will have imaginary solutions;

For given equation, the coefficients are: a=-1, b=-14, c=-45. Thus, D=(-14)²-4*(-1)*(-45)

D=196-180=16

D=16 thus D > 0

Incorrect because the D>0.

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The expression indicated that the values of a will be between 4.01 and 4.99 and b will be between 2.01 and 3.99.

From the first expression, 4 < a < 5. This means that 4 is less than a and a is less than 5. This means the values of a will be between 4.01 and 4.99.

Also, 2 < b < 4. This means that 2 is less than b and b is less than 4. Therefore, the values of b will be between 2.01 and 3.99.

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Answer:

The answer to a is 4.5, and the answer to b is 3.

Step-by-step explanation:

The averages are found as shown:

4+5=9

9/2=4.5

2+4=6

6/2=3

To find averages, first add all of the certain amount of numbers shown, then divide it all by the same amount of numbers there are.

Example:

5+7+9=21

21/3=7

Answer:

97 1/3 or 97.3333

Step-by-step explanation:

multiply 2 2/3 by 36 1/2

:)

Answer:

1320

Step-by-step explanation:

The sample ad 600 chips. They wanted to test 36000 chips. 600*60=36000

If 22 out of 600 chips were defective, and 600*60=36000

Then 1320 chips were defective out of the 36000 because 22*60=1320.

Answer:

well jus subtract

Step-by-step explanation\

think about it

Answer:

The total amount of students in the primary school is 1,980.

Step-by-step explanation:

130, 210, 290, ......

210 - 130 = 80

The difference between each grade is 80 students.

(g = grade)

g1 = 130, g2 = 210, g3 = 290, g4 = 370, g5 = 450, g6 = 530

130+210+290+370+450+530 = 1980

Using proportions, it is found that the correct option regarding how much faster she is in the first 5 minutes compared to the last 5 is given by:

B. 0.3 mile/minute faster

A proportion is a fraction of a total amount

Researching the problem on the internet, it is found that on the first 5 minutes, she bikes 2 miles, hence the ratio is:

r1 = 2/5 = 0.4 miles/minute.

On the last 5 minutes, she bikes 0.5 miles, hence:

r2 = 0.5/5 = 0.1 miles/minute.

The difference is given by:

D = 0.4 - 0.1 = 0.3 miles/minute.

Which means that option B is correct.

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Answer:

30% or 4/12

Step-by-step explanation:

Answer:

33.333...% (2/3)

Step-by-step explanation:

the number 1 makes up one third of the numbers on the spinner.

After solving the equation (work shown in image) your answer would be x > -2. I drew an image of how the number line should look at least similar to, using the solution.

*whenever you divide or multiply with a negative number reverse/flip the sign

< or > signs will always have an open circle

≥ or ≤ signs will have a closed/filled in circle

TIP: To know which way the arrow should point, look at the sign and think of it as an arrow.

< would have the arrow on the number point

this way: <-

or > which would have the arrow on the number line point this way: ->