Carlos builds a robot that moves with small wheels. each wheel has six 5 inch long metal spokes that meet in the center what is the length of the arc

The slope of the line passing through the y intercept and the vertex of the quadratic  x²+10x-5 is 5.

The provided quadratic equation is,

y = x²+10x-5

The vertex of a quadratic equation,

(-b/2a, -D/4a)

Where,

a = 1,

b = 10,

c = -5,

D = (b²-4ac)

D = (10²-4(-5)(1))

D = 100+20

D = 120,

Putting all the values to find the vertex of the equation,

(-10/2,-120/4)

(-5,-30)

So, the vertex are now known,

To find the y intercept, putting x = 0 and solving the equation for y,

y = (0)²+10(0)-5

y = -5

The y intercept is,

(0,-5)

If there are two points on the line, let say (a,b) and (c,d), then the slope of the line is,

M = (d-b)/(c-a)

Now, we know two points,(-5,-30) and (0,-5).

We can now find the slope of line,

M = (-5+30)/(0+5)

M = 25/5

M = 5

To know more about slope of line, visit,

https://brainly.com/question/3493733

#SPJ9

The equation of the quadratic with a directrix of y= -5 and vertex of (-2, -3) is: y = 1/8 (x + 2)² - 3

Quadratic equation when the directrix is at y direction is of the form:

(x - h)² =  4P (y - k)

OR

standard vertex form, y = a(x - h)² + k     where a = 1/4p

The vertex

v (h, k) = (-2,-3)

h = -2

k = -3

P in this problem, is the distance between the vertex and the directrix

P = -3 - -5 = -3 + 5 = 2

p = 2

substitution of the values into the equation gives

(x - h)² =  4P (y - k)

(x - -2)² =  4 * 2 (y - -3)

(x + 2)² =  8 (y + 3)

rearranging the equation

8 (y + 3) = (x + 2)²

y + 3 = 1/8 (x + 2)²

y = 1/8 (x + 2)² - 3 (standard vertex form)

Learn more about vertex of quadratic equations at:

https://brainly.com/question/29244327

#SPJ1

The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .

The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.

Given that,

equation of given line with a slope of m = 3

y=3x-5​

A line perpendicular to that line will have a slope that is the negative reciprocal of 3.

The reciprocal of 3 is 1/3. So the negative reciprocal of 3 is -1/3.

Therefore, we want to write the equation of a line with slope, m = -1/3, and passes through the point (6, 4) = (x, y).

y = mx + b

4 = (-1/3)(6) + b      

(we've set up the equation with only one unknown, b, that we can now solve for)

4 = -2 + b

b = 6

With a slope, m = -1/3, and a y-intercept, b = 6, the equation of our line relating x and y is:

y = (-1/3)x + 6

Hence, The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .

To learn more about equation of line from the given link:

https://brainly.com/question/13763238

#SPJ9

y = 2x - 5 Eq(1)

6x - 2y= 20 Eq(2)

We are going to use the elimination method to solve the system.

y-2x = -5 Transpose x to the othe side in Eq(1)

2y - 4x = -10 Multiply all terms of Eq(1) by 2. Then add Eq(1) to Eq(2)

2y - 4x = -10

+ -2y +6x= 20

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

2x = 10 Operating like terms

x= 10/2 Isolating x

x = 5

Replacing x in Eq(1)

y = 2*(5) -5

y= 10 - 5 = 5

The answer is the point with coordinates ( 5 (x-coordinate) , 5(y-coordinate)).

We have two parallel lines intersected by other line.

We have to relate the angles.

We will take the angle with measure 17° as reference (red angle).

The angle <1 has a measure that is supplementary to the red angle, as <1 is supplementary to the <4, which is a corresponding angle to the red angle.

It has no direct relationship with the red angle.

The angle <2 is supplementary to <1, so it will have the same measure as the red angle (m<2 = 17°).

The relationship with the red angle is that they are alternate exterior angles.

Angle <3 has no direct relationship with the red angle. As it is vertical with <1 it has the same measure (m<3 = 163°) and is supplementary to the red angle.

Angle <4 and the red angle are corresponding angles.

They have the same measure, so they are congruent.

Angle <5 and the red angle form a linear pair, so they are supplementary. The measure of <5 is then m<5 = 163°.

Angle <6 and the red angle are vertical angles, so they have the same measure.

Angle <7 and the red angle form a linear pair, so they are supplementary. The measure of <7 is then m<7 = 163°.

Answer:

Angle <1:

Measure = 163°

Relationship: No name for relationship and supplementary.

Angle <2:

Measure = 17°

Relationship: Alternate exterior and congruent.

Angle <3:

Measure = 163°

Relationship: No name for relationship and supplementary.

Angle <4:

Measure = 17°

Relationship: Corresponding and congruent.

Angle <5:

Measure = 163°

Relationship: Linear pair and supplementary.

Angle <6:

Measure = 17°

Relationship: Vertical and congruent.

Angle <7:

Measure = 163°

Relationship: Linear pair and supplementary.

We have a deck of 52 cards.

We have to calculate the probability that when a card is randomly drawn from the deck, this cart is a red four.

There is only one red four in the deck. Then, if we calculate the probability of an event as the quotient between the number success events (getting a red four, in this case) and the total possible events (getting any card), we will get:

As there is only one card in the deck that gives a success event within the 52 cards, the probability is 1 in 52.

Answer: the probability is 1/52.

The mean height is given as 64.1 . We want to obtain the probability that he mean height for the sample is greater than 65 inches ​if the standard deviation is 2.52.

To proceed we, find the z-score of 65 in the distribution, we make use of the formula;

x = 65, mu = population mean = 64.1, sigma = standard deviation = 2.52, n = sample size = 70.

inserting these values, we have;

The problem now boils down to finding the probability of the z-score greater than 0.043

From z-score tables. the probability of the z-score greater than 0.043;

Therefore, the probability that the mean height for the sample is greater than 65 inches is 0.48285

The hypotenuse (longest side) of a right angled triangle can be derived using the Pythagoras' theorem as shown;

The answer is 10.82 inches, to 2 decimal places

Answer:

Step-by-step explanation:

A crucial step in null hypothesis testing is finding the likelihood of the sample result if the null hypothesis were true. This probability is called the p value. A low p value means that the sample result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis.

The value of a nickel is 5 cents

The value of the quarter is 25 cents

Since Priam has a total of 9.30 dollars = 930 cents, then

Simplify the equation by dividing all terms by 5

Since he has 6 nickels less than 3 times the quarters, then

Substitute n in equation (1) by equation (2)

Add the like terms on the left side

Add 6 to both sides

Divide both sides by 8

The number of quarters is 24

Substitute q by 24 in equation 2 to find n

The number of nickels is 66

He has 66 nickels and 24 quarters

The slope of two perpendicular lines is the negative reciprocal of each other.

Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.

Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.

where m = slope.

Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.

Step-by-step explanation:

The slope of two perpendicular lines is the negative reciprocal of each other.

Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.

Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.

y-y_1=m(x-x_1)y−y

1

=m(x−x

1

)

where m = slope.

\begin{gathered}\begin{gathered} y-(-13)=\frac{1}{2}(x-0) \\ y+13=\frac{1}{2}(x) \\ y=\frac{1}{2}x-13 \end{gathered}\end{gathered}

y−(−13)=

2

1

(x−0)

y+13=

2

1

(x)

y=

2

1

x−13

Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.

Solution

We have the following data:

0, 0, 0, 0, 1, 1, 1, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5

And the mean would be:

Mean = 2.958

And the median

Median = 4

Then if we add a 5 then the median would be the same 4

And the mean = 3.04

then the solution is:

The mean would increase

And for the other part of the question

we have:´

4+3+1+2 = 10 people made 3 or less trips to the movie

12x^3

Name: Monomial , because it has only 1 term

Degree: 3, exponent of the monomial

the answer is 1 1/4 cups of vinegar

Step-by-step explanati

Number of students qualify for a karate tournament if they train and compete at Blue Bear High School is equal to 60.

As given in the question,

Total number of students enrolled in Blue Bear High School =175

Number of students train in karate = 25

Number of students compete with other school in karate =35

Number of students practice martial arts but not karate=100

Number of students qualify for a karate tournament if they train and compete at Blue Bear High School

= 25 + 35

= 60

Therefore, number of students qualify for a karate tournament if they train and compete at Blue Bear High School is equal to 60.

Learn more about number here

brainly.com/question/17429689

#SPJ1

Given data:

The given principal is P=$3,300.

The given rate of interest is r=3.3%.

The given time is t=20 years.

The expression for the final amount of money is,

Substitute the given values in the above expression.

Thus, the final amount after 20 years is 5,478.

Answer: The Answer is the addition symbol

Step-by-step explanation:

8 x 50 = 400

8 x 7 = 56

400 + 56 = 456

8 x 57 = 456

SOLUTION

This is a right-triangle problem.

We will use the SOHCAHTOA principle.

In this triangle, we will relate the opposite side and the hypotenuse side to get the value of x. That will be the CAH relationship.

The final answer is 73.87 degrees.

Answer:

Step-by-step explanation:

The answer is  B!

Answer:

I don't know if it is the answer

k=12

1) Gathering the data, and setting this table:

Blocks | Pounds

5 60

6 72

7 84

8 96

2) Since we have this table, and a proportional relationship means a linear function without linear coefficient, i.e. y =mx

Then we can write:

y =12x

3) So, as we can write it y=kx, then the constant of proportionality k =12 because the weight in pounds is 12 times the number of blocks.

5 x 12 = 60

6 x 12 =

Given:

The expression is ___-(-5) = -7.

The objective is to find the missing value using number line.

Consider the missing value as x.

Now, the expression can be rearranged as,

So, we have to solve -7-5 on number line, which means starting from -7 subtract 5 in the number line.

Hence, the missing value is -12.

Answer:

3nd one

Step-by-step explanation:

Hope I helped!

If I got it incorrect, please tell me, so I can at least try and see what I did wrong.

The easiest expression to simplify by using the associative property is expression "b", since there is an addition already set (120 + 80 =200) to be performed.

'The other expressions involve more steps.

Answer:

[tex]x=\frac{-1}{7}[/tex]

Step-by-step explanation:

[tex]8=x/7+9\\[/tex]

Subtract 9 from both sides

[tex]-1=x/7[/tex]

Multiply both sides by 7

[tex]\frac{-1}{7} =x[/tex]

Swap the order because you're a smart person

[tex]x=\frac{-1}{7}[/tex]

SOLUTION:

Case: System of equations

Given: A table of value of snacks and drinks for Sidney and Erica

Required: Write a system of equations to determine the price of each candy and each drink.

Method:

Step 1: Assume the price of snacks be represented by s and drinks by d

Step 2: Equation for Sidney

Step 3: Equation for Erica

Final answer:

The system of equations is:

Explanation

Step 1

let x represents the number of minutes.

hence:

Plan A costs $19 plus an additional $0.07 for each minute of calls

Plan B costs $12 plus an additional $0.11 for each minute of calls

Step 2

there is a number of minutes x, such both plnas cost the same,so