Use the given information to create the equation for the rational function. The function is written in factored form to help you see how the given information shapes our equation. Enter values for factors from smallest to largest.Vertical asymptotes at x=-4 and x=-1, x-intercepts at (1,0) and (5,0), y-intercept at (0,7).The numerator is: Answer (x-Answer )(x-Answer )The denominator is: (x+Answer )(x+Answer )

The measure of the arc or angle is:

m∠NLM = 60 deg

From the given figure, line LN is the diameter. Thus, the measure of arc LN is 180° (semicircle).

Thus, we can say:

arc NM + arc ML = 180°

(3x + 21) + (8x + 16) =  180°

11x + 37 = 180

11x = 180 - 37

11x = 143

x = 143/11

x = 13

arc NM = 8x + 16

put x = 13:

arc NM = 8(13) + 16 = 120°

Recall that:

The measure of inscribed angle is half the measure of its intercepted arc. That is:

m∠NLM = 1/2 * 120°

m∠NLM = 60°

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Let's simplify the expression:-

\(\bigstar{\boxed{\frac{3}{1} *\frac{1}{2}}\)

Multiply 3 times 1 and 1 times 2:-

\(\bigstar{\boxed{\pmb{\frac{3}{2} }}\)

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

The equation that represent the given situation is y = 15x + 70

When she plants 3 stalks, each plant yields 115 ounces of beans

The first point = (3, 115)

When she plants 8 stalks, each plant yields 190 ounces of beans

The second point = (8, 190)

The slope of the line m = \(\frac{y_2-y_1}{x_2-x_1}\)

Substitute the values in the equation

The slope of the line m = (190-115) / (8-3)

= 75/5

= 15

The point slope form is

\(y-y_1=m(x-x_1)\)

Choose one point and substitute the values in the equation

y - 115 = 15(x - 3)

y - 115 = 15x - 45

y = 15x - 45 + 115

y = 15x + 70

Hence, the equation that represent the given situation is y = 15x + 70

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Answer:

30

Step-by-step explanation:

150/5 = 30

Answer: 30

Step-by-step explanation:

Based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

To determine whose purple paint will be redder based on the percent of red paint, we need to compare the ratios of red paint to the total paint used by Isaiah and Casho.

Isaiah's Ratio:

Isaiah mixes 3 cups of blue paint and 7 cups of red paint, making a total of 3 + 7 = 10 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (7 cups) by the total amount of paint (10 cups) and multiply by 100 to get the percentage:

Red paint percentage for Isaiah = (7 cups / 10 cups) * 100 = 70%

Casho's Ratio:

Casho mixes 4 cups of blue paint and 13 cups of red paint, making a total of 4 + 13 = 17 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (13 cups) by the total amount of paint (17 cups) and multiply by 100 to get the percentage:

Red paint percentage for Casho = (13 cups / 17 cups) * 100 = 76.47% (rounded to two decimal places)

Comparing the percentages, we can see that Casho's purple paint will be redder because Casho's paint has a higher percentage of red paint (76.47%) compared to Isaiah's paint (70%).

Therefore, based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

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Answer: Need more info. We need to know how many minutes over the 300 minutes were used in order to calculate the correct monthly fee.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to identify the x-intercepts on the graph.

An "x-intercept" is a point where the graph crosses or touches (intercepts) the x-axis. The y-value there is always 0.

The given graph crosses the x-axis where x = -2 and x = 3. This means the x-intercept points are ...

  (-2, 0) and (3, 0)

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Answer:

y = (x + 1)(x - 2)(x -3)

Step-by-step explanation:

Looking at the graph we see our zeros which is on the x-axis is -1 , 2, 3.

Thus create an equation.

y = (x + 1)(x - 2)(x -3)

Answer:

1) 30 pounds is the weight of the bag all together

2) science book is the heaviest book

Step-by-step explanation:

bag=4 pounds

library book=2 pounds

maths book=2×4=8 pounds

science book=8×2=16 pounds

4+2+8+16=30 pounds all together

heaviest book= science book (16 pounds)

Answer:

ax^ + bx + c

squared coefficient = 1

linear coefficient = -8

constant = -5

Step-by-step explanation:

Answer:

A). The ratio of a circle's circumference to its diameter

Step-by-step explanation:

Step-by-step explanation:

10/15 and 5/15 aren't correct. Both aren't equal to a whole number. Irrational numbers.

15/1 is correct. The denominator is over 1, which makes the numerator equal to a whole number, 15.

Answer:

$3,000

Step-by-step explanation:

There two possible outcomes:

There is a 3/4 chance that the bid is rejected for a value of -$1,400

There is a 1/4 chance that the bid is accepted for a value of $17,600 - $1,400.

The expected value of the situation is:

\(E = \frac{3}{4}*(-1,400)+\frac{1}{4}*(17,600-1,400)\\E=\$3,000\)

The expected value is $3,000.

Answer:

Step-by-step explanation:

5 feet

Since the height of the water is 4.75 feet, the equation is

4.75 = x + (-0.25)

To solve, add 0.25 to each side:

4.75+0.25 = x+(-0.25)+0.25

5.00 = x

Answer: B,  5.0

Step-by-step explanation:

The sales 12 weeks after release is $586,000 . Option A is the correct answer.

To create a table of values, we can plug in different values of t and find the corresponding values of s:

t s

0 10

1 19.882

2 26.248

3 31.177

4 35.064

5 38.185

6 40.731

7 42.837

8 44.6

9 46.095

10 47.384

11 48.508

12 49.498

To graph the function, we can plot the values from the table on a coordinate plane. The horizontal axis represents time in weeks, and the vertical axis represents sales in thousands of units. The resulting graph is a curve that starts at (0,10) and increases as t increases.

To estimate the sales 12 weeks after release, we can look at the graph and see that the corresponding value of s is around 49.5 thousand units. Therefore, the answer is about $586,000 (49.5 x 1000 x 12). Option A is the correct answer.

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Answer: the present age of son is 15 years, and the present age of father is 45 years.

Step-by-step explanation:

Let the age of son be 'x' and that of his father be 'y'.

So according to the question, the 1st equation that can be formed will be:

y = 3(x) ->(1)

[as father's age is 3 times the age of son]

Now after 5 years:

Age of son = (x+5)

Age of father = (y+5)

So according to the question, the 2nd equation that can be formed will be:

(y+5) = 2.5×(x+5) ->(2)

[as father is now two and half times old as his son]

Substituting the value of equation (1) in (2), we get:

(3x+5) = 2.5×(x+5)

=> 3x + 5 = 2.5x + 12.5

=> 3x - 2.5x = 12.5 - 5

=> 0.5x = 7.5

=> x = 7.5/0.5 = 15

Thus, the present age of son is 15 years.

Note : we can calculate the age of father by putting the value of x in equation (1) or (2):

y = 3(x) = 3 × 15 = 45 (putting x in equation 1)

Thus, the present age of father is 45 years.

The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.

Answer:

y = -5/2x + 27/2

Step-by-step explanation:

line formula is y = mx + b

perpendicular means number next to the x (slope or m) becomes a negative reciprocal

2/5x -> -5/2x

then use point slope formula

y - y1 = m (x - x1)

y - 6 = -5/2 (x - 3)

y - 6 = -5/2x + 15/2

y = -5/2x + 15/2 + 6

y = -5/2x + 15/2 + 12/2

y = -5/2x + 27/2

Answer:

20

Step-by-step explanation:

The theoretical probability of drawing 2 red marbles from the bag with replacement is one-fifth, which means that the probability of drawing 2 red marbles in any one trial is 1/5 or 0.2.

The number of times Jonah is expected to select 2 red marbles in 100 trials can be predicted using the expected value formula:

Expected value = (Number of trials) x (Probability of success in one trial)

Expected value = 100 x 0.2

Expected value = 20

Therefore, a reasonable prediction of the number of times Jonah will select 2 red marbles in 100 trials is 20. Therefore, the answer is 20.

Answer: 20 i took the test

Step-by-step explanation:

Answer:

The multiples of 7 between 1 to 100 are 7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 , 63 , 70, 77, 84, 91, 98.

Using matrices the simultaneous equation is solved to get x = 3 and y = 5

This method required finding determinants in three occasions then dividing

The given equation

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right] \left[\begin{array}{c}x\\y\\\end{array}\right]= \left[\begin{array}{c}19\\8\\\end{array}\right]\)

the determinant is

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right]\)

3 * 1 - 2 * 1 = 3 - 2 = 1

Solving for x

determinant while replacing x values

\(\left[\begin{array}{cc}19&2&\\8&1\\\end{array}\right]\)

19 * 1 - 2 * 8 = 19 - 16 = 3

solving for x = 3/1 = 3

Solving for y

determinant while replacing y values

\(\left[\begin{array}{cc}3&19&\\1&8\\\end{array}\right]\)

3 * 8 - 19 * 1 = 24 - 19 = 5

solving for y = 5/1 = 5

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Let x= be the amount in the account with .5%

Let y be the amount in the account with .25%

We know that interest is

I = PRT

I = 21.25 and time is 1 year so t=1

I = x(.005)(1) + y (.0025)

We also know that the amount invested is 5000

x+y = 5000

The system of equations is

21.25 = .005x + .0025y

x+y = 5000

21.25 = .005x+.0025y

Let x = 0

21.25 = .0025y

21.25/.0025 =y

The y intercept is 8500

Let y =0

21.25 = .005x

21.25/.005 =x

The x intercept is 4250

x+y = 5000

Let x = 0

The y intercept is 5000

Let y =0

The x intercept is 5000

Using substitution

x = 5000-y

21.25 = .005(5000-y) + .0025y

21.25 = 25 - .005y +.0025y

21.25-25 = -.0025y

-3.75 = -.0025y

-3.75/-.0025 = y

1500 = y

Now find x

x+y = 5000

x+1500=5000

x = 5000-1500

x = 3500

Answer:

It would be 4.929 because it is decided by

200 ml = 40 tsp

Answer:

q = 0.105uC

Step-by-step explanation:

We can determine the force on one ball by assuming two balls are stationary, finding the E field at the lower right vertex and calculate q from that.

Considering the horizontal and vertical components.

First find the directions of the fields at the lower right vertex. From the lower left vertex the field will be at 0° and from the top vertex, the field will be at -60° or 300° because + charge fields point radially outward in all directions. The distances from both charges are the same since this is an equilateral triangle. The fields have the same magnitude:

E=kq/r²

Where r = 20cm

= 20/100

= 0.2m

K = 9.0×10^9

9.0×10^9 × q /0.2²

9.0×10^9/0.04

2.25×10^11 q

These are vector fields of course

Sum the horizontal components

Ecos0 + Ecos300 = E+0.5E

= 1.5E

Sum the vertical components

Esin0 + Esin300 = -E√3/2

Resultant = √3E at -30° or 330°

So the force on q at the lower right corner is q√3×E

The balls have two forces, horizontal = √3×E×q

and vertical = mg, therefore if θ is the angle the string makes with the vertical tanθ = q√3E/mg

mg×tanθ = q√3E.

..1

Then θ will be...

Since the hypotenuse = 80cm

80cm/100

= 0.8m

The distance from the centroid to the lower right vertex is 0.1/cos30 =

0.1/0.866

= 0.1155m

Hence,

0.8×sinθ = 0.1155

Sinθ = 0.1155/0.8

Sin θ = 0.144375

θ = arch sin 0.144375

θ = 8.3°

From equation 1

mg×tanθ = q√3E

g = 9.8m/s^2

m = 3.0g = 0.003kg

0.003×9.8×tan(8.3)

0.00428 = q√3E

0.00428 = q×1.7320×E

Where E=kq/r²

Where r = 0.2m

0.0428 = kq^2/r² × 1.7320

K = 9.0×10^9

0.0428/1.7320 = 9.0×10^9 × q² / 0.2²

0.02471×0.04 = 9.0×10^9 × q²

0.0009884 = 9.0×10^9 × q²

0.0009884/9.0×10^9 = q²

q² = 109822.223

q = √109822.223

q = 0.105uC

Answer:Area = Length times Width

 5 1/4  times 3 3/4

5 x 4 + 1 = 21

21/4

3 x 4 +3 = 15

15/4

21/4 x 15/4 = 315 / 16 or 19 11/16 ft^2

Step-by-step explanation:

Answer:

if you want x it is 30 ........

The number of M&M's that were in the bowl before Amelia arrived is; 12

Let the original amount in the bowl be x. Thus;

If Amelia grabbed 50%, then amount left = (100% - 50%)x = 50%x = 0.5x

Now, we are told that domicick took 50% of what was keft after amelia. Thus; New amount left = 100%x - (0.5x + 0.25x) = 0.25x

Now, we are told that there were finally 3 left after all the deductions. Thus;

0.25x = 3

x = 3/0.25

x = 12

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Answer:A

Step-by-step explanation:

the correct choice is: B. The numbers in the pattern are odd.

To determine if the numbers in the pattern are even, odd, or alternate between even and odd, let's examine the first few numbers in the pattern:

First number: 41

Second number: 41 - 4 = 37

Third number: 37 - 4 = 33

Fourth number: 33 - 4 = 29

As we can see, the numbers in the pattern are decreasing by 4 in each step. The first number (41) is odd, and subsequently, each number is decreasing by an even value (4). Therefore, all the numbers in the pattern will be odd.

So, the correct choice is:

B. The numbers in the pattern are odd.

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Answer:

10 multiplied by the sum of 14 and 11

Step-by-step explanation:

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