in the x-y plane, what is the y- intercept of the graph of the equation y=6 (x-1/2) (x+3)

Work Shown:

[tex]a^2+b^2 = c^2\\\\5^2+b^2 = 13^2\\\\25+b^2 = 169\\\\b^2 = 169-25\\\\b^2 = 144\\\\b = \sqrt{144}\\\\b = 12\\\\[/tex]

I used the pythagorean theorem.

The inference based on the information about ordering is that D. Yes, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts.

It should be noted that a inference simply means the conclusion that can be deduced based on the information given.

In this case, the Main Street Theatre company must actually cast 3 girls in the role of young Cosette.

Hence, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts. Therefore, ordering matters.

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Using the Fundamental Counting Theorem, it is found that:

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For the 2 letters(26 outcomes each), and 3 numbers(10 outcomes each), we have that the parameters are:

[tex]n_1 = 26, n_2 = 26, n_3 = 10, n_4 = 10, n_5 = 10[/tex]

Hence the number of catalog numbers is:

[tex]N = 26^2 \times 10^3 = 676000[/tex]

The ID number is divisible by 5 if the last digit is either 5 or 0, hence [tex]n_5 = 0[/tex] and the probability is:

[tex]p = \frac{26^2 \times 10^2 \times 2}{26^2 \times 10^3} = 0.2[/tex]

There is a 0.2 = 20% probability that the ID number is divisible by 5.

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Using the given exponential function, we have that:

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

In this problem, the function is:

[tex]A(t) = 523(0.5)^{\frac{t}{30}}[/tex]

Hence the initial amount is of 523 grams.

The amount after 50 years will be given by:

[tex]A(50) = 523(0.5)^{\frac{50}{30}} = 165[/tex]

The amount after 50 years will be of 165 grams.

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The circumference of the larger circle is about 12.57 inches. The circumference of the smaller circle is about 3.14 inches. So, the total length of gold leaf on a tag is approximately 15.71 inches.

The circumference will be:

= 2πr

= 2 × 3.14 × 2

= 12.57 inches.

The circumference of the smaller circle will be:

= 2πr

= 2 × 3.14 × 0.5

= 3.14

The total length will be:

= 12.57 + 3.14

= 15.71 inches.

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Answer:

Step-by-step explanation:

First, let's start by removing the parentheses and simplifying the expression.

3.125 + - 3.9 - 2.46

Adding a negative number is the same as subtracting it, so we can remove the + sign.

3.125 - 3.9 - 2.46

From there, we can do simple subtraction and get:

-3.235

Answer:

Step-by-step explanation:

let the number at unit place=x

ten's place=y

hundred's place=z

x,y,z are integers.

x+y+z=9

also digit=100z+10y+x

y=2z

x+2z+z=9

x+3z=9

x=1,3,5,7,9

for x=1

1+3z=9

3z=9-1=8

z=8/3 (rejected as z is an integer.)

when x=3

3+3z=9

3z=9-3=6

z=6/3=2

z=2

y=2z=2×2=4

so number=100×2+10×4+3=200+40+3=243

The maximum number of the data points that may not actually be on the line is 15

The number of points is given as:

Points = 15

A line of best fit implies that the model is a regression model

In a regression model, all the data points may not pass through the line of best fit.

This means that the maximum number of the data points that may not actually be on the line is 15

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The volume of the cuboid is 183.96 m³

A cuboid is a plane shape with a six-faced solid called a hexahedron. The volume of a cuboid is Length × width × height

From the information given:

The volume of the cuboid is;

=  (7.3 × 6 × 4.2) m³

= 183.96 m³

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Step-by-step explanation:

so, what do we need to do ?

just solve these equations and find Sam's age (and Harry's) ?

x = 3y

x = 10 + 2y

so, we simply use the first equation in the second :

3y = 10 + 2y

y = 10

x = 3y = 3×10 = 30

Sam is currently 30 years old, Harry is 10.

The regression equation is (d) log(y) = 0.064x + 1.706

The table of values is given as:

x   2   3   4   5   6

y   73  77  85  101  133

Calculate the logarithm of the y values.

So, we have:

x          2   3   4   5   6

log(y)   1.86  1.89  1.93  2  2.12

Next, we enter the above values in a regression calculator.

From the calculator, we have the following summary:

The regression equation is then represented as:

log(y) = bx + a

Where:

b = SP/SSX = 0.64/10 = 0.064

a = MY - bMX = 1.96 - (0.064*4) = 1.706

So, we have:

log(y) = 0.064x + 1.706

Hence, the regression equation is (d) log(y) = 0.064x + 1.706

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Answer: D. log(y) = 0.064x + 1.706

Step-by-step explanation: I got it right on my test

The attached figure represents the complete flowchart.

The given statement is:

∠1 ≅ ∠2

To prove

∠3 ≅ ∠4

By vertical angle theorem, we have:

∠2 ≅ ∠4

By transitive property of congruence, we have:

∠2 ≅ ∠3

By transitive property of congruence, we have:

∠1 ≅ ∠3

By vertical angle theorem, we have:

∠3 ≅ ∠4

See attachment for the complete flowchart.

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Answer:

constant (unchanged) ratio of two variable quantities

Step-by-step explanation:

y = k x ( or y = k x )

y = 15 when x = 24, find x when y = 25. find the constant of variation.

Answer:

Since there are 20 chickens in one supermarket, and 25 chickens in the other supermarket, there are 45 chickens to choose from.

The question asks the value of f(x) when x = 4 in the equation

x = 4 is less than or equal to 4, so we use the first equation in the piecewise functions => {4x when x≤4}

Solving for f(x):

4(4)=16

16 is the answer!

Hope it helps!

Answer:

1960cm squared

Step-by-step explanation:

in case you're still confused ask where you're still confused and I'll offer my assistance.good day.

Answer:

3 is the mode

Step-by-step explanation:

Answer:

slope: 14

y intercept: (0,9)

Step-by-step explanation:

in the form y = mx + b, the slope is m: 14

to solve for the y intercept, we set x as 0: 14 * 0 + 9 = y interecept is 9.

Answer:

3x^2+3x/2-9

Step-by-step explanation:

collect like term

The percentage increase China's population from 1970 to 1995 is: 56.25%.

Percentage increase = (Final Value - Original Value)/Original value × 100.

Given the following:

Original value = 0.8 billion

Final Value = 1.25 billion

Final Value - Original Value = 1.25 - 0.8

Final Value - Original Value = 0.45

Percentage increase = 0.45/0.8 × 100 = 56.25%.

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The volume of the baseball roundibg off to nearest whole number is 14 cube inches.

If radius of a sphere is r and the volume of that spherical figure is given by V then,

[tex]V=\frac{4}{3}\pi r^3[/tex]

So in the problem the object is a baseball which is a sphere for sure.

Given that the diameter of that baseball is 3 inches.

So the radius of that baseball is given by = 3/2 = 1.5 inches.

Hence the volume of that base ball is

[tex]=\frac{4}{3}\pi\times(1.5)^3 \approx 14.1372 \approx 14[/tex]

Thus the volume of the baseball rounding off to nearest whole number is given by 14 cube inches.

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Answer:

b. 0

c. 4

d. 2

e. [tex]\frac{76}{35}[/tex]

Step-by-step explanation:

b.) When translated it will become this expression 10 - [(2x15)/3] = 0

c.) It will become [tex]\frac{4(12-7)}{5}[/tex]

d.) This will transform to  [tex]\frac{(\frac{78-13}{5}) + 5}{9}[/tex]

e.) The first eq is [tex]\frac{4(7+3)}{8}[/tex], then after the changes it becomes [tex]\frac{4[\frac{(7+3)+9}{7}]}{5}[/tex]

Answer:
I can help, its 45

Answer:

30245x⁴ - x³ + 90735x - 3

Step-by-step explanation:

1. Expand the expression

(30245x - 1)(x³ + 3)

2. Multiply

30245x x x³ + 30245x x 3-(x³ + 3)

3. Determine the sign

304245x⁴ + 90735x - (x³ + 3)

4. Rewrite the expression

30425x⁴ + 90735x - x³ - 3

= 30245x⁴ - x³ + 90735x - 3

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A) The collection of positive integers whose sum is 100 are: 23, 17, 6, 54, 0.

B) Another collection of positive integers whose sum is 100 are: 13, 27, 4, 56, 0.

C) Due to the fact that the units can be commuted, their sum is always equal to 20.

D) The smallest possible value is 0 and the largest is 57.

A) The formation of a collection of positive integers can be done by trial and error. For example, only using the digits {0, 1, 2, 3, 4, 5, 6, 7}.

For example, we can have;

23 + 17 + 6 + 54 + 0 = 100

Where the numbers used are: 23, 17, 6, 54, 0.

B) Another example is;

13 + 27 + 4 + 56 + 0 = 100

C) If we add the units digits of these 5 numbers, we get:

3 + 7 + 6 + 4 + 0 = 20

Now, if we compute the units digits between the different numbers, to get for example: 27, 13, 6, 54, 0

The sum is still equal to 100, and the units digits are the same ones, so we still have that the sum of the units digits is equal to 20.

d) The smallest integer that we use is 0.

For the largest we just commute the tens and units digits so we make the larger integer possible, which is:57.

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The solution to the inequality is (-4, ∞)

The second inequality is given as:

8 - y < 12

Subtract 8 from both sides

-y < 4

Rewrite as:

y > -4

In interval form, we have:

y = (-4, ∞)

Hence, the solution to the inequality is (-4, ∞)

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Answer:

In 3 years, Dianna will be 4 times as old as she was 33 years ago. How old is Dianna now?

Choose the most logical value for the variable to represent.

x= Diana's age now

This question is impossible to fully answer without further context. (Who is Dianna? Why do we need her age?)

However, it can be noted that [tex]x[/tex] is easily the most common variable name whenever you have a missing value in an equation. Generally, it is understood by mathematicians that [tex]x[/tex] and most other letters denote an unknown value, something to either use in solving the equation or something to find on its own.