Lesson 4: Proportional Relationships a 2. A recip Equations the qu a. Let's write equations describing proportional relationships. b. 4.1: Number Talk: Division Find each quotient mentally. C. 645 - 100 645:50 48.6 - 30 48.6 + x

Answer:

At the same rate, she will travel 638 miles if she drives 11 hours.

Step-by-step explanation:

[tex]\frac{754 miles}{13 hours\\} = \frac{x}{11 hours}[/tex]

x=11*754/13

x=638

Chris, this is the solution to the exercise:

• Point 1 = (7, 6)

• Point 2, (0, 2)

Now, let's use the formula to calculate the distance between the two points, as follows:

d = √(0 - 7)² + (2 - 6)²

d = √-7² + (-4)

d = √49 + 16

d = √65

d = 8.0622

d = 8.1 (rounding to the nearest tenth)

Notice that each new term is half the previous one. For example, 32 is half 64, 16 is half 32, and so on.

Having said that, the constant ratio is 1/2. Using this ratio we can find the next three terms.

Answer:

A. -7

Step-by-step explanation:

g(x) = -4x+5    

We know that g(x)= (3) so just substitute 3 for x.

g(3)= -4(3)+5

g(3)= -12+5

g(3)=-7 answer.

Answer and Explanation:

Let x represent the number of hours Sandy needs to work.

We can go ahead and set up the required inequality as shown below;

Let's go-ahead and determine x by splitting the compound inequality above as shown below;

After rounding off the number we get ; 9,300

When a number is rounded to the closest thousand, it is changed to an approximated value that is simpler to recall and utilize. The closest value to the supplied integer is this value, which is a multiple of 1000. For instance, 342984 becomes 343000 if it is rounded to the closest thousand.

So as in this question the number given is 9340

Since we have to round it off to thousands

and the number next to 9 is 3

Thus we can say that after rounding off the number will be

9,300.

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Answer:

11.4

Step-by-step explanation:

Answer:

11.4

p.s you try it may help

The average distance between students in public is smaller than that in private.

While the data for the public appears to closely follow a bimodal distribution, the data for the private appears to be negatively skewed, meaning that the tail is lopsided to the left. However, it might be nearly symmetrical. While the modal class for the public is 11–50, it is 101–500 for private.

While the mean for public data is close to 50, it is close to 100 for private data.

Therefore, it is clear from the graphs that students' average distances from Public are closer than those from Private.

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Points are (1, -3)

In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities. In mathematics, an equation is a relationship between two expressions that is expressed as an equality on each side of the equal to sign. An equation would be 3y = 16, for instance.

Given Data

Slope = -[tex]\frac{1}{2}[/tex]

Points (-1, -5)

The line's general equation is y=ax+b.

Since we are aware that the slope is -[tex]\frac{1}{2}[/tex], an is equal to -[tex]\frac{1}{2}[/tex].

We also understand that if x = -1, then y = -5.

Let's connect it:

-5=1*(-1)+b

-5=-1+b

b= -4

So, y=x -4 is the line's equation.

Let x = 1

y = 1 - 4

y = -3

(1, -3)

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The slope of the line that passes through (2, 2) and (10, 6) is; 1/2.

The slope of parallel lines is the same. Slopes of perpendicular lines are negative reciprocals of each other. The slope of a line or straight object is the ratio of how much amount of rising occurs in correspondence to the increment in the run.

Its slope would be:

[tex]m = \dfrac{y-q}{x-p}[/tex]

We have been given that the line that passes through (2, 2) and (10, 6).

Let ( p,q) and (x,y) are (2, 2) and (10, 6) respectively.

Slope = [tex]m = \dfrac{y-q}{x-p}[/tex]

m = (2-6)/(2-10)

m = 4/8

m = 1/2

Then the slope is 1/2.

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Answer:

The slope is [tex]-\frac{1}{4}[/tex].

Step-by-step explanation:

This is the slope formula equation.

[tex]y=mx+b[/tex]

[tex]x+4y=16[/tex]

First, you divide the entire equation by 4 to get rid of the 4 in 4y.

[tex]\frac{x}{4} +y=4[/tex]

Then, you subtract  [tex]\frac{x}{4}[/tex] on both sides.

[tex]y=-\frac{x}{4} +4[/tex]

In front of the x should be and invisible 1. So this should be your slope.

[tex]m=-\frac{1}{4}[/tex]

We want to rewrite the following parametric equations

as one equation. Using the following property

We can eliminate the parameter theta adding the square of the coordinates

And this is the standard equation of an ellipse

The constrain

tells us that x can only assume negative values, therefore, the graph is only the left side of the ellipse.

Answer: I would say it is C

Step-by-step explanation: If you think about it, if you have a pencil and the pencil is in A form, and you have to put it to B form, it kinda makes sence. BUT, I honestly don't know, so don't trust me...

GL LUCK THO AND GOD BLESS

Part a: The value of y is 11 for x = 2.

Part b: The graph for the function y = x² + 4x -1 is drawn.

Part c: Range; (-∞,-3.75]∪[-0.25,∞)

Part d: The function is  y =  -5 - (x + 2)².

Part e: The approximate value of √3  is 1.732.

For the given function;

y = x² + 4x -1, the values of y for the corresponding x is given in tables shown.

Part a: value of y when x = 2.

Put x = 2 in the function;

y = x² + 4x -1

y = 2² + 4×2 -1

y = 11

The value of y is 11 for x = 2.

Part b: The graph for the function y = x² + 4x -1 is drawn using the scale of 10 small divisions as 1 unit along x and y axis.

Part c: Range of value of x for which y ≥ -2.

Locate the point of x from the graph for which the value of y  y ≥ -2.

Range; (-∞,-3.75]∪[-0.25,∞)

Part d: The function in the form of y = k - (x - h)², where k and h are the vertex.

The vertex from the graph is found as (-2, -5) (h, k)

Putt in the equation;

y = k - (x - h)²

y = -5 - (x - (-2))²

y =  -5 - (x + 2)²

Part e: 2 - √3 is the root of the equation 0 = x² + 4x -1.

It  2 - √3 is the root of the equation, then by putting this value at x the equation becomes zero.

The approximate value of √3  is 1.732 which is found by long division method.

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Answer:

The answer is 10 and one half pounds

Explanation:

3.5/7 = 2

21/2 = 10.5

10 and one half pounds use to make 21 small vases.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Sandy uses clay= 3 1/2 pounds for 7 vase

So, for 1 vase amount of clay used

= 7/2 x 1/7

= 1/2 pounds

Now, for 21 small vases amount of clay used

=21 x 1/2

= 21/2

= 10 1/2 pounds.

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The linear model that determines your profit or loss based on the number of sandwiches is 15y-275, where y is the number of sandwiches sold.

A continuous response variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behaviour of complex systems, as well as analyzing experimental, financial, and biological data. Linear regression is a statistical technique for developing a linear model.

It is given that the investment amount is $275.

The charge per sandwich is $15

So, generated revenue= 15 y

where y is the number of sold sandwiches.

Profit/ Loss= Revenue- total investment= 15y-275

So, the linear model determining the profit or loss is 15y-275, where y is the number of sandwiches.

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The parent function of g(x) = x + 9 is the function f(x) = x.

The function f(x) = x is a linear function, that is, it has degree 1 (the higher exponent of the variable x is 1).

In order to get g(x) from f(x), we can see that the function value was increased by 9 units:

Adding 9 units to the function means we have a translation of 9 units up.

Therefore the correct option is the third one.

Graphing g(x), we have:

The cost of the cotton candy that Jessica purchased is $3.

The first step is to determine total amount spent on snacks. The total amount spent is the sum of the amount paid by Tom and Jessica.

Total amount spent = $9 + $4 = $13

Two ice creams and one cotton candy is bought. This can be represented with:

$13 = total cost of ice cream + cost of the cotton candy

$13 = (2 x$5) + c

$13 = $10 + c

c = $13 - $10

c = $3

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we have the expression

we have that

x=5 is a zero of the given equation

so

Divide x^3-125 by (x-5)

x^3-125 : (x-5)

x^2+5x+25

-x^3+5x^2

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

5x^2-125

-5x^2+25x

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

25x-125

-25x+125

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

0

therefore

x^3-125=(x-5)(x^2+5x+25)

The given sequence is

1, 1/2, 1/4, 1/8......

we can see that the ratio of the consecutive terms is the same. We have

1/2/1 = (1/4)/(1/2) = (1/8)/(1/4) = 1/2

This means that it is a geometric sequence

To find the amount of the substance left after 21 half lifes, we would find the 21st term of the sequence. The formula for finding the nth term of a geometric sequence is

an = a1r^(n - 1)

a1 = 1

n = 21

r = 0.5

Thus,

a21 = 1 * 0.5^(21 - 1) = 0.5^20

a21 = 0.00000095367

a21 = 1/1048576

The answer makes sense in the problem context because it follows the common ratio that was established at the begining.

Let's try to factorize this polynomial

in the blank spaces we have to put numbers that multiplied are 24, and substracted are +2. So we have 6 and 4

So the factored form of the polynomial is (x+6)(x-4)

Answer:

d

Step-by-step explanation:

The number of years must be non-negative.

This eliminates all of the options except for d.

The value of y based on the information given about the expression (8^7)² = 2^y is 21.

It should be noted that based on the information, the power rule will be essential. This will be illustrated thus:

(8^7)² = 2^y

It should be noted that 8 = 2 × 2 × 2 = 2³

Therefore, 8^7 = 2^(3 × 7) = 2^21

Therefore, the value of y is 21.

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ok

To solve this problem, I'll use trigonometric functions,

The trigonometric function that relates the opposite side and the hypotenuse is sine

Formula

sin 48 = Opposite side / hypotenuse

hypotenuse = 105 ft

opposite side = H

Substitution

sin 48 = H/105

Solve for H

H = 105*sin 48

Simplification

H = 105*0.743

Result

H = 78 ft

Answer:

  B. The parabola opens upward. It is stretched taller by a factor of 3.

Step-by-step explanation:

You want to know how the quadratic opens, and how it is stretched or compressed, given its equation is f(x) = -3x^2 +6x +5.

The "leading coefficient" is the coefficient of the highest-degree term. That term is -3x^2, and its coefficient is -3.

The minus sign tells you the parabola opens downward.

The magnitude of 3 tells you the parabola is stretched vertically (taller) by a factor of 3.

The equation of tangent is y = -2x + 20. The slope of the tangent line is negative 2. And coordinate of point A is (10, 0). And the length of AB is 22.36 units.

The equation of the circle with center at origin and radius r is given as,

x² + y² = r²

The slope of the tangent line to the circle at points (8, 4) is given as,

2x + 2y (dy/dx) = 0

dy / dx = - 8 / 4

m = - 2

Then the equation of the line is given as,

y = -2x + c

The equation is passing through (8, 4), then we have

4 = -2(8) + c

c = 4 + 16

c = 20

The equation is y = -2x + 20. Then the x-intercept is given as,

y = 0

-2x + 20 = 0

2x = 20

x = 10

Then the length of the line is given as,

AB² = (10 - 0)² + (0 - 20)²

AB² = 100 + 400

AB = √(500)

AB = 22.36 units

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The inequality that can be used to calculate total cost (T) based on the number of guests (g) is 225 + 15g ≤ 1000.

If you have a total budget of $1000, 51.67 guests can be invited.

Total cost = Cost of hall rent + Caterer's charge per guest(Number of guests)

225 + 15g ≤ T

If you have a total budget of $1000

225 + 15g ≤ T

225 + 15g ≤ 1000

15g ≤ 1000 - 225

15g ≤ 775

g ≤ 775 / 15

g ≤ 51.66666666666666

Approximately,

g ≤ 51.67

So therefore, the inequality to represent the situation is 15g ≤ 1000 - 225 and about 51.67 guests can be invited if you have a budget of $1000

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Answer:

a. x ≥ 6

Explanation:

If a number is at least 6, then, the number is greater than or equal to 6.

Since the symbol ≥ means greater than or equal, the correct answer is:

a. x ≥ 6

The solved equation for h is h= S/ pi x r^2-1/3.

The problem we are dealing with here is related to the literal equation,  where a literal equation is an equation that comprises basically letters. Formulas are an illustration of strict equations. Each variable within the condition "truly" speaks to an important part of the full relationship expressed by the equation. To illuminate a literal equation implies modifying the equation so a different variable stands alone on one side of the equals sign. We got to be told which variable we need to solve.

For the given equation,S=  1/3 x pi x r^2 + pi x r^2 x h

for th the equation will be

=>S=  pi x r^2(1/3 +h)

=>S/ pi x r^2= 1/3+h

=>h= S/ pi x r^2-1/3

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S = 1/3 x pi x r^2 + pi x r^2 x h , solve for h

For you to input the information in a Matix you only have to consider the coefficients corresponding to each variable in each equation, in this case the matrix is:

1 -1 4 : 4

6 -8 1 : -1

4 1 0 : 0

This is the matrix for the given equations