Teresa stated that the heights of the students in her class were not a function of their ages. Which reasoning could justify Teresa’s statement?

To solve the given system of inequalities, we need to find the values of x that satisfy both inequalities. The solution is x ≤ 5.

To solve the given inequalities, we need to find the values of x that satisfy both inequalities. Let's start with the first inequality:

3x - 8 ≤ 23

Adding 8 to both sides, we get:

3x ≤ 31

Dividing both sides by 3, we get:

x ≤ 31/3

Now, let's move on to the second inequality:

-4x + 26 ≥ 6

Subtracting 26 from both sides, we get:

-4x ≥ -20

Dividing both sides by -4 (and reversing the inequality sign since we're dividing by a negative number), we get:

x ≤ 5

Therefore, the solution to the system of inequalities is x ≤ 5. Answer choice B is correct.

Answer:

I have a minimum of 85 beads.

Step-by-step explanation:

Let in the final 4 groups that I have made there is only 1 bead in each.

So, the total number of beads in each of the previous groups will be (1 × 4 + 1) = 5.

Now, in each of the previous 4 groups, there are 5 beads and there is a remaining one bead.

So, the total number of beads in each of the previous groups will be (5 × 4 + 1) = 21.

Now, in each of the first 4 groups, there are 21 beads and there is a remaining one bead.

So, the total number of beads that I had initially will be (21 × 4 + 1) = 85.

Therefore, I have a minimum of 85 beads. (Answer)

==========================================

Explanation:

See the attached image below. The information that the tower is 500 ft is never used. Focus solely on triangle ABD (ignore point C).

AB = 200

AD = x = unknown

angle ABD = angle B = 47 degrees

Use the cosine rule to help find x

---------

cos(angle) = adjacent/hypotenuse

cos(B) = AB/BD

cos(47) = 200/x

x*cos(47) = 200

x = 200/cos(47)

x = 293.255837127926

Rounding to the nearest foot, we get 293 feet as the answer.

The length of the guy wire is 273.5 feet.

Trigonometric ratio show the relationship between the sides and angles of a right angled triangle.

Let d represent the length of the guy wire.

Using trigonometric ratios:

[tex]sin(47)=\frac{200}{d} \\\\d=\frac{200}{sin(47)} \\\\d=273.5\ feet[/tex]

The length of the guy wire is 273.5 feet.

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Answer:

f(x) has a vertical asymptote at x = 5 and a horizontal asymptote at y = 2.

[tex]g(x) = \frac{1}{x-5}+2[/tex] is shifted 5 units to the right and 2 units up from f(x), as shown in figure a.

Step-by-step explanation:

Question # 4 Solution

[tex]f(x) = \frac{1}{x-5}+2[/tex]

Determining Vertical Asymptote:

Setting the denominator equal to zero, we can determine the value of vertical asymptote.

As,

    x - 5 = 0

    x = 5

So, x = 5 is the Vertical Asymptote:

Determining Horizontal Asymptote

[tex]f(x) = \frac{1}{x-5}+2[/tex]

[tex]f(x) = \frac{2x-10}{x-5}[/tex]

If the degree of both numerator and denominator is same, then the horizontal asymptote can be obtained by determining the ratio of leading coefficient of the nominator to the leading coefficient of denominator.

As the leading coefficient of nominator is 2, and the leading coefficient of denominator is 1. So, the ratio of the leading coefficient of nominator to the leading coefficient of denominator is will get the horizontal asymptote.

Hence, y = 2/1 → y = 2 will be the horizontal asymptote.

So, f(x) has a vertical asymptote at x = 5 and a horizontal asymptote at y = 2.

Question # 5 Solution

A translation makes any graph of function move up or down - Vertical Translation -  and right or left - Horizontal Translation.

For example, if we replace the graph of y = f(x) with the graph of y = f(x - 5), meaning the graph y = f(x) will shift right by 5 units  so it is f(x - 5).

Important Note: Adding moves the graph to the left; subtracting moves the graph to the right.

As [tex]g(x) = \frac{1}{x-5}+2[/tex] compare to the parent function f(x) = 1/x.

The graph of f(x) = 1/x is shown in figure a. If we compare the graph of f(x) = 1/x with the graph of g(x) = 1 ÷ (x - 5), meaning the graph g(x) = 1 ÷ (x - 5) is shift right by 5 units, as shown in figure (a).

Now, take [tex]g(x) = \frac{1}{x-5}+2[/tex], we observe that graph [tex]g(x) = \frac{1}{x-5}+2[/tex] is now 2 units up from f(x). Adding 2 units to the output shifts the graph up by 2 units, as shown in figure a.

Hence, [tex]g(x) = \frac{1}{x-5}+2[/tex] is shifted 5 units to the right and 2 units up from f(x). The figure a shows the complete result of the graph [tex]g(x) = \frac{1}{x-5}+2[/tex].

Keywords: graph shift, vertical asymptote, horizontal asymptote

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The ordered pair solution of y = (2/5)x + 2 corresponding to -5 is (x, y) = (-5, 0)

Solution:

Given that we have to find the ordered pair solution of [tex]y = \frac{2}{5}x + 2[/tex] corresponding to -5

Let us find the ordered pair corresponding x = -5

Ordered pairs are often used to represent two variables

The number which corresponds to the value of x is called the x-coordinate and the number which corresponds to the value of y is called the y-coordinate

Substitute x = - 5 into the function and evaluate for y

[tex]y = \frac{2}{5}x + 2\\\\y = \frac{2}{5}(-5) + 2\\\\y = 2(-1) + 2\\\\y = -2 + 2\\\\y = 0[/tex]

Therefore the ordered pair is x = -5 and y = 0 which is (x, y) = (-5, 0)

Answer:

1/4 are white. So, 3/4.

Step-by-step explanation:

Answer:

No solution

Step-by-step explanation:

4(a+2)=8+4a-2

4a+8=8+4a-2

0+8=8-2

0= -2

no solution

Answer:

no solution

Step-by-step explanation:

Given

4(a + 2) = 8 + 4a - 2 ← distribute left side

4a + 8 = 6 + 4a ( subtract 8 from both sides )

4a = - 2 + 4a ( subtract 4a from both sides )

0 = - 2 ← not possible

This indicates the equation has no solution

Answer:

all work is shown and pictured

The solution of the expression is,

⇒ c = 10/3

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expression is,

⇒ 5/2c = 8 1/3

Now,

We can simplify the expression is,

⇒ 5/2c = 8 1/3

⇒ 5/2c = 25/3

⇒ c = 25/3 × 2/5

⇒ c = 10/3

Thus, The solution of the expression is,

⇒ c = 10/3

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Answer:

11/18 miles

Step-by-step explanation:

3 2/3=11/3

2/12=1/6

1/6*11/3=11/18

Answer:

10,000

Step-by-step explanation:

14,500      *4 is less that five.

round it down and you get

The solution to the system of equations is: x = 0 and y = 3

To find the solution to the system of equations, we need to find the values of "x" and "y" that satisfy both equations simultaneously. We can do this by setting the two expressions for "y" equal to each other since they both represent the same value of "y".

Since both equations are equal to "y," we can set them equal to each other:

2x + 3 = -3x + 3

Now, let's solve for "x":

2x + 3x = 3 - 3

Combine the "x" terms:

5x = 0

Now, divide both sides by 5 to solve for "x":

x = 0

Now that we have the value of "x," we can find the corresponding value of "y" using either of the original equations. Let's use the first equation:

y = 2x + 3

y = 2(0) + 3

y = 3

So, the solution to the system of equations is:

x = 0

y = 3

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Answer:

B

Step-by-step explanation:

edge

The scatterplot that has a stronger correlation is B.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The correlation coefficient helps us to know how strong is the relation between two variables.

The value is always between +1 to -1, where, the numerical value shows how strong the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

1 indicates a strong positive relationship.

-1 indicates a strong negative relationship.

A result of zero indicates no relationship at all, therefore, an independent variable.

Since the scatterplot is the relationship between the two variables and as in the first graph the value of a single x can return multiple values for y.

Therefore, the scatterplot that has a stronger correlation is B.

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The height of the triangle is: 6 inches

Step-by-step explanation:

Given

Area = A = 54 square inches

Let be be the base of the triangle and

h be the height

Then

b = 3h

The area of triangle is given by:

[tex]Area = 0.5 * base * height\\Putting\ values\\54 = 0.5 * 3h * h\\54 = 1.5h^2\\\frac{54}{1.5} = \frac{1.5h^2}{1.5}\\h^2 = 36[/tex]

Taking square root on both sides

[tex]\sqrt{h^2} = \sqrt{36}\\h = 6[/tex]

Hence,

The height of the triangle is: 6 inches

Keywords: Linear equations, square roots

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. -6,-3,0,3,6,9,12

Answer:

. -6,-3,0,3,6,9,12

Answer:

[tex]\large \boxed{y + 1 = 4(x - 1)}[/tex]

Step-by-step explanation:

The point-slope formula for a straight line is

y - y₁= m(x - x₁)

x₁ = 1; y₁ = -1; m = 4  

Substitute the values

[tex]\begin{array}{rcl}y - (-1) & = & 4(x - 1)\\y + 1 & = & 4(x - 1)\\\end{array}\\\text{The equation for the line in point-slope form is $\large \boxed{\mathbf{y + 1 = 4(x - 1)}}$}[/tex]

The figure shows the graph of the equation with slope 4 passing through (1, -1).

The point-slope form of the equation for the line that passes through the point (1, –1) with a slope of 4 is [tex]y + 1 = 4(x - 1).[/tex]

To select the equation in point-slope form for the line that passes through the point (1, –1) and has a slope of 4, we use the formula [tex]y - y1 = m(x - x1),[/tex] where (x1, y1) are the coordinates of the given point and m is the slope of the line. In this case, the point-slope form of the equation becomes [tex]y + 1 = 4(x - 1).[/tex]

This equation represents a line with a slope (slope) of 4, which means for every one unit increase in x, y increases by 4 units. The equation is structured around a specific point, (1, –1), highlighting the characteristic of point-slope form that the line passes through the given point.

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Answer:

There is no picture

Step-by-step explanation:

Answer:veg students: 50

Step-by-step explanation:

Answer:

120 degrees

Step-by-step explanation:

The angles in a pentagon add up to 540 degrees. This means that we can set up an equation to find this. We'll call the measure of the angle that we want to find x.

112+68+3x=540

Solving this, we get 180+3x=540, and 3x=360. That means that x is 120 degrees.

The interior angles of the pentagon is A = { 112° , 68° , 120° , 120° , 120° }

The sum of the interior angles of a polygon is given by the formula

Sum of Interior angles of a polygon with n sides is

nθ = 180 ( n - 2 )

where n is the number of sides

θ = angle in degrees

Given data ,

Let the polygon be represented as A = pentagon

The number of sides n = 5

So , the sum of interior angles of A = nθ = 180 ( n - 2 )

nθ = 180 ( 5 - 2 ) = 540°

The 2 angles of the pentagon = 112° , 68°

And , let the remaining angles = x + x + x

So , x + x + x + 112° + 68° = 540°

On simplifying , we get

3x + 180° = 540°

3x = 360°

x = 120°

Hence , the angles are 120° each

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Answer:

No, it will not pass through origin.

Step-by-step explanation:

Given:

The equation of the line is:

[tex]y=5683x+976[/tex]

The coordinates of the origin are [tex]x=0,y=0[/tex]. So, if the line passes through the origin, then the 'y' value at [tex]x=0[/tex] must be 0.

Let us check the 'y' value at [tex]x=0[/tex].

Plug in [tex]x=0[/tex] in the above equation. This gives,

[tex]y=5683\times 0 + 976[/tex]

[tex]y=0+976[/tex]

[tex]y=976[/tex]

So, at [tex]x=0[/tex], the value of 'y' is 976 which is not equal to 0.

Hence, it will not pass through the origin as for [tex]x=0[/tex], the value of 'y' is not 0.

The equation y = 5683x + 976 has a y-intercept of 976, not 0; hence it does not pass through the origin.

To determine whether the equation y = 5683x + 976 will pass through the origin, you need to check if the point (0,0) satisfies the equation. An equation of a line will pass through the origin if its y-intercept is 0. The y-intercept is the value of y when x is 0. Looking at the given equation, if we substitute x with 0, we get y = 5683(0) + 976, which simplifies to y = 976. Therefore, the y-intercept is 976, not 0. This means the line does not pass through the origin since the y-intercept is a point on the y-axis located at (0, 976).

Answer:

-5x + 3(10x - 8)= 51

-5x + 30x - 24 = 51

25x - 24 = 51

25x = 75

x = 3

y = 10(3) - 8

y = 30 - 8

y = 22

(3, 22)

Answer:

Harry rides further.

Step-by-step explanation:

First, you have to find the least common denominator of 8 and 5, which is 40.

3*5=15, 2*8=12

Hope this helps!!!

Karen rides farther.

Comparing numbers in math is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.

Given that, Harry rides his bike 25 3/8 miles. Karen rides her bike 25 2/5 miles, we are asked to find who rides farther,

Harry's distance = 25 3/8 = 203/8

Karen's distance = 25 2/5 = 127/5

Subtracting Harry's distance by Karen's distance,

203/8 - 127/5

= 1015-1016/40

= -1/40

Since, the result is in minus that means 127/5 is greater than 203/8.

Therefore, Karen's covers more distance than Harry.

Hence, Karen rides farther.

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Answer:

Number of photographs Bob has can be represented as ⇒ [tex]11p[/tex]

Step-by-step explanation:

Given:

Alan has 11 photographs.

Bob has [tex]p[/tex] times as many photographs as Alan.

To find the expression representing the number of photographs Bob has.

Solution:

Since Bob has [tex]p[/tex] times as many photographs as Alan has so, in order  to find the number of photographs Bob has, we will multiply [tex]p[/tex] with number of photographs Alan has.

Alan having 11 photographs, Bob will have as much as:

⇒ [tex]11\times p[/tex]

⇒ [tex]11 p[/tex] photographs

Answer:

54

Step-by-step explanation:

144 divided by 8 is 18

so that means that their hourly rate 18 pizzas per hour

so multiply 18 by 3 and get 54

Given that Pizza Land can deliver 18 pizzas per hour, they can deliver 54 pizzas in three hours.

The question is asking us to figure out how many pizzas can be delivered in 3 hours, if Pizza Land can deliver 144 pizzas in 8 hours. This is a rate problem. To solve it, we first need to find out how many pizzas are delivered per hour. We do this by dividing 144 (the total number of pizzas delivered) by 8 (the total number of hours). This gives us 18 pizzas per hour.

Now that we know how many pizzas are delivered per hour, we can multiply this by 3 (the number of hours we are interested in) to get the total number of pizzas that can be delivered in 3 hours. So, 18 pizzas/hour x 3 hours gives us 54 pizzas that can be delivered in 3 hours.

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Answer:

the answer is 12

Step-by-step explanation:

[tex] = (3 + 2(6) - 1) - 3(3) + 7 \\ = (14) - 9 + 7 \\ = 14 - 2 \\ = 12[/tex]

Answer:

6x+128

Step-by-step explanation:

I don't know if this is what you meant or not, but I simplified it. First, you collect your like terms and add them up. Like terms would be 8x, and the two -x because they all have x. The other set of like terms would be 75, 50, and 3 because they are all numbers without variables. Add the two groups up separately, and then put them in order with the x in front.

Answer:

The expression is  [tex]a_{10}[/tex] = 100+(10 - 1)50 .

Step-by-step explanation:

Given as :

The amount of money added as prize money =  $50

The amount that first caller will win =  [tex]a_{1}[/tex] = $100

Let The amount that 10th caller win = $A

∴ common difference for the callers amount = $50

Now, According to question

The given statement is in arithmetic expression

So, For A.P , The nth term is written as

nth term = first term  + (n - 1) × common difference

I.e [tex]a_{10}[/tex] = [tex]a_{1}[/tex] +  (n - 1) × common difference

Here n = 10

Or, A = $100 +  (10 - 1) × 50

So, The expression =  [tex]a_{10}[/tex] = 100+(10 - 1)50

Hence, The expression is  [tex]a_{10}[/tex] = 100+(10 - 1)50 . Answer

Answer:

The answer is A.

Step-by-step explanation:

a10=100+(10-1)50

Got it correct in the quiz.

Answer:

Figure show the equation of line : y=[tex]\frac{-2}{3} x+1[/tex]

Step-by-step explanation:

Given equation of line is y=[tex]\frac{-2}{3} x+1[/tex]

To plot the equation of line:

For equation of line, we need at least two points

Let x=0

y=[tex]\frac{-2}{3} x+1[/tex]

y=[tex]\frac{-2}{3}0+1[/tex]

y=1

The required point is (0,1)

Let x=3

y=[tex]\frac{-2}{3} x+1[/tex]

y=[tex]\frac{-2}{3}3+1[/tex]

y=(-1)

The required point is (3,-1)

Using points (0,1) and (3,-1) to plot the graph.

Figure show the equation of line : y=[tex]\frac{-2}{3} x+1[/tex]

Answer:

[tex]y = - \frac{3}{4}x - 7[/tex]

Step-by-step explanation:

We have to find the equation of the straight line which has the slope equal to [tex]- \frac{3}{4}[/tex] and passes through the point (-4,-4).

As the slope of the equation is [tex]- \frac{3}{4}[/tex], hence by slope-intercept form the equation of the straight line will be given by  

[tex]y = - \frac{3}{4}x + c[/tex] .......... (1), where c is any constant which we have to evaluate from the given point on the line (-4,-4).

So, the point (-4,-4) satisfies the equation (1) and hence,

[tex]- 4 = - (\frac{3}{4}) \times (- 4) + c[/tex]

⇒ - 4 = 3 + c

⇒ c = - 7

Therefore, the equation of the straight line will be  

[tex]y = - \frac{3}{4}x - 7[/tex] (Answer)

Answer: 71300000

Step-by-step explanation:

Answer:

7.13 x 10^7.

Step-by-step explanation:

2.3x10^-5)(3.1x10^12

= 2.3x3.1 x 10^-5 x 10^12

= 7.13 x 10^(-5+12)

= 7.13 x 10^7.