how would i explain my students proportional reasoning

The equation that represents the graph of f(x) is [tex]f(x) = \sqrt {x - 1[/tex]

The complete question is in the attached image

The parent square root function is:

[tex]g(x) = \sqrt x[/tex]

From the graph,

g(x) is shifted one unit right to get f(x)

This is represented as:

f(x) = g(x - 1)

So, we have:

[tex]f(x) = \sqrt {x - 1[/tex]

Hence, the equation that represents the graph of f(x) is [tex]f(x) = \sqrt {x - 1[/tex]

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The radius of the circular vase is 6.37 * 10^-3 m.

The term pressure is defined as the ratio of force to area. Hence we can write;

P = F/A

F =  15 N

P = 750 N/m2

A = F/P

A = 15 N/750 N/m2

A = 0.02 m^2

Now;

A = πr^2

r = √A/ π

r = √ 0.02/3.142

r = 6.37 * 10^-3 m

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Answer:

34 mm

Step-by-step explanation:

P = 2 x (L + B) for a rectangle

P = 2 x (10 + 7) = 2 x 17 = 34

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{6x + 2 = 2x - 1}[/tex]

[tex]\huge\textbf{SUBTRACT 2x to BOTH SIDES:}[/tex]

[tex]\mathbf{6x + 2 - 2x = 2x - 1 - 2x}[/tex]

[tex]\huge\textbf{Simplify it!}[/tex]

[tex]\mathbf{4x + 2 = -1}[/tex]

[tex]\huge\textbf{SUBTRACT 2 to BOTH SIDES:}[/tex]

[tex]\mathbf{4x + 2 - 2 = -1 - 2}[/tex]

[tex]\huge\textbf{Simplify it!}[/tex]

[tex]\mathbf{4x = -3}[/tex]

[tex]\huge\textbf{DIVIDE 4 to BOTH SIDES:}[/tex]

[tex]\mathbf{\dfrac{4x}{4} = \dfrac{-3}{4}}[/tex]

[tex]\huge\textbf{Simplify it!}[/tex]

[tex]\mathbf{x = \dfrac{-3}{4}}[/tex]

[tex]\mathbf{x = -\dfrac{3}{4}}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -\dfrac{3}{4}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assigiment \& enjoy your day!}[/tex]

The surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:

V =  a × b × c unit³

The surface area of the prism = 2[(5×4)+(15×4)+(15×5)]

                                                  = 310 inches²

The volume of the prism = 5 × 4 × 15

                                         = 300 in³

Hence, the surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.

The complete question is:

A rectangular prism with a base that is 5 inches by 4 inches and a height of 15 inches. Find the volume and the surface area of the rectangular prism?

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Answer:

  A. No.

Step-by-step explanation:

The job of science is to explain relationships in the real world. Scientists do this by making observations, forming theories regarding relationships, and conducting experiments to test those theories.

An observation of correlation may result in a theory that one of the correlated phenomena causes another. The correlation, by itself, does not demonstrate causation. Any number of other factors could be involved.

Answer:

13, -2

Step-by-step explanation:

Answer:

I found 14 but their might be more!
hope that helps! :)

Step-by-step explanation:

3.

A = pi x r^2

48 = 3.141... x r^2

÷ by value of pi

15.278... = r^2

Square root the ans, to get r

Thus, R = 3.908..... So, radius is 3.9

2.

Circumference = pi x diameter

87. = 3.141... x d

÷ by value of pi

27.692............. = diameter

Radius is twice the diameter. So, divide diameter by 2 to find the radius.

27.692.....÷ 2 = 13.846...

Thus, radius is 13.8cm

Hope this helps!

For a randomly chosen Monday, the probability there will be less than 340 column inches of classified advertisement is 0.8413.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with a population mean of 320 and a population standard deviation of 20 inches.

[tex]P(X < 340) = P(z < \dfrac{(340-320)}{20})[/tex]

                    =  P(z < 1)

                    = 0.8413

Hence, For a randomly chosen Monday, the probability there will be less than 340 column inches of classified advertisement is 0.8413.

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The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds

An equation is an expression that shows the relationship between two or more variables and numbers.

From the graph of the function h(t) = 1 + 4t - 1.86t²:

The maximum height the rock reaches 3.15 feet.

Time spent on air = 2.38 - (-0) = 2.38 seconds

The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds

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It would take about  8 hours 20 minutes for the 1000 mL of D5W to infuse completely.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that the drop factor is 10 gtt/mL, hence:

Infuse rate = 20 gtt/min ÷ 10 gtt/mL = 2 mL/min

Time taken = 1000 mL / 2 mL per min = 500 min = 8 hours, 20 minutes.

It would take about  8 hours 20 minutes for the 1000 mL of D5W to infuse completely.

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Answer:

Step-by-step explanation:

900mL of RL is infusing at 80 gtt/min (80 macrodrops/min). Drop factor: 15 gtt/mL

The median for height is: 167

The median for Weight is: 183

The middle value or the average of the two middle value of an ordered data set is the median of the data.

Given the following data:

Height: 178, 163, 174, 186, 154, 167, 167, 181, 159, 165, 177, 191, 158

Arranged in an ordered form, we would have:

54, 158, 159, 163, 165, 167, [167,] 174, 177, 178, 181, 186, 191

The middle value is 167. The median for height is: 167.

Weight: 157, 163, 190, 187, 183, 173, 184, 189, 193, 192, 177, 173, 168

Arranged in an ordered form, we would have:

157, 163, 168, 173, 173, 177, [183,] 184, 187, 189, 190, 192, 193

The middle value is 183. The median for weight is: 183.

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By Green's theorem,

[tex]\displaystyle \int_C P(x,y)\,dx + Q(x,y)\,dy = \iint_D \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \, dA[/tex]

where [tex]D[/tex] is the interior of [tex]C[/tex]. It's easy to see that

[tex]D = \left\{(x,y) ~:~ 1 \le x \le 3 \text{ and } 1 \le y \le 4\right\}[/tex]

Now,

[tex]\dfrac{\partial Q}{\partial x} = \dfrac{\partial}{\partial x}(-x^2) = -2x[/tex]

[tex]\dfrac{\partial P}{\partial y} = \dfrac{\partial}{\partial y}(\ln(x) + y) = 1[/tex]

so that the line integral reduces to

[tex]\displaystyle \int_C (\ln(x)+y)\,dx - x^2\,dy = -\int_1^3 \int_1^4 (2x+1) \, dy\,dx = \boxed{-30}[/tex]

By applying the law of sine, the length of side BD is equal to 9.05 cm and the image of right-angled triangle BCD is shown in the image attached below.

In order to determine the length of side BD, we would apply the law of sine because both side BD and side BC represent the opposite side and hypotenuse of right-angled triangle BCD respectively.

Mathematically, the law of sine is given by this mathematical expression:

sin(θ) = Opp/Hyp

Where:

Substituting the parameters into the formula, we have;

sin(θ) = BD/BC

sin(74) = BD/9.41

Cross-multiplying, we have:

BD = 9.41 × sin(74)

BD = 9.41 × 0.9613

BD = 9.05 cm.

By applying the law of sine, the length of side BD is equal to 9.05 cm and the image of right-angled triangle BCD is shown in the image attached below.

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Answer:

m∠V = 28°

Step-by-step explanation:

In ΔUVW:

To find the measure of angle V, first find the value of x.

Interior angles of a triangle sum to 180°.

⇒ m∠U + m∠V + m∠W = 180°

⇒ (9x - 8) + (2x + 2) + (3x + 4) = 180

⇒ 9x + 2x + 3x - 8 + 2 + 4 = 180

⇒ 14x - 2 = 180

⇒ 14x = 182

⇒ x = 13

Substitute the found value of x into the expression for angle V:

⇒ m∠V = 2(13) + 2

⇒ m∠V = 26 + 2

⇒ m∠V = 28°

Therefore, the measure of angle V is 28°.

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Answer:

[tex]k=2[/tex]

Step-by-step explanation:

The constant of proportionality is given as  [tex]k=\frac{y}{x}[/tex] .

Notice that when [tex]x=2[/tex] it follows that [tex]y=4[/tex].

Substitute [tex]x=2[/tex] and [tex]y=4[/tex] into the formula for the constant:

[tex]k=\frac{4}{2}=2[/tex] .

Therefore, the constant is equal to 2.

Answer:

30%

Step-by-step explanation:

[tex]\frac{145}{500} = 0.29[/tex] ≅ 0.30 or 30%

The length of the line AB as described by points A and B in the task content is; √125.

a) The length of AB as described is;

AB = √((7-2)² + (4-(-6))²)

AB = √(25 + 100) = √125.

b) The slope of AB is;

Slope, m = (7-2)/(4-(-6)) = 5/10

Slope = 1/2.

c). The coordinates of the midpoint of AB are;

x = (4+(-6))/2 = -1

y = (7+2)/2 = 4.5

The midpoint is; (-1, 4.5).

2) The radius of the circle as described with centre (0, 0) that passes through the point (5, –3) is;

Radius = √((5-0)² + (-3-0)²)

Radius = √(25+9) = √34 = 5.8

3) Hence, the equation of a circle with centre (0, 0) that passes through the point (5, –3) is;

(x-5)² + (x-3)² = 5.8².

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Step-by-step explanation:

try this option, all the details are in the attachment.

Answer:

12:20

Step-by-step explanation:

i hope the answer will help you

The  congruence theorems or postulates could be given as reasons why LMN is congruent to OPQ are LA and AAS.

Congruence theorems is one that explain that in a case whereby  three sides of two triangles are equal to another, we can say they are congruent to each other.

From the given figure, there are two angles as well as one non-included side which is seen to be a  congruent.

According to LA theorem , a triangle is congruent in a case whereby,  leg as well as  an acute angle of one right triangle of two right triangles are congruent to each other.

AAS theorem also explains that incase  two angles and any of the side of a triangle are congruent to each other , the triangles are congruent.

Therefore, with these theorem, congruence theorems or postulates could be given as reasons why LMN is congruent to OPQ are LA and AAS.

CHECK THE FIQURE FOR THE COMNPLETE QUESTION

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The true statement about the number of correct answers is that the: A. median = mode.

Mathematically, the mean for the number of correct answers can be calculated by using the following formula:

Mean = [F(x)]/n

Total frequency, n = 3 + 4 + 6 + 9 + 8 = 30.

F(x) = [(1 × 3) + (2 × 4) + (3 × 6) + (4 × 9) + (5 × 8)] = 105.

Mean = 105/30

Mean = 3.5.

For the median, we have:

The median for the number of correct answers is the average of the 15th and 16th number:

Median = (4 + 4)/2

Median = 8/2

Median = 4.

For the mode, we have:

The mode for the number of correct answers is the answer with the highest frequency, which is 4 with a frequency of 9.

Therefore, the true statement about the number of correct answers is that the median is equal to mode.

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Complete Question:

The table below shows the number of correct answers that students gave on a recent -question quiz. Which of the following statements is true?

A. median = mode

B. mode > median

C. mode < mean

D. mean > median Reset Selection

The equation based on the information given will be x⁴ + 8x² - 12.

It should be noted that from the information given, the expression to compute will be:

= g - g(x)²

This will be:

= 4 - (4 - x²)²

= 4 - (4 - x)(4 - x)

= 4 - (15 - 8x² + x⁴)

= x⁴ + 8x² - 12

The complete question is:

Use f(x) = 2x − 3 and g(x) = 4 − x² to evaluate the expression g - g(x)².

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Answer:

is it asking how many times u would get then number 5 when u roll or asking how you would expect for the first 5 rolls?

The circumference equal to 25 units

The perimeter of square is 4 times the side.

P= 4* side

The perimeter of the square,

4x = P

Now P is =  32 units then,

32 units = 4(x)

x = 8 inches

So,  the diameter of the cylinder formed by the rotation of 8 inches  

Now, the circumference of the base is

C = 2πr = πD

If r =8  inches

C = π(8 units) = 8π units

C = 8(3.14) = 25.12 units

Hence, the circumference equal to 25 units

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Using a system of equations, it is found that the cost of a t-shirt is of $3 and the cost of a notebook is of $5.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The variables are given as follows:

Considering the costs of the purchases of Clubs A and B, the matrices give the equations as follows:

Hence, replacing the second equation into the first:

3x + 2(8 - x) = 19

x = 3.

y = 8 - x = 8 - 3 = 5.

The cost of a t-shirt is of $3 and the cost of a notebook is of $5.

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The test value and the p value for the probability are 10.5 and 0.0148.

Based on the information, the observed and expected values will be:

Observed. Expected

75. 75

100. 120

90. 75

15. 30

The p value based on the test statistic from the distribution table will be 0.0148.

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