(Question 23)
When solved for x, which inequality represents the number line?
1. 6x-3>21+3x
2. 6x-3>21-3x
3. 6x+3>21-3x
4. 6x+3>21+3x

Answer:

Chances of both even number = 30 times

Step-by-step explanation:

Given:

Chances of both even number = 1/4

Total number of tosses = 120

Find:

How many times both dice show even number

Computation:

Chances of both even number = [Chances of both even number][Total number of tosses]

Chances of both even number = 1/4 [120]

Chances of both even number = 30 times

cos θ = - \(\sqrt{2}\) / 6

sin θ = \(\sqrt{1-\frac{2}{6} }\)

sin θ = \(\sqrt{\frac{4}{6} }\)

sin θ = 2/\(\sqrt{6}\)

tan β = 5/12

sin β = 5/5

cos β = 12/5

sin ( θ + β ) = sin θ cos β + cos θ sin β

sin ( θ + β ) =  2/\(\sqrt{6}\) * 12/5 + ( - \(\sqrt{2}\) / 6 ) * 5/5

sin ( θ + β ) = 2/2.44 * 2.4 + 1.414/6 * 1

sin ( θ + β ) = 0.8196 * 2.4 + 0.2356 * 1

sin ( θ + β ) = 1.96 + 0.2356

sin ( θ + β ) = 2.1956

Answer:

Clyde has 14 pencils in his backpack

Step-by-step explanation:

Let x be the number of pencils that Clyde has in his backpack.

We can translate this statement “Steve hade 17 pencils in his backpack. this represents 5 more than 6/7 the number of pencils that Clyde has in his backpack” mathematically like this :

\(17=5+\frac{6}{7} x \\\\ \Longleftrightarrow 17-5=\frac{6}{7} x \\\\ \Longleftrightarrow 12=\frac{6}{7} x \\ \\\Longleftrightarrow x=\frac{12\times 7}{6} =14\)

Let he has n pencils

So

\(\\ \rm\hookrightarrow \dfrac{6n}{7}+5=17\)

\(\\ \rm\hookrightarrow \dfrac{6n}{7}=12\)

\(\\ \rm\hookrightarrow 6n=84\)

\(\\ \rm\hookrightarrow n=14\)

Answer:

the answer is two

Step-by-step explanation:

The equation is

The figure is similar to a parallelogram , with a base length equivalent to the circumference of the circle and a height equivalent to the radius of the circle

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the radius of the circle be represented as r

Now , the equation will be

The circumference of the circle C = 2πr

And , the circle is divided into 24 sectors and it is placed side-by-side

The figure formed is in the shape of a parallelogram

The base length of the parallelogram = circumference of the circle

And ,

Height of the parallelogram = radius of the circle r

Hence , the base length is the circumference and height is the radius of the circle

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Answer:

answer is E

Step-by-step explanation:

4 x 12 i= 48

square root of 4=2

12= 4x3

square root of 4 again = 2

2x2 =4

so left with 4 square root 3

The equivalent expressions are (a) \(4\sqrt 3 = \sqrt{24} \cdot \sqrt{2}\),  (d) \(4\sqrt 3 = \sqrt{12} \cdot \sqrt{4}\) and (e) \(4\sqrt 3 = \sqrt{48}\)

Equivalent expressions are expressions that have equal values

The expression is given as:

\(4\sqrt 3\)

Express 4 as the square root of 16

\(4\sqrt 3 = \sqrt{16} \times \sqrt 3\)

Combine the roots

\(4\sqrt 3 = \sqrt{16\times 3}\)

\(4\sqrt 3 = \sqrt{48}\)

Express 48 as the product of 12 and 4

\(4\sqrt 3 = \sqrt{12 \cdot 4}\)

Split, into factors

\(4\sqrt 3 = \sqrt{12} \cdot \sqrt{4}\)

Express 48 as the product of 24 and 2 in \(4\sqrt 3 = \sqrt{48}\)

\(4\sqrt 3 = \sqrt{24 \cdot 2}\)

Split

\(4\sqrt 3 = \sqrt{24} \cdot \sqrt{2}\)

Hence, the equivalent expressions are (a), (d) and (e)

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Answer:

1

Step-by-step explanation:

65.751 = 6 x 10 + 5 x 1 + 7 x 1/10 + 5 x 1/100 + 1 x 1/1,000

6 x 10 = 60

5 x 1 = 5

7 x 1/10 = 0.7

5 x 1/100 = 0.05

1 x 1/1000 = 0.001

60 + 5 + 0.7 + 0.05 + 0.001 = 65.751

The correct answer is B. 2, as the scale factor used to create the dilated polygon is 2.

To determine the scale factor used to create the image, we can compare the corresponding side lengths of the original polygon ABCD and the dilated polygon A'B'C'D'.

Let's calculate the lengths of the corresponding sides:

Side AB: The length of side AB is 3 - 1 = 2 units in the original polygon. In the dilated polygon, the length of side A'B' is 6 - 2 = 4 units.

Side BC: The length of side BC is -2 - (-1) = -1 units in the original polygon. In the dilated polygon, the length of side B'C' is -4 - (-2) = -2 units.

Side CD: The length of side CD is 1 - 3 = -2 units in the original polygon. In the dilated polygon, the length of side C'D' is 2 - 6 = -4 units.

Side DA: The length of side DA is -1 - (-2) = 1 unit in the original polygon. In the dilated polygon, the length of side D'A' is -2 - (-4) = 2 units.

Now, let's compare the corresponding side lengths:

AB: A'B' = 4 units / 2 units = 2

BC: B'C' = -2 units / -1 units = 2

CD: C'D' = -4 units / -2 units = 2

DA: D'A' = 2 units / 1 unit = 2

The scale factor used to create the image is the ratio of the corresponding side lengths.

In this case, all the corresponding side lengths have a ratio of 2.

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Answer:

  see below for the tables

Step-by-step explanation:

The differential equation is separable, so the solution is ...

  \(\displaystyle\dfrac{dy}{dx}=2xy\\\\\int{\dfrac{dy}{y}}=\int{2x}\,dx\\\\\ln{y}=x^2+C\\\\\text{Considering the initial condition, $C=-1$}\\\\\boxed{y=e^{x^2-1}}\)

__

The values for yn are y+y'·h = y+2xyh. We take the "absolute error" to be the (signed) difference between the calculated yn and the actual value y(x).

Answer:

x^2-10

Step-by-step explanation:

the area of whole square is x^2, not shaded area is 5*2=10, so shaded area equals to x^2-10

Answer:

-4, 3

Step-by-step explanation:

To find x intercepts, set y equal to 0;

0 = 5(x+4)(x-3); when x = -4 or x = 3, y will be zero (these are the x intercepts),

Answer:

y= -1/2x -3

Step-by-step explanation:

An equation of the line that passes through the point (8, -7) and is parallel to the line x + 2y = 18 is y = -x/2 -3.

Given that, the equation of a line is x + 2y = 18 and the coordinate plane is (8, -7).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

Here,  x + 2y = 18

⇒ 2y=18-x

⇒ y=9-x/2

The slope of a line x + 2y = 18 is -1/2

The slope of a line parallel to given line is m1=m2=-1/2

Substitute m=-1/2 and (x, y)=(8, -7) in y=mx+c, we get

-7=-1/2 (8)+c

⇒ -7=-4+c

⇒ c=-3

Put m=-1/2 and c=-3 in y=mx+c, we get

y = -x/2 -3

Therefore, an equation of the line that passes through the point (8, -7) and is parallel to the line x + 2y = 18 is y = -x/2 -3.

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Answer:

Check pdf

Step-by-step explanation:

Answer:

y-intercept = -5

slope = 4

equation = 4x - 5

Step-by-step explanation:

The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.

To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.

By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).

Slope (m) = (change in y) / (change in x)

= (0 - (-8)) / (4 - 0)

= 8 / 4

= 2

Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.

Using the point (0, -8):

-8 = 2(0) + b

b = -8

Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.

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Answer:

  C. RP = 4.5

Step-by-step explanation:

You want to know what condition is sufficient to show ∆ABC ~ ∆QPR, given  three sides and 2 angles in ∆ABC, and 2 sides in ∆QPR.

Similarity can be shown if all three sides are proportional, or if two angles are congruent.

The offered answer choices only list one angle, so none of those will work. The answer choice that makes the third side of ∆QPR be in the same proportion as the corresponding side of ∆ABC is the condition of interest.

  C. RP = 4.5

__

Additional comment

The side ratios in the two triangles are ...

  AB : BC : CA = 10 : 9 : 6

  QP : PR : RQ = 5 : PR : 3

For these ratios to be the same, PR must be half of BC, just as the other segments in ∆QPR are half their counterparts in ∆ABC.

Answer:

y is just being multiplyed by -4 :)

Step-by-step explanation:

in other words -4x

Answer:

y = -4x

Step-by-step explanation:

Answer:

7:16 is your answer :) hope it helps :)

Step-by-step explanation:

Yes, knowing the value of b, the slope of the regression line, allows us to predict the correlation coefficient value with accuracy.

Regression and correlation techniques can be used to establish links between variables.

Every day, we refer to any form of association as a "correlation," using that word.

To determine whether or if there is a relationship between the variables under investigation, correlation analysis is used.

Although regression illustrates how the variables are related,

Correlation and regression analysis can be shown graphically using scatter plots.

According to the question,

If we know the value of the slopes of the regression line say byx and bxy

We can Calculate the value of Correlation coefficient by using the relation

=> r = √(byx × bxy)

Hence , Yes We can accurately guess the value of correlation when slope of regression line is given

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73 degrees is the equivalent meausure of m<A

From the given line geometry below, the sum of the adjacent angles is 180 degrees as shown:

m∠A + m∠B = 180

Given the following

∠A = 6x - 35

∠B = 3x + 53

Substitute the given parameters

6x - 35 + 3x + 53 = 180

9x + 18 = 180

9x = 180 - 18

9x = 162
x = 162/9

x = 18

Determine the measure of <A

<A = 6x - 35

<A = 6(18) - 35

<A = 108 - 35

<A = 73 degrees

Hence the measure of angle A from the given diagram is 73 degrees

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The outcomes that are contained in the events are

1 - P(X) = 4/5 and 1 - P(X) is the same as P(Not X)

From the question, we have the following parameters that can be used in our computation:

X = gray colours

Given that

gray colours = 3 and 10

We have

X = 3 and 10

Not X =1, 2, 4, 5, 6, 7, 8

The probability is then calculated as

P(X) = 2/10 = 1/5

For P(Not X), we have

P(Not X) = 1 - 1/5 = 4/5

In (a), we have

P(Not X) = 1 - 1/5 = 4/5

This means that

P(Not X) = 1 - P(X)

So, the solution is

1 - P(X) = 4/5

Using the above (a) and (b) as a guide, we have the following:

1 - P(X) is the same as P(Not X)

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For given function function f(x)=-x+3-2, the domain is x > -3 and the range is y ≤ 2. So, correct option is D.

The function f(x)=-x+3-2 is a linear function in the form y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is -1 and the y-intercept is 1. Therefore, the graph of the function is a straight line that intersects the y-axis at (0,1) and has a slope of -1, meaning that it decreases by 1 for every 1 unit increase in x.

The domain of the function is the set of all possible values of x for which the function is defined. Since there are no restrictions on the value of x in the equation f(x)=-x+3-2, the domain is all real numbers, or (-∞, ∞).

The range of the function is the set of all possible values of y that the function can output. In this case, the lowest possible value of y occurs when x approaches positive infinity, and the highest possible value of y occurs when x approaches negative infinity. Therefore, the range is all real numbers less than or equal to 2, or y ≤ 2.

So, the domain is x ∈ (-∞, ∞) and the range is y ≤ 2. Alternatively, the domain can also be expressed as x > -3, since that is the minimum value of x at which the function is defined.

Correct option is D.

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Complete question is:

What are the domain and range of the function f(x)=-x+3-2?

A) domain: -3 -2

B) domain: -3 -3 range: y<-2

C) domain: x>-3 range:y>-2

D) domain : x>-3 range: y ≤ 2

Answer:

Great Britain we’re colonizers

Step-by-step explanation:

Answer:

C) 0.08

Step-by-step explanation:

Answer:

600000Ω

Step-by-step explanation:

1μA = 10⁻⁶ A

200μA = 0.0002 A

Potential difference = V = 120 V

Current = I = 0.0002 A

Resistance = R

R = V / I

  = 120 / 0.0002

  = 600000Ω

Answer:

5 feet and 6 inches

Step-by-step explanation:

5 feet is 60 inches

Answer:

5 feet 6 inches

a foot is 12 inches. Go by 12s until you get to a number that's as close as you can make it without going overboard, then count what's left. 12 × 5 = 60, 66 - 60 = 6, hence 5 feet 6 inches

Answer:

2x8=16

3x5=15

Step-by-step explanation: I hope you have/had an amazing day<3

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer:

w(25) = 96

There are 96 wolves in the year 2020

Step-by-step explanation:

Given:

\(w(x)=14\cdot 1.08^{x}\)

w(25) =

\(w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96\)

Number of years : 1995 + 25 = 2020

In 2020, there are 96 wolves