Select the inequality that represents the relationship described below.
The sum of three times a number and seven is greater than four times the number.
O A.
3x-7> 4x
B.
3 - 7x> 4x
C.
3x + 7 > 4x
OD. 3 + 7x> 4x

Answer:

answer is c i did the test

Step-by-step explanation:

The perimeter of triangle ABC can be calculated by adding the distance between points A and B, B and C, and A and C. The respective distances are roughly 5, 4.12, and 5.1, thus, the estimated perimeter of the triangle is 14.22.

To calculate the approximate perimeter of a triangle given its vertices, one should first calculate the distance between each pair of vertices. In the context of the triangle △ABC with vertices at A(3,4), B(−1,1), and C(−2,5), the distance formula, which stems from the Pythagorean Theorem, is applied. The formula is as follows: D = √[(x2-x1)² + (y2-y1)²].

For the distance between A and B, the formula would play out as follows: D = √[((-1)-3)² + (1-4)²] = √[16 + 9] = √25 = 5.

For AB to C, the calculation would be: D = √[((-2)-(-1))² + (5-1)²] = √[1+16] = √17 ≈ 4.12

For AC: D = √[((-2)-3)² + ((5-4)²] = √[25 + 1]= √26 ≈ 5.1.

Essentially, you sum these distances up to get the perimeter, which in this case is approximately: 5 + 4.12 + 5.1 = 14.22

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To find the approximate perimeter of triangle ABC, we use the distance formula to calculate the lengths of the sides.

To find the approximate perimeter of triangle ABC, we need to calculate the distances between its vertices. Using the distance formula, we can calculate the length of each side.

Side AB: sqrt((3-(-1))^2 + (4-1)^2) = sqrt(16+9) = sqrt(25) = 5

Side BC: sqrt((-1-(-2))^2 + (1-5)^2) = sqrt(1+16) = sqrt(17)

Side AC: sqrt((3-(-2))^2 + (4-5)^2) = sqrt(25+1) = sqrt(26)

The perimeter of triangle ABC is approximately 5 + sqrt(17) + sqrt(26).

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It is equal to 0..... it is

Step-by-step explanation:

yes

Final answer:

Demand is considered inelastic when the elasticity of demand is less than one, signifying that consumers are less responsive to price changes.

Explanation:

When discussing the elasticity of demand, it is important to understand how demand responds to changes in price. If the elasticity of demand is less than one, this is known as inelastic demand. In this scenario, a 1 percent increase in the price that consumers pay will lead to a less than 1 percent change in the quantity purchased, showing a low responsiveness to price changes.

Conversely, demand is considered elastic when elasticity is greater than one, showing high responsiveness to price changes. If elasticity is exactly one, it is referred to as unitary elasticity, indicating that the percentage change in quantity demanded is equal to the percentage change in price.

Answer:

Last one is your answer

Step-by-step explanation:

Answer:

I believe the answer to this question is: 1 x 10^21 equal to 1000000000000000000000.

Answer:

Therefore the slope of

[tex]y= -3.2x + 9.7[/tex]

is

[tex]Slope =-3.2[/tex]

Step-by-step explanation:

Given:

A regression line was calculated as

[tex]y= -3.2x + 9.7[/tex]

To Find:

Slope = ?

Solution:

General Slope-Point Form is given as

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

Where,

[tex]m=Slope\\c=y-intercept[/tex]

On Comparing with given Regression line we get

[tex]Slope = m = -3.2[/tex]

Therefore the slope of

[tex]y= -3.2x + 9.7[/tex]

is

[tex]Slope =-3.2[/tex]

Answer:5y+5

Step-by-step explanation:

2+y+y+y+y+y+3

Collect like terms

y+y+y+y+y+3+2

5y+5

Answer:

Total cost of painting the pyramid including the base = 19,200

Total cost of painting the pyramid excluding the base = 12,000

Step-by-step explanation:

Data provided in the question:

Height of the doll = 8 cm

Slant height of the pyramid, s = 5 cm

Base dimensions = 6 × 6

Cost of painting = 200 per cm²

Now,

Area of the base = 6 × 6 = 36 cm²

Area of the Pyramid = Area of the base + [tex]\frac{1}{2} \times P\times s[/tex]

here,

P is the perimeter of the base = 4 × side

= 4 × 6

= 24 cm

Thus,

Area of the Pyramid = 36 + [tex]\frac{1}{2} \times24\times 5[/tex]

or

Area of the Pyramid = 36 + 60 = 96 cm²

Total cost of painting the pyramid including the base = 96 cm² × 200

= 19,200

Total cost of painting the pyramid excluding the base = 60 cm² × 200

= 12,000

Answer:

A function and its inverse

Step-by-step explanation:

The property (fg)(x)= x holds for a function and its inverse.

For instance:

Let

[tex]f(x) = 2x[/tex]

and

[tex]g(x) = \frac{x}{2} [/tex]

These two functions are inverse of each other.

[tex]f(g(x)) = 2( \frac{x}{2} ) = x[/tex]

The correct pair is B: [tex]\(f(x)=\frac{2}{x}\) and \(g(x)=\frac{2}{c}\)[/tex], satisfying [tex]\((f \circ g)(x)=x\).[/tex]

To find which pairs of functions satisfy the condition [tex]\((f \circ g)(x) = x\),[/tex] let's compute [tex]\(f(g(x))\)[/tex] for each pair of functions and see if it equals [tex]\(x\).[/tex]

A. [tex]\(f(x) = x^2\) and \(g(x) = \frac{1}{x}\):[/tex]

[tex]\[f(g(x)) = f\left(\frac{1}{x}\right) = \left(\frac{1}{x}\right)^2 = \frac{1}{x^2}\][/tex]

[tex]\(f(g(x)) \neq x\),[/tex] so option A is not correct.

B. [tex]\(f(x) = \frac{2}{x}\) and \(g(x) = \frac{2}{c}\):[/tex]

[tex]\[f(g(x)) = f\left(\frac{2}{c}\right) = \frac{2}{\frac{2}{c}} = c\][/tex]

[tex]\(f(g(x)) = x\)[/tex] if [tex]\(c = x\).[/tex] So, option B is correct.

C. [tex]\(f(x) = \frac{x - 2}{3}\) and \(g(x) = 2 - 3x\):[/tex]

[tex]\[f(g(x)) = f(2 - 3x) = \frac{(2 - 3x) - 2}{3} = \frac{-3x}{3} = -x\][/tex]

[tex]\(f(g(x)) \neq x\)[/tex], so option C is not correct.

D. [tex]\(f(x) = \frac{1}{2x - 2}\) and \(g(x) = \frac{1}{2x + 2}\):[/tex]

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

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

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

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

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

[tex]\(f(g(x))\)[/tex] does not simplify to [tex]\(x\)[/tex], so option D is not correct.

Thus, the correct answer is option B: [tex]\(f(x) = \frac{2}{x}\) and \(g(x) = \frac{2}{c}\).[/tex]

Complete Question:

For which pairs of functions is (fg)(x)=x?

A. f(x)=x^2 and g(x)=1/x

B.f(x)=2/x and g(x)=2/c

C. f(x)=x-2/3 and g(x)=2-3x

D. f(x)=1/2x-2 and g(x)=1/2x+2

Answer:

B is the answer to the equation

The wheel covered 785 feet in one complete turn

Solution:

Given that, The first Ferris wheel was built in 1893 in Chicago

Diameter of wheel = 250 feet

Let us find the radius of wheel

[tex]Radius = \frac{diameter}{2}\\\\Radius = \frac{250}{2}\\\\Radius = 125[/tex]

Thus radius of wheel is 125 feet

We have to find the distance covered in one complete turn

The number of feet the wheel rotated in one turn is equal to its circumference

The circumference of circle is given as:

[tex]C = 2 \pi r[/tex]

Where, "r" is the radius and [tex]\pi[/tex] is a constant equal to 3.14

Substituting the values we get,

[tex]C = 2 \times 3.14 \times 125\\\\C = 785[/tex]

Thus the wheel covered 785 feet in one complete turn

Answer:

14

Step-by-step explanation:

12+b=26

b=26-12

b=14

Answer:14

Step-by-step explanation:You first want to do 12+12 because that =24 and then keep on adding until u get 26

Answer: 18cm

Step-by-step explanation:

Let original drawing's base be b.

We are using scale factor of 0.4, so

0.4 of b = 7.2cm

0.4 × b = 7.2cm

b = (7.2/0.4)cm

b = 18cm

The base of the original drawing must be 18 cm.

Option B is the correct answer.

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

Scale factor = 0.4.

From the figure,

Original height = 25.6 cm

Original base = b cm

Scale height.

= 25.6 x 0.4

= 10.24 cm

Scale base = 7.2 cm

Now,

Original base.

b x 0.4 = 7.2

b = 7.2 / 0.4

b = 18 cm

Thus,

The base of the original drawing must be 18 cm.

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Answer:

Slope [tex]\dfrac{20}{3}[/tex]

y-intercept [tex]\dfrac{10}{3}[/tex]

Equation [tex]y=\dfrac{20}{3}x+\dfrac{10}{3}[/tex]

150 miles traveled

Step-by-step explanation:

The line shown on the diagram passes through the points (4,30) and (7,50). Find the slope of the line:

[tex]\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{50-30}{7-4}=\dfrac{20}{3}[/tex]

The equation of the line is

[tex]y-30=\dfrac{20}{3}(x-4)\\ \\y=\dfrac{20}{3}x+\dfrac{10}{3}[/tex]

Hence, y-intercept is [tex]\dfrac{10}{3}[/tex]

When [tex]x=22,[/tex] then

[tex]y=\dfrac{20}{3}\cdot 22+\dfrac{10}{3}=\dfrac{440+10}{3}=150\ miles[/tex]

Answer:

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

Step-by-step explanation:

The function notation of a linear function is given by y = f(x) = ax + b.

Now, the given equation is - x + 5y = 5

So, we have to arrange it for the function notation.

Now, - x + 5y = 5

⇒ 5y = x + 5

⇒ [tex]y = \frac{1}{5}(x + 5)[/tex]

⇒ [tex]y = \frac{1}{5}x + 1[/tex]

Therefore, the function notation of the given equation will be

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

Answer:

The slope of the line passing through the given points (-2,-7) and (9,-7) is m=0

Step-by-step explanation:

Given that the line passing through the points (-2,-7) and (9,-7)

To find the slope of the line passing through the points :

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] be the given points (-2,-7) and (9,-7) respectively

Substitute the points in the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-7-(-7)}{9-(-2)}[/tex]

[tex]=\frac{-7+7}{9+2}[/tex]

[tex]=\frac{0}{11}[/tex]

Therefore m=0

Therefore Slope m is 0

Therefore the slope of the line passing through the given points (-2,-7) and (9,-7) is m=0

The number of batches of cookies made is [tex]7\frac{1}{2}[/tex]

Solution:

Given that, baker has 10 cups of sugar to make cookies

Each batch calls for [tex]1\frac{1}{3}[/tex] cups of sugar

To find: Number of batches of cookies can be made

From given information,

Total number of cups of sugar = 10

Cups of sugar for 1 batch = [tex]1\frac{1}{3} = \frac{3 \times 1 + 1}{3} = \frac{4}{3}[/tex]

Therefore, number of batches of cookies can be made is found by dividing the total number of cups of sugar by cups of sugar for 1 batch

Thus we get,

[tex]\text{Number of batches of cookies can be made} = \frac{\text{Total number of cups of sugar}}{\text{Cups of sugar for 1 batch}}[/tex]

Substituting the values, we get

[tex]\text{Number of batches of cookies can be made} = \frac{10}{\frac{4}{3}}\\\\\text{Number of batches of cookies can be made} = 10 \times \frac{3}{4}\\\\\text{Number of batches of cookies can be made} = \frac{15}{2}\\\\\text{In mixed form, we get }\\\\\rightarrow \frac{15}{2} = 7\frac{1}{2}[/tex]

Thus number of batches of cookies made is [tex]7\frac{1}{2}[/tex]

The probability that John will practice his trombone is 34%.

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Given that,

If it rains ​tomorrow, the probability is 0.9. If it does not rain ​tomorrow, there is only a 0.5 chance. And, the chance of rain tomorrow is 70​%.

Calculation of probability:

= 0.9 (0.1) + 0.5 (0.5)

= 0.34

= 34%

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The probability that John will practice his trombone is 0.7 or 70%, calculated using the law of total probability considering the two scenarios of snow and no snow.

To calculate the probability that John will practice his trombone, we need to consider two scenarios: one where it snows and one where it does not. We can solve this by using the law of total probability.

Let's denote the probabilities as follows:
P(Snow) is the probability it will snow, which is given as 0.5.
P(Practice|Snow) is the probability John will practice given that it snows, which is 0.9.
P(Practice|No Snow) is the probability John will practice given that it does not snow, which is 0.5.

The total probability that John will practice is:

P(Practice) = P(Snow) * P(Practice|Snow) + P(No Snow) * P(Practice|No Snow)
          = 0.5 * 0.9 + 0.5 * 0.5
          = 0.45 + 0.25
          = 0.7

Therefore, the probability that John will practice his trombone is 0.7 or 70%.

Answer:

The value of given expression is 3.8.

Step-by-step explanation:

Given:

[tex]1.8+0.5(y+6)-2^3[/tex]

We need to find the simplified value of given expression using y =14

Solution:

Now we will substitute y =14 we get;

[tex]1.8+0.5(y+6)-2^3\\\\1.8+0.5(14+6)-2^3[/tex]

Now using PEDMAS we will first solve the parenthesis we get;

[tex]1.8+0.5\times20-2^3[/tex]

Now we will solve the exponent function we get;

we know that;

[tex]2^3=8[/tex]

So we can say that;

[tex]1.8+0.5\times20-8[/tex]

Now we will solve the multiplication operation.

[tex]1.8+10-8[/tex]

Now we will perform addition operation.

[tex]11.8-8[/tex]

And finally we will perform subtraction operation.

3.8

Hence The value of given expression is 3.8.

Step-by-step explanation:

Given that , the scale on map is 1 : 320000.

Its means that if the scale shows 1 unit  then actual length is 320000 units

So If the  shows 1  cm then the actual distance = 320000 cm

                                                                              =[tex]\frac{320000}{100000}[/tex] km = 3. 2 km

Answer:

5 is greater

Step-by-step explanation:

Answer:

x ≈ 745.5 ft

Step-by-step explanation:

The angle at the lower right of the triangle is 28° ( alternate angle )

Using the sine ratio in the right triangle

sin28° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{350}{x}[/tex]

Multiply both sides by x

x × sin28° = 350 ( divide both sides by sin28° )

x = [tex]\frac{350}{sin28}[/tex] ≈ 745.5 ft ( to the nearest tenth )

Answer:

The points (12,3), (-2,-5) and (1,15) through which the line can pass.

Step-by-step explanation:

A line passes through the point (0, –1) and has a positive slope.

(i) The slope of the line passing through the points (0,-1) and (12,3) will be

[tex]\frac{- 1 - 3}{0 - 12} = \frac{1}{3} > 0[/tex]

(ii) The slope of the line passing through the points (0,-1) and (-2,-5) will be

[tex]\frac{- 1 + 5}{0 + 2} = 2 > 0[/tex]

(iii) The slope of the line passing through the points (0,-1) and (- 3,1) will be

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

(iv) The slope of the line passing through the points (0,-1) and (1,15) will be

[tex]\frac{- 1 - 15}{0 - 1} = 16 > 0[/tex]

(v) The slope of the line passing through the points (0,-1) and (5,-2) will be

[tex]\frac{- 1 + 2}{0 - 5} = - \frac{1}{5} < 0[/tex]

Therefore, the points (12,3), (-2,-5) and (1,15) through which the line can pass. (Answer)

Answer:

A, B, D

Step-by-step explanation:

just took it on edg

The expression 1/4x + 19/4 can be factored by taking out the common factor of 1/4, resulting in the completely factored form (1/4)(x + 19).

The student has asked to factor the expression 1/4x + 19/4 completely. To begin with, we note that both terms in the expression share a common factor of 1/4. Thus, we can factor out this common factor. The expression becomes:

(1/4)(x + 19)

The 1/4 is factored out, and we are left with the binomial x + 19 inside the parentheses. This is the completely factored form of the expression. Remember that factoring is essentially reversing the distribution process. In this case, we took out the common factor of 1/4 that was distributed across the x and 19.

Final answer:

To find the difference between 83456 and 728.88, subtract the second number from the first, resulting in the answer 82727.12.

Explanation:

To find the difference between the two numbers 83456 and 728.88, we simply subtract the second number from the first:

Write the numbers in a vertical column, aligning the digits by place value.

Perform the subtraction, starting from the rightmost digits (the ones place) and moving to the left, borrowing as needed.

Subtract each digit in the smaller number from the corresponding digit in the larger number.

83456
-  728.88
_______
82727.12

The difference is 82727.12.

Answer:

i) the value of a = 0 is non-permissible

ii) the value of b = 0 is non-permissible

Step-by-step explanation:

i) the given expression is [tex]\frac{5a^{2} + 80a }{50ab^{2} }[/tex]

ii) if a = 0 then the expression will become infinity hence the value of a = 0 cannot be used

iii) if b = 0 then the expression will become infinity, hence the value of b = 0 also cannot be used.

iv) In the numerator of the expression if it is factorized we get 5a[tex]\times[/tex] ( a + 16)

    if a = -16 then the value of the expression becomes zero.