Given the functions f(x) = 3x - 1 and g(x) = 3x + 4, which operation results in the smallest coefficient on the x term?

Answer:

slope(m) is -4

Step-by-step explanation:

[tex]m=\frac{-17-(-1)}{5-1} \\\\m=\frac{-16}{4} \\\\m=\frac{-4}{1} \\\\m=-4[/tex]

now substitute with one of the points

y=mx+b

-1=-4+b

+4  +4

3=b

now you have both m and b

y=-4x+3

i'm going to assume (3,1)(3,1) was a typo.

here is an equation for a line with a slope of (-4/3) that crosses through (3,1)

y = -4/3x + 5;

steps;

1 = -4/3(3)+ b

1 = -4 +b

5 = b

Answer:i'm going to assume (3,1)(3,1) was a typo.

here is an equation for a line with a slope of (-4/3) that crosses through (3,1)

y = -4/3x + 5;

steps;

1 = -4/3(3)+ b

1 = -4 +b

5 = b

Step-by-step explanation:

The perimeter of the semi-circle is 59.1 cm

In this question, we have been given the diameter if the semi-circle

d = 23 cm

We need to find the perimeter of the semi-circle.

We know that, the perimeter of the semi-circle of radius 'r' is P = πr + 2r

For diameter d = 23 cm, the radius would be,

r = 11.5 cm

So, the perimeter would be,

P = πr + 2r

P = π × 11.5 + 2 × 11.5

P = (π + 2) × 11.5

P = 59.13 cm

Therefore, the perimeter of the semi-circle is 59.1 cm

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Answer:

1075

Step-by-step explanation:

4300x0.25

Answer:

No, because any number than produces and decimal that continuse forever is not rational.

Step-by-step explanation:

Hope it helps! =D

18 inches=  1 1/2 feet= 1.5 feet

18 inches = 1.5 feet

what is distance ?

Distance is a numerical or occasionally qualitative measurement of how far apart objects or point are . it is a total movement of an object without any regard to direction.

(1) Now we make a proportion to find feet for given inches

   feet/inches = feet / inches

   1.5/18 = x/36

   1.5 * 36 = 18*x

   54 = 18 x (Divide by 18 on both sides)

    x = 3

    3 feet long is a 36 inch board

 (2) 72 inch board

      1.5 * 72 = 18*x

      108 = 18 x (Divide by 18 on both sides)

       x = 6

      6 feet long is a 72 inch board

(3) 144 inch board

     1.5 * 144 = 18*x

     216 = 18 x (Divide by 18 on both sides)

      x = 12

      12 feet long is a 144 inch board

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Main Answer:

[tex]x=\frac{-2\±\sqrt{10}}{3}[/tex]

Explanation:

The given equation is,

[tex]3x^{2} +4x=2[/tex]

The

The quadratic formula to find the value of x for the equation [tex]ax^{2} +bx+c=0[/tex]  is,

[tex]x=\frac{-b\±\sqrt{b^{2}-4ac}}{2a}[/tex]

The values are,

a = 3, b = 4, c = -2

Now, substitute the values of a, b and c

[tex]x=\frac{-4\±\sqrt{(4)^{2}-4(3)(-2)}}{2(3)}[/tex]

[tex]x=\frac{-4\±\sqrt{16-12(-2)}}{6}[/tex]

[tex]x=\frac{-4\±\sqrt{40}}{6}[/tex]

[tex]x=\frac{-4\±2\sqrt{10}}{6}[/tex]

[tex]x=\frac{2(-2\±\sqrt{10})}{6}[/tex]

[tex]x=\frac{-2\±\sqrt{10}}{3}[/tex]

A ball's position, in meters, as it travels every second is 282.5 sec.

Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation. The sum is the entire value, and the addends are the integers that are being added. The mathematical operation of addition is the process of adding two or more numbers together to determine the total, or sum.

Given that,

The position function s(t) = 2.3t² + 225.

The velocity of the ball after 5 seconds is

s(t) = 2.3t² + 225.

t= 5

s(5) = 2.3(5)² + 225.

s(5) = 2.3(25) + 225.

s(5)= 57.5+ 225

s(5)= 282.5

Therefore,  it travels every second is 282.5 sec.

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The numerical value of x in the two congruent alternate exterior angles is 20.

Alternate exterior angle theorem states that "if a transversal intersects two parallel lines, the alternate angle s formed are congruent.

From the diagram, the two angles forms an alternate exterior angle , the two angles are congruent.

( 5x - 8 ) = ( 3x + 32 )

Solve for x

5x - 8 = 3x + 32

Collect like terms by moving all terms containing variable x to left and the constant terms to the right side of the equation.

5x - 8 = 3x + 32

5x - 3x = 32 + 8

2x = 40

Divide both sides by 2

2x/2 = 40/2

x = 40/2

x = 20

Therefore, the numerical value of x is 20.

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Answer:

1) 180°-105°-29°

=46° (angles in ∆)

2) 180-78-55

180-78-55 =47° (angle ²)

then angle ¹ is

180-78-47

=55° (angles on a straight line)

3) I just realised I solved angle 2 so I'll make the answer bold for you :)

I hope this is correct lol

We have a vertical and a horizontal lines, the equations are:

Line A: x = -5  (vertical one)

Line B: y = -5  (horizontal one)

Remember that the general linear equation in the slope-intercept form is:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Now, line A passes through  (–5, –2), (–5, 7), then the slope is:

a = (7 + 2)/(-5 + 5) = 9/0

Notice that if we divide by zero, the slope tends to infinity, so we have a vertical line.

In this case, the line A will be x = -5.

Now line B passes through points: (7, –5), (–2, –5)

Then the slope is:

a = (-5 + 5)/(-2 - 7) = 0/-9 = 0

Then the line is:

y = 0*x + b

And passes through (7, –5), then:

-5 = 0*7 + b

-5 = b

So this line is y = -5.

Concluding, we have:

Line A: x = -5

Line B: y = -5

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Answer:

Line A: no slope

The equation of line A is x = -5

Line B has a slope of 0

The equation of line B is y = -5

Step-by-step explanation:

I did it already :)

The greatest common factor, GCF, of the given terms is 2a⁴b

From the question, we are to determine the GCF of the given expressions. GCF means Greatest common factor

The given expressions are 18a^4b^9c^2 and 34a^6b^5 and 22a^8bc^7

First, we will write the expressions properly

The given expressions are 18a⁴b⁹c² and 34a⁶b⁵ and 22a⁸bc⁷

To determine the GCF of the expressions, we will express each one of them as a product of their factors

That is,

18a⁴b⁹c² = 2 × 3 × 3 × a × a × a × a × b × b × b × b × b × b × b × b × b × c × c

34a⁶b⁵ = 2 × 17 × a × a × a × a × a × a × b × b × b × b × b

22a⁸bc⁷ = 2 × 11 × a × a × a × a × a × a × a × a × b × c × c × c × c × c × c × c

Hence, the GCF is 2 × a × a × a × a × b = 2a⁴b

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The equation of each line using function notation is:

1. C. f(x) = 3x - 1.

2. D. f(x) = x.

3. D. f(x) = 4x + 4.

4. B. f(x) = -3/2x - 2

To use function notation, substitute the value of the slope (m) and the value of the y-intercept (b) into f(x) = mx + b.

Slope (m) = rise/run.

Y-intercept (b) is the point on the y-axis when the line intercepts the y-axis.

1. Slope (m) = rise/run = 3/1

Slope (m) = 3

Y-intercept (b) of the line = -1.

Substitute m = 3, and b = -1 into f(x) = mx + b:

f(x) = 3x - 1

The equation is: C. f(x) = 3x - 1.

2.  Slope (m) = rise/run = 2/2

Slope (m) = 1

Y-intercept (b) of the line = 0.

Substitute m = 1, and b = 0 into f(x) = mx + b:

f(x) = (1)x + 0

f(x) = x

The equation is: D. f(x) = x.

3. Slope (m) = rise/run = 4/1

Slope (m) = 4

Y-intercept (b) of the line = 4.

Substitute m = 4 and b = 4 into f(x) = mx + b:

f(x) = 4x + 4

The equation is: D. f(x) = 4x + 4.

4. Slope (m) = rise/run = -3/2

Slope (m) = -3/2

Y-intercept (b) of the line = -2.

Substitute m = -3/2 and b = -2 into f(x) = mx + b:

f(x) = -3/2x - 2

The equation is: B. f(x) = -3/2x - 2

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-3/2<h<0 is the answer.

Given,

1+5h <h+1 <7+5h

Solution:

1+5h <h+1 <7+5h

If a < u <b, then a<u , u<b

Therefore,

1+5h <h+1  and h+1 <7+5h

1+5h <h+1

1+5h= h+1

4h = 0

h = 0

Therefore,

h<0

h+1 <7+5h

h+1 = 7+5h

4h = -6

h = -3/2

h > -3/2

Combine the intervals

h<0 and h> -3/2

By combining the above two, we get

-3/2<h<0

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The function table should be completed as follows:

x                h(x)__

-4               -8

-3               -5

2                 10

4                 16

5                 19

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.

Next, we would evaluate the given function by substituting the value of x as follows:

When x = -4, we have:

Function, h(x) = 3x + 4

Function, h(-4) = 3(-4) + 4

Function, h(-4) = -12 + 4

Function, h(-4) = -8

When x = -3, we have:

Function, h(x) = 3x + 4

Function, h(-3) = 3(-3) + 4

Function, h(-3) = -9 + 4

Function, h(-3) = -5

When x = 2, we have:

Function, h(x) = 3x + 4

Function, h(2) = 3(2) + 4

Function, h(2) = 6 + 4

Function, h(2) = 10

When x = 4, we have:

Function, h(x) = 3x + 4

Function, h(4) = 3(4) + 4

Function, h(4) = 12 + 4

Function, h(4) = 16

When x = 5, we have:

Function, h(x) = 3x + 4

Function, h(5) = 3(5) + 4

Function, h(5) = 15 + 4

Function, h(4) = 19

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Answer: angle CPB is an acute angle.

Answer: C. ∠CPB is the correct answer.

Step-by-step explanation:

Answer:

The test where Ella got 13/15 has the higher ratio of correctly spelled words to total words.

Step-by-step explanation:

On the last week's test, Ella got a 16/20, which equates to 80% correctly spelled words compared to total words. On this week's test, she got a 13/15, which equates to 86.6% correctly spelled words compared to total words. Since 86.6 > 80, the test where Ella got a 13/15 has the higher ratio.

The average fraction of students in  Mr. Zanker's class and  Mr. Haynes  who went on the field trip is 11/8.

From the question, the fraction of the students in Mr. Zanker's class that attended the field trip is  3/4.

The  fraction of the students in  Mr. Haynes class that attended the field trip is 5/8 .

Then the we can calculate the average fraction of student in the class of the two teacher is

= (3/4 + 5/8) = 11/8.

Therefore, the average fraction of the number of the student can be calculated as 11/8.

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Answer:

c

Step-by-step explanation:

[tex]a) (1/6)^{-8}=6^8>1 \\ \\ b) (5^{-4})^{-9}=5^{36}>0 \\ \\ c) 2^{-3}=1/8<1 \\ \\ (d) \frac{6^{-4}}{6^{-5}}=6>1[/tex]

The exact solution and its approximation rounded to two decimal places are 2. 6213 and 2. 62 respectively.

An algebraic expression can be described as a mathematical or arithmetic expressions that is composed of arithmetic terms, factors, constants, variables, and coefficients.

These expressions are also made up of arithmetic operations which includes;

From the information given, we have that;

(2x − 1)^2 = 18

Find the square root of both sides, we have;

√(2x − 1)^2 = √18

Note that square root rules out the square, we have;

2x - 1 = 4. 24264

collect like terms

2x = 4. 24264 + 1

2x = 5. 24264

Make 'x' the subject

x = 5. 24264/2

x = 2. 6213

Hence, the value is 2. 6213

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Answer:

Step-by-step explanation:

The differences-of-means ​estimator, denoted by E(Y|X=1) -E(Y|X=0), is an estimator of the causal effect of X on Y because the differences-of-means estimator​ estimates that (A) the change in the expectation of Y as a result of an observation being in the treatment group as opposed to the control group.

So, in the given situation: The differences-of-means estimator estimates the change in the expectation of Y as a result of an observation being in the treatment group as opposed to the control group, and is denoted by E(Y|X=1) -E(Y|X=0).

Therefore, the differences-of-means ​estimator, denoted by E(Y|X=1) -E(Y|X=0), is an estimator of the causal effect of X on Y because the differences-of-means estimator​ estimates that (A) the change in the expectation of Y as a result of an observation being in the treatment group as opposed to the control group.

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The complete question is given below;
Suppose you have a binary randomized controlled experiment designed to measure the causal effect of X on Y. Let the control group be identified by X​ = 0 and the treatment group by X​ = 1.

The differences-of-means ​estimator, denoted by E(Y|X=1) -E(Y|X=0), is an estimator of the causal effect of X on Y because the differences-of-means estimator​ estimates:

A. the change in the expectation of Y as a result of an observation being in the treatment group as opposed to the control group.

B. the expectation of Y for observations within the control group.

C. the expectation of Y for observations within the treatment group.

D. All of the above.

Six students measure the acceleration of an object in free fall. The students want to state that the absolute deviation for each measured value x from the mean is at most d is 0.86.

The average of absolute deviations from a central point makes up the average absolute deviation (AAD) of a data collection. It is a statistical summary of the statistical variability or dispersion. A mean, median, mode, or the result of any other central tendency measure or any reference value associated with the specified data set can all serve as the central point in the general form. The mean absolute deviation and the median absolute deviation are part of AAD (both abbreviated as MAD).

Find the mean of the data set first, then use that value to calculate the mean absolute deviation of the data. Divide the total number of data values by the sum of the individual data values. Assess the magnitude of the absolute difference between each data point and and the mean.

The measured data is

x = [10.56, 9.52, 9.73, 9.80, 9.78, 10.91]

There are 6 measurements.

Calculate the mean.

m = (10.56+9.52+9.73+9.80+9.78+10.91)/6 = 10.05

Calculate deviations from the mean.

y = |x - m|

  = [0.51, 0.53, 0.32, 0.25, 0.27, 0.86]

The greatest deviation from mean is d = 0.86.

Calculate the average absolute deviation.

(0.51+0.53+0.32+0.25+0.27+0.86)/6 = 0.4567

The answer is: d = 0.86

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Answer:

44, 54, 82. Acute

Step-by-step explanation:

x + x + 10 + 2x - 6 = 180 (Triangle Sum Theorem)

4x + 4 = 180 (Combine Like Terms)

4x = 176 (Subtraction Property of Equality)

x = 44 (Division Property of Equality)

Now that we have found the value of x, we need to substitute it with the provided angles.

∡1 = x = 44°

∡2 = x + 10 = 54°

∡3 = 2x - 6 = 2(44) - 6 = 82°

So, the answer is an Acute triangle (Option 4).

Value of x is 2 and value of k is 0.999.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.

Given Data

At t=0, Water Volume is 3,000 Litres

The volume of water in the tank equals t hours later.

As it is also stated, there is x% less water in the tank at the conclusion of every hour than there was at the beginning.

After an hour, the amount of water is equal to 3,000 - = 3,000 - 30 x

Water consumption after two hours = (3,000 - 30 x) - (3,000 - 30 x)

×= (3,000 - 30 x) (3,000 - 30 x)

Also,

= 288120

⇒300000 - 3000 x - 3000 x + 30 x²

= 288120

⇒ 30 x ² - 6,000 x + 11880= 0

When we multiply both sides by 30, we get

⇒ x² - 200 x + 396=0

reducing the quadratic equation to factors

(x -198)(x-2) = 0

x = 198,

x = 2

Which suggests that x = 2 might be the answer to this equation.

Also,

V₁ = 3000- 30(2)

V₁ = 3000 - 60

V₁ = 2940

k = [tex]\frac{2940}{3000}[/tex]

k = 0.999(approximately)

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The time shown by the speedometer with speed of 10 m/s is 1 s.

The time shown by the speedometer with speed of 20 m/s is 1 s.

The time shown by the speedometer with speed of 30 m/s is 1 s.

The time read by the speedometer is given as;

t = 3 s.

The speedometer has low precision and as such we can do value approximation.

For the speedometer showing the speed 10 m/s. The time is calculated as, t = (v - u)/g

where g = 10 m/s²

t = (10 - 0)/10

t₁ = 1 seconds

For the speedometer showing the speed 20 m/s. The time is calculated as, t = (v - u)/g

where g = 10 m/s²

t = (20 - 0)/10

t₂ = 2 seconds

For the speedometer showing the speed 30 m/s. The time is calculated as, t = (v - u)/g

where g = 10 m/s²

t = (30 - 0)/10

t₂ = 3 seconds

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Answer:

A

Step-by-step explanation:

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