Question 11(Multiple Choice)
(05.06 MC)
Using the graph of the function g(x) = log3 (x-4), what are the x-intercept and asymptote of g(x)?

The x-intercept is 3, and the asymptote is located at x = 4.
The x-intercept is 5, and the asymptote is located at x = 4.
The x-intercept is 4, and the asymptote is located at y = 5.
The x-intercept is 5, and the asymptote is located at y = 3.

Answer:

y > 3x + 2

Step-by-step explanation:

The slope is 3.       slope = (-7 - 2)/(-3 - 0) = -9/(-3) = 3

The y-intercept is 2.

The equation of the line is y = 3x + 2

The shading is "above" the line.

Answer: y > 3x + 2

Voluntary sampling is one type of sampling method that is not probability based this means that the survey's findings cannot be reliably extrapolated or generalized.

What is voluntary sampling?

A sample made up of people who freely decided to take part in the sample group is known as a voluntary sampling. Those who want to participate in a voluntary sampling typically do so because they are passionate about the topic of the survey. According to definitions, a sample with self-selected individuals is one that includes voluntary responses.

Researchers who wanted to be able to generalize their findings to the entire community would not choose volunteer sampling because it does not produce a representative sample.

A convenience sample is one that the researcher can use at their discretion, such as voluntary sampling.

However, because only those who have strong opinions about the poll will typically agree to participate, voluntary sampling can result in bias.

The survey's findings cannot be confidently extrapolated or generalized because of the possibility of bias.

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Answer:

A ≈ 75 in²

Step-by-step explanation:

the area (A) of the circle is calculated as

A = πr² ( r is the radius )

here r = 5 and using 3 for π , then

A = 3 × 5² = 3 × 25 = 75 in²

Answer:

75 in^2

Step-by-step explanation:

Since the formula to find the area of a circle is already up, we can use that to solve the question.

The image gave us the value of the radius right away, so the question will be a lot easier to solve.

--> The reason why the radius is needed is that the 'r' in the formula means radius. We need the value of the radius to find the area of the circle.

Now, we can just replace r with 5.

--> A = 25 [tex]\pi[/tex]

Since the question told us to replace [tex]\pi[/tex] with 3, we can do that.

--> A = 25 x 3

--> A = 75

We can conclude that the area of the circle is 75 in^2.

A graph for the data (time and distance) shown in the given table is plotted in the image attached below.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, the data of a linear graph are directly proportional and as such as the value on the x-axis increases or decreases, the values on the y-axis also increases or decreases.

In this exercise, you're required to plot a graph for the data (time and distance) that are recorded for an object that is starting from rest.

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the linear function is given by:

y = 67.814x

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Step-by-step explanation:

I am not sure I can read the original expression right, the picture is too blurry for the small digits.

is it 3^(5/5) ?

or rather 3^(5/6) ?

in any case, you should know that a number written like this always has the structure

a^(b/c)

so,

a = 3

b = 5 (or whatever is the numerator or top of the fraction)

c = 5 (or whatever is the denominator or bottom of the fraction).

the denominator of a fraction in an exponent gives us the grade of root to be taken.

the numerator gives us the power of the base number.

and if the exponent is negative it would mean that the whole thing is a 1/... fraction.

like 3^-2 means 1/3².

Answer: -4, -3, -2

Step-by-step explanation:

By inspection, we know [tex]x=-2[/tex] is a root.

We can thus rewrite the equation as

[tex](x+2)\left(\frac{x^3 + 9x^2 + 26x+24}{x+2} \right)=0\\\\(x+2)(x^2 + 7x+12)=0\\\\(x+2)(x+3)(x+4)=0\\\\x=-4, -3, -2[/tex]

Check the picture below.

so the lateral area of the pyramid is really just the area of four triangles whose base is 10 and height is also 10, now, we're excluding the bottom because that's not lateral area.

[tex]\stackrel{\textit{area of four triangles}}{4\left[\cfrac{1}{2}(\stackrel{b}{10})(\stackrel{h}{10}) \right]}\implies 2(100)\implies \text{\LARGE 200}~ft^2[/tex]

The midpoint between A and E is (0,1)

The coordinates of the cities are given as:

A(-2,3), B(2,7), C(7,8), D(6,3) and E(2,-1).

From the above, we have:

A = (-2,3)

E = (2,-1)

The midpoint between A and E is calculated using

Midpoint = 1/2 * (x1 + x2, y1 + y2)

Substitute the known values in the above equation

Midpoint = 1/2 * (-2 + 2, 3 - 1)

This gives

Midpoint = 1/2 * (0, 2)

Evaluate the product

Midpoint = (0, 1)

Hence, the midpoint between A and E is (0,1)

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Answer:

Q₃ = 185

Step-by-step explanation:

the first step is to find the median of the data set

the median is the middle value of the data arranged in ascending order

112 , 130 , 132 , 140 , 149 , 151 , 163 , 172 , 185 , 190 , 200

                                            ↑ middle value

median = 151

the upper quartile Q₃ is the middle value of the data to the right of the median

163 , 172 , 185 , 190 , 200

                   ↑ middle value

upper quartile Q₃ = 185

Answer:

3,360

Step-by-step explanation:

so, to start with, there are 8 over 5 permutations (the sequence of the picked beads matters, but no repetitions of beads are possible) to pick 5 items out of 8 available ones.

that is

8! / ((8-5)!) = 8! / 3! = 8×7×6×5×4 = 6,720

rotations and reflections are the same thing here for a 1- dimensional sequence.

1 2 3 4 5 rotated around the middle (3) is

5 4 3 2 1

a reflection is again

5 4 3 2 1

so, we need to consider that instead of 8 beads for the first choice we have only 4 beads to choose from to leave the other 4 beads as choices for the last position.

once we have this established, it is sure that the first and the last position cannot have mirrored beads in any permutation. and therefore rotational or reflectional permutations are impossible.

in other words, half of the possible permutations would be rotations/reflections, and we need to eliminate them.

so, the calculation is

4×7×6×5×4 = 8×7×6×5×4/2 = 6,720/2 = 3,360

Step-by-step explanation:

Total Angle in a triangle is 180°

so D = 140 + 25 = 165°

D = 190° - 165° = 15°

Your answer is 15°.

Answer:

angle d = [tex]\boxed{15}^ {\circ}[/tex]

Step-by-step explanation:

The angles in a triangle add up to 180°.

∴ ∠d + 25° + 140° = 180°

⇒ ∠d + 165° = 180°

⇒ ∠d = 180° - 165°

⇒ ∠d = 15°

5. m∠C = 95°

6. m∠C = 70°

7. The other acute angle in the right triangle = 70°

8. m∠C = 70°

9. m∠C = 60° [equilateral triangle]

10. Measure of the exterior angle at ∠C = 110°

11. m∠B = 70°

12. m∠Z = 70°

A triangle is a 3-sided polygon with three sides and three angles. The sum of all its interior angles is 180 degrees. Some special triangles are:

5. m∠C = 180 - 50 - 35 [triangle sum theorem]

m∠C = 95°

6. m∠C = 180 - 25 - 85 [triangle sum theorem]

m∠C = 70°

7. The other acute angle in the right triangle = 180 - 90 - 25 [triangle sum theorem]

The other acute angle = 70°

8.  m∠C = 180 - 55 - 55 [isosceles triangle]

m∠C = 70°

9. m∠C = 60° [equilateral triangle]

10. Measure of the exterior angle at ∠C = 50 + 60

Measure of the exterior angle at ∠C = 110°

11. m∠B = 115 - 45

m∠B = 70°

12. m∠Z = 180 - 35 - 75

m∠Z = 70°

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Answer:

-1

Step-by-step explanation:

Since we have the linear equation, 2x-5, and it's increasing since the slope is positive, that means we want the maximum x-value, to find the maximum y-value, or possible value.

This means, we want to find the maximum x-value of 2x+5 that is less than or equal to 9, and since we want the maximum x-value, we want the right side to also be the maximum, and since we have a less than or equal to symbol, we can have the equation equal to 9, which is the make value. So we get the following equation

[tex]2x+5=9\\[/tex]

Subtract 9 from both sides

[tex]2x=4[/tex]

Divide both sides by 2

[tex]x=2[/tex]

This is the maximum x-value we can get from the inequality, and now we plug this into the equation 2x-5

[tex]2(2)-5[/tex]

4-1

-1

So the maximum value is -1

Answer:

H:182000

L=28000

Step By Step

H=House

L=Lot

H+L=210000

H(6.5)=L

L+(L(6.5)=210000

L=28000

28000(6.5)=H

H:182000

Answer:

1.89

Step-by-step explanation:

34 ÷ (14 − 5) × 2

34 ÷ (9) × 2

34 ÷ 18

1.89

Numerical expression:

numerical expression is a phrase involving numbers.

In mathematics, a numerical expression is a set of numbers that have been written together by utilizing arithmetic operators addition, subtraction, multiplication, and division.

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By  evaluating  the expression 34 ÷ (14 − 5) × 2  we get = 1.89

Children can use the acronym BODMAS to help them remember the proper sequence to carry out mathematical operations when solving problems. The abbreviation BODMAS stands for B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction.

A numerical expression is a sentence that uses numbers. A numerical expression in mathematics is a group of integers that have been combined using the addition, subtraction, multiplication, and division arithmetic operators.

Appling the BODMAS

= 34 ÷ (14 − 5) × 2

= 34 ÷ (9) × 2

= 34 ÷ 18

= 1.89

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9 hours long after the second runner started will the second runner overtake the first runner.

What does it mean to do speed?

Runner I = 6 mph

Runner II = 7 mph

Difference in time= 90 minutes

Train A will have covered 9 miles before Runner II starts

catch up distance= 9 miles

catch up speed = 7-6 mph

catch up speed = 1 mph

Catchup time = catchup distance/catch up speed

catch up time= 9/1

catch up time= 9 hours

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Answer:

D) 14

Step-by-step explanation:

12+12+12 is 36 we don't know hold old the fourth sibling is so they are X

to get the average of 12.5 you need to add all the siblings ages then divide it by 4

(36+X)/4=14 so the other sibling is 14

Answer:

B

Step-by-step explanation:

12.5x3=37.5

37.5 +11.5 =49

49÷4 =12.25

Answer: they can buy about 8 dvds

Step-by-step explanation:

this is because 30 + 66 = 96 and if you do 96 divided by 12 it gives you 8

The quadratic graph which has only one zero among the answer choices as given in the task content is; Choice B; y=x^2+8x+16.

It follows from simplification of quadratic equations in a bid to solve for their zeros by means of factorisation that;

The given quadratic equations in answer choice B can be evaluated for its zeroes as follows;

0=x²+8x+16

0 = x² +4x +4x +16

(x+4) (x+4) = 0

Hence, it follows that x = -4 is the only zero of the given quadratic graph in discuss and hence, Choice B is correct.

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Answer:

x=1.08 (3SF)

Step-by-step explanation:

hope it helps!!!!

Answer:

-1.8

Step-by-step explanation:

its bigger than -9 and -4.2

Answer:5.50 a hour

Step-by-step explanation:

Expected value of playing the game  = $0.8

What is cost ?

Cost of playing = $2

Expected return

10% chance to win $1 = $1  10% = $0.1

25% chance to win back $2 = $2  25% = $0.5

50% chance to win $5 = $5  50% = $2.5

15% chance to lose $2 (being cost) = $2  15% = ($0.3)

= $0.1 + $0.5 + $2.5 - $0.3 = $2.8

Now for this we have to pay fixed cost $2

Thus, expected value of playing game = $2.8 - $2 = $0.8

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Answer: x = 52 m

Step-by-step explanation:

     The formula we will use, which solves for the area of a trapezoid, is [tex]a=\frac{a+b}{2} h[/tex] where a is a base, b is a base, and h is the height.

    We will input the known values, then solve for x.

         [tex]\displaystyle a=\frac{a+b}{2} h[/tex]

         [tex]\displaystyle 1,188\;\text{m}^2=\frac{36\;\text{m}\;+x}{2}*27\;\text{m}[/tex]

         [tex]\displaystyle 1,188\;\text{m}^2=(18\;\text{m}+\frac{x}{2})*27\;\text{m}[/tex]

         [tex]\displaystyle 1,188\;\text{m}^2=486\;\text{m}+\frac{27x}{2}[/tex]

         [tex]\displaystyle 702\;\text{m}^2=\frac{27x}{2}[/tex]

         [tex]\displaystyle 1,404\;\text{m}^2=27x[/tex]

         [tex]\displaystyle x=52\;\text{m}[/tex]

Answer: Choice D

[tex]\frac{-19}{\text{x}-5}[/tex]

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

Work Shown:

[tex]\frac{\text{x}^2+10\text{x}+25}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}+5)}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}+5}{1} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}-5)}{1(\text{x}-5)} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\[/tex]

[tex]\frac{\text{x}^2-25}{\text{x}-5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-(\text{x}^2-6)}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-\text{x}^2+6}{\text{x}-5}\\\\\\\frac{-19}{\text{x}-5}\\\\\\[/tex]

This matches with choice D as the final answer.

Keep in mind that we can only subtract fractions when the denominator is the same. The rule is [tex]\frac{a}{c}-\frac{b}{c} = \frac{a-b}{c}[/tex]

Answer:

The maximum area of the enclosure is 562500 square feet

The function is give as:

V(x) = 1500x - x^2

Differentiate

V'(x) = 1500 -2x

Set to 0

2x = 1500

Divide by 2

x = 750

Substitute x = 750 in V(x) = 1500x - x^2

V(x) = 1500*750 - 750^2

Evaluate

V(x) = 562500

Hence, the maximum area of the enclosure is 562500 square feet

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Based on the given table, the common ratio, explicit formula and temperature of the coffee after 15 minutes is 0.98, Tn = 97 × 0.98^(n-1) and 73.1°C

Common ratio, r = second minutes / first minutes

= 95.1 / 97

= 0.98041237113402

Approximately,

r = 0.98

nth term of the sequence, Tn = ar^n -1

Tn = 97 × 0.98^(n-1)

Temperature of the coffee after 15 minutes, T15 = 97 × 0.98^(n-1)

= 97 × 0.98^(15-1)

= 97 × 0.98^14

= 97 × 0.7536419414749019520643907584

= 73.1032683230654893502459035648

Approximately,

T15 = 73.1°C

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The options C and E is a correct options which are

C. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

According to the statement

we have given that the radius of the clock face is 10 inches and the face of a clock is divided into 12 equal parts.

And we have to choose the three statements which are correct from the given options.

So,

Check the all given options to find the correct options.

So, OPTION A :

360/12=30 degrees between each number

3-1 = 2 2*30 = 60 degrees so A is FALSE

Now, OPTION B:

C=2 x π x r

r=10

using 3.14 for PI = 10*3.14 =31.4 x 2 = 62.8 so B is TRUE

Now OPTION C:

30 x 4 = 120 degrees = TRUE

Now, OPTION D:

10-3 = 7

7/12 x 62.8 = 0.5833*62.8 = 36.63 inches = FALSE

Now, OPTION E:

1/12=0.0833 x 62.8 = 5.23 rounded to 5.2 = TRUE

So, The options C and E is a correct options which are

C. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

Disclaimer: This question was incomplete. Please find the full content below.

Questions:

The face of a clock is divided into 12 equal parts. The radius of the clock face is 10 inches. Assume the hands of the clock will form a central angle.

Which statements about the clock are accurate? Check all that apply.

A. The central angle formed when one hand points at 1 and the other hand points at 3 is 30°.

B. The circumference of the clock is approximately 62.8 inches.

C.The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

D. The length of the major arc between 3 and 10 is approximately 31.4 inches.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

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