50 Points! Multiple choice algebra question. Photo attached. State the number of real zeros for the function whose graph is shown. Thank you!

The correct statements that apply to the given limits are:

Option A: Multiply by (√(x + 2) + 3)/(√(x + 2) + 3)

Option D: "Divide out a common factor of x - 7."

Option E: The limit of the given expression is 1/6.

Option: We generally multiply by the conjugate of the expression to eliminate square roots in simplification. Thus, option A applies.

Option B: Get x - 1 in the numerator:

This statement is not correct. The expression does not involve x - 1 in the numerator.

Option C: Get (x - 7)(√(x + 2) - 3) in the denominator:

This statement is not correct due to the fact that we want to simplify the expression, and not introduce a more complex denominator.

Option D: Divide out a common factor of x - 7:

This statement is correct because by factoring out (x - 7) from both the numerator and denominator, we can cancel out the common factor.

Option E: Calculate the limit as 1/6:

After canceling out the common factor of x - 7, the simplified expression becomes:

lim x -> 7 (√(x + 2) - 3)/(x - 7)

= lim x -> 7 1/(√(x + 2) + 3)

To find the limit, we substitute the value x = 7 into the simplified expression:

lim x -> 7 1/(√(7 + 2) + 3) = 1/(√(9) + 3) = 1/(3 + 3) = 1/6

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The numerical value of the logarithm expression that is [tex]log\frac{a^2}{b^4c^4}[/tex] is 10 when log a = -1, log b = -6 and log c = 3.

Given that,

We have to find the numerical value of the logarithm expression that is [tex]log\frac{a^2}{b^4c^4}[/tex] when log a = -1, log b = -6 and log c = 3.

We know that,

The use of a logarithm can be applied to solve issues that cannot be resolved using the concept of exponents simply. A logarithm is simply a different way to define exponents.

So,

Take the logarithm expression that is [tex]log\frac{a^2}{b^4c^4}[/tex]

= [tex]log\frac{a^2}{b^4c^4}[/tex]

= log a² - log(b⁴c⁴)            [ from [tex]log\frac{x}{y}[/tex] = log x-log y ]

= log a² - (log b⁴ + log c⁴)     [ from log (xy) = log x + log y ]

= 2log a  - 4log b - 4log c       [ from log xⁿ = nlog x ]

= 2( -1) - 4(-6) - 4(3)

= -2 + 24 - 12

= 24 - 14

= 10

Therefore, The numerical value of the logarithm expression that is [tex]log\frac{a^2}{b^4c^4}[/tex] is 10.

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The value of the given limit expression is 1.

Given is limit expression [tex]\lim _{x\to \infty }\left(x^{\frac{1}{3x}}\right)[/tex], we need to use L’Hôpital’s Rule to solve it,

So,

[tex]\lim _{x\to \infty \:}\left(x^{\frac{1}{3x}}\right)[/tex]

Using the exponent rule,

[tex]=\lim _{x\to \infty \:}\left(e^{\frac{1}{3x}\ln \left(x\right)}\right)[/tex]

Applying the chain rule,

[tex]\lim _{x\to \infty \:}\left(e^{\frac{1}{3x}\ln \left(x\right)}\right) = 1[/tex]

Hence the value of the given limit expression is 1.

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Assuming [tex]f(x)=x^2[/tex].

[tex]y=x^2\\x=-\sqrt y \vee x=\sqrt y[/tex]

Since [tex]x\geq0[/tex] only [tex]x=\sqrt y[/tex] is valid.

Therefore

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

The total area of the regions between the curves is 389.0 square units

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

f(x) = x⁴ - 12x³ + 48x²

g(x) = 44x + 105

With the use of graphs, the curves intersect ar

x = -1 and x = 5

So, the area of the regions between the curves is

Area = ∫x⁴ - 12x³ + 48x² - 44x - 105

This gives

Area = ∫x⁴ - 12x³ + 48x² - 44x - 105

Integrate the expression

Area =  x * (x⁴ - 15x³ + 80x² - 110x - 525)/5

Recall that x = -1 and x = 5

So, we have

Area =  (-1) * ((-1)⁴ - 15(-1)³ + 80(-1)² - 110(-1) - 525)/5  - (5) * ((5)⁴ - 15(5)³ + 80(5)² - 110(5) - 525)/5

Evaluate

Area =  388.8

Approximate

Area =  389.0

Hence, the total area of the regions between the curves is 389.0 square units

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The area of the object in the image shown in the attachment below is calculated as: 62 cm².

The area of the object can be found by decomposing the figure into two rectangles - larger rectangle and smaller rectangle.

Area of the larger rectangle = length * width

Length of the larger rectangle = 5 cm

Width of the larger rectangle = 4 cm

Area of the larger rectangle = 5 * 4 = 20 cm²

Area of the smaller rectangle = length * width

Length of the larger rectangle = 7 cm

Width of the larger rectangle = 6 cm

Area of the larger rectangle = 7 * 6 = 42 cm²

Area of the object = 20 + 42 = 62 cm².

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The probability of rolling a sum from 2 to 12 on 2 dices is 100%

Given the data,

The two dice should be rolled.

Now, there are 36 possibilities that might occur while rolling two normal six-sided dice. The reason for this is that when rolling two dice, the total number of outcomes is the product of the numbers of outcomes for each die, and each die has six potential outcomes (numbers 1 through 6).

The resultant 36 results are as follows:

1-1, 1-2, 1-3, 1-4, 1-5, 1-6

2-1, 2-2, 2-3, 2-4, 2-5, 2-6

3-1, 3-2, 3-3, 3-4, 3-5, 3-6

4-1, 4-2, 4-3, 4-4, 4-5, 4-6

5-1, 5-2, 5-3, 5-4, 5-5, 5-6

6-1, 6-2, 6-3, 6-4, 6-5, 6-6

When using two dice, there are a total of 36 possibilities that might occur.

As a result, the results' total ranges from 2 to 12.

Hence , the probability is 100 %

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The value of the composite function (f . g)(1) when evaluated is 6

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

The graph of the function f(x)

Also, we have

The graph of the function g(x)

The composite function (f . g)(1) is calculated as

(f . g)(1) = f(1) * g(1)

From the graph, we have the following values

f(1) = -2

Also, we have

g(1) = 3

So, we have

(f . g)(1) = 2 * 3

Evaluate

(f . g)(1) = 6

Hence, the composite function (f . g)(1) when evaluated is 6

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Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{40}\\ a=\stackrel{adjacent}{ST}\\ o=\stackrel{opposite}{24} \end{cases} \\\\\\ ST=\sqrt{ 40^2 - 24^2}\implies ST=\sqrt{ 1600 - 576 } \implies ST=\sqrt{ 1024 }\implies ST=32 \\\\[-0.35em] ~\dotfill\\\\ \tan(S )=\cfrac{\stackrel{opposite}{24}}{\underset{adjacent}{32}} \implies \tan(S )=\cfrac{3}{4}[/tex]

The area of the shaded region, to the nearest hundredth can be calculated as approximately: 1,195.71 mm².

The area of the shaded region can be found using the area of circle, which is: Area = πr²

Therefore, area of the shaded region = area of larger circle - area of smaller circle.

Area of larger circle:

radius (r) = 14 + 6.6 = 20.6 mm

Area of larger circle = 3.14 * 20.6² = 1,332.4904 mm²

Area of smaller circle:

radius (r) = 6.6 mm

Area of larger circle = 3.14 * 6.6² = 136.7784 mm²

Area of the shaded region = 1,332.4904 - 136.7784 = 1,195.71 mm².

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Answer:

16 x 15 x 14 = 3,360

1: The required table is described below.

2: The range is (0,36)

3: X-intercepts are (-6,0) and (6,0) and the Y-intercept is (0,36)

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

We are given that,

y = -x² + 36

The equation of the rainbow is represented by the parabola,

Now, we are required to find a linear equation which cuts the graph of the parabola at two points.

Let us consider the equation joining the points (-6,0) and (0,36), given by .

y = 6x + 36

So, the corresponding table for the linear equation is given by,

x            y = 6x + 36

-6                      0

0                       36

1                        42

6                       72

Now, we will answer the questions corresponding the functions.

1. Domain and Range of the rainbow.

Since, the equation of the rainbow is

y = -x² + 36

So, from the figure, we get that,

Domain is the set of all real numbers.

Range is the set {y | y ≤ 36}

Here, domain represents the points which are used to plot the path of the rainbow and range represents the points which are form the rainbow.

Not all points make sense in the range as the parabola is opening downwards having maximum point as (0,36).

2. X and Y-intercepts of the rainbow.

As, the 'x and y-intercepts are the points where the graph of the function cuts x-axis and y-axis respectively i.e. where y=0 and x=0 receptively'.

We see that from the figure below,

X-intercepts are (-6,0) and (6,0) and the Y-intercept is (0,36)

Here, these intercepts represents the point where the parabola intersects the individual axis.

3. Is the linear function positive or negative.

As the linear function is  represented by the upward flight of the drone.

So, the linear function is a positive function.

y = 6x + 36

4. The solution of the system of equations is the intersection points of their graphs.

So, from the figure, we see that the equations intersect at the points (-6,0) and (0,36).

Thus, the solution represents the position when both the drone and rainbow intersect each other.

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Bill's share = $56 Therefore, Bill received $56.

Let's start by setting up some equations based on the given information:

David's share = 1/7 * (Alex's share + Bill's share + Carl's share)

Alex's share = 3/4 * (Bill's share + Carl's share)

Bill's share = 2/5 * Carl's share

The sum of all four shares is $168.

We can use the fourth equation to solve for one of the shares in terms of the others:

Alex's share + Bill's share + Carl's share + David's share = $168

Alex's share + Bill's share + Carl's share = $168 - David's share

Substituting the other equations into this expression, we get:

Alex's share + (2/5 * Carl's share) + Carl's share + (1/7 * (Alex's share + (2/5 * Carl's share) + Carl's share)) = $168

Simplifying this equation, we get:

(8/7) * Alex's share + (22/35) * Carl's share = $168

Now we can use the other equations to solve for Carl's share, and then for Bill's share:

From Bill's share = 2/5 * Carl's share, we get Carl's share = (5/2) * Bill's share

From Alex's share = 3/4 * (Bill's share + Carl's share), we get Alex's share = (3/4) * ((7/2) * Bill's share) = (21/8) * Bill's share

Substituting these expressions into the equation we derived earlier, we get:

(8/7) * (21/8) * Bill's share + (22/35) * (5/2) * Bill's share = $168

3 * Bill's share = $168

Bill's share = $56

Therefore, Bill received $56.

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The solution to the system of linear equations is (14, 16/3).

To find the solution to the given system of linear equations, we can use the method of substitution. First, we can solve the second equation for y by dividing both sides by 3, which gives us y = 16/3. .

We can then substitute this value of y into the first equation and solve for x. This gives us x - 3(16/3) = -2, which simplifies to x = 14. This point represents the intersection of the two lines, where they cross over each other on the coordinate plane.

The other answer choices given in the question are not valid solutions to the system of equations.

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Answer:

C

Step-by-step explanation:

Answer:

1/4, 4/7, 2/3, 1/2

Step-by-step explanation:

Applying the inscribed angle theorem, the indicated measures in the circle are: a) m<JIK = 51°; b) m<KJL = 51°.

Recall that the measure of an intercepted arc is equal to twice the measure of an inscribed angle, based on the inscribed angle theorem.

We are given the following:

m(IJ) = 78°

m<IJL = 39°

Therefore, we have:

a. m<JIK = 1/2(m(JK)) [based on the inscribed angle theorem]

m(JK) = 180 - m(IJ)

m(JK) = 180 - 78 = 102°

Thus:

m<JIK = 1/2(102)

m<JIK = 51°

b. m<KJL = 1/2(m(KL) [based on the inscribed angle theorem]

m(IL) = 2(IJL)

m(IL) = 2(39) = 78°

m(KL) = 180 - m(IL) = 180 - 78

m(KL) = 102°

m<KJL = 1/2(m(KL) = 1/2(102)

m<KJL = 51°

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Complete Question:

In the circle below, IK is a diameter. Suppose m(IJ) = 78° and m(IJL) = 39°. Find the following.

a. m<JIK

b. m<KJL

Missing image is attached below.

The mean score of the test is 7.13.

The median score of the test is 7.

To get mean score, we have to multiply each test score by its corresponding frequency, sum up products and then divide by the total frequency.

Mean score = EF/ n

Mean score = (34 + 41 + 50 + 63 + 73 + 85 + 91 + 106) / (4 + 1 + 0 + 3 + 3 + 5 + 1 + 6)

= (12 + 4 + 0 + 18 + 21 + 40 + 9 + 60) / 23

= 164 / 23

= 7.13

To find the median score, we will arrange the scores in ascending order: [tex]3, 4, 4, 4, 4, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10.[/tex]

Since there are 23 scores, the median will be the 12th score (in the middle). So, the median score = 7.

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Answer:

To find the z-score of a data value, we use the following formula:

z = (x - μ) / σ

where z is the z-score, x is the data value, μ is the mean of the distribution, and σ is the standard deviation.

Given a normal distribution with a mean (μ) of 146 and a standard deviation (σ) of 4, and a data value (x) of 153, we can plug these values into the formula:

z = (153 - 146) / 4

z = 7 / 4

z = 1.75

Thus, the z-score of the data value 153 is 1.75.

The domain of y = cot x is (d) all x ≠ kπ, where k is an integer

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

y = cot x

The domain of the function y = cot x is the set of input values the function can take

As a general rule

The function y = cot x is undefined at the points x = πk where x is an integer

This means that the domain of the function is the set of all real numbers except x = πk

Hence, the domain of y = cot x is (d)

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Answer:

y = 4 - 1.25x

Step-by-step explanation:

5x + 4y = 16

subtract 5x from both sides

4y = 16 - 5x

divide all by 4

y = 4 - 1.25x

The calculated full capacity of the tank is 90 liters

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

Proportion = 4/5

This is represented as

Size = 72 liters

Using the above as a guide, we have the following:

4/5 * x = 72 liters

Where

x = the full capacity of the tank

So, we have

x = 72 * 5/4

Evaluate

x = 90

Hence, the full capacity of the tank is 90 liters

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Based on proportions, if a lorry tank was ⁴/₅ full of petrol when the gauge indicates 72 liters, the full capacity of the tank is 90 liters.

Proportion refers to the fraction or portion of a whole value, quantity, or number.

Proportions are ratios equated to each other.

We can depict proportions using fractions, decimals, or percentages.

The fraction of the lorry tank of petrol = ⁴/₅ (0.80)

If ⁴/₅ = 72 liters, proportionately, the full tank = 90 liters (72 ÷ 0.80)

Thus, we can conclude that when the lorry tank is full the quantity of petrol in it is 90 liters.

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Answer:

The range is the difference between the highest and lowest values in a set of data. In this case, the range is 15 - 1 = 14.

The interquartile range (IQR) is the difference between the third and first quartiles of a set of data. The first quartile (Q1) is the middle value of the lower half of the data, and the third quartile (Q3) is the middle value of the upper half of the data. In this case, the IQR is Q3 - Q1 = 12 - 5 = 7.

There are no outliers in this data set. An outlier is a data point that is significantly different from the rest of the data points. In this case, all of the data points are within 14 of the mean, which is 8.5. Therefore, there are no outliers.

Here is a summary of the range and IQR of the data set:

Range: 14

IQR: 7

Step-by-step explanation:

Answer: Range: 14 IQR: 7

Step-by-step explanation:

If in a large population, about 70% of families have a pet. A researcher takes a random sample of 6 families and surveys whether they have a pet. The probability of families that have a pet is: 0.0595.

Number of trial=  6

Probability of success = 0.7

Probability of failure = 1 - 0.7 = 0.3

Probability that exactly 2 of the families have a pet

Let make us of binomial distribution formula to determine the probability

P(X = 2) = (6 choose 2) * 0.7² *[tex]0.3^{4}[/tex]

= 15 * 0.49 * 0.0081

= 0.0595

Therefore the probability  is 0.0595.

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answer :

median or 37

explanation :

median is not influenced by an outlier like 65 in the dataset

steps :

to get the median

arrange the weights in order from smallest to largest:

34, 35, 35, 37, 37, 37, 38, 39, 65

median = middle value = 37

37 has :

four weights before it &

four weights after it

so the median weight is 37 pounds.

Point K is located at 3.5 on the number line.

To find point K on the number line, we need to apply the ratio LK to KM, which is 6:3. First, we can simplify this ratio to 2:1.

Next, we will find the total distance between points L and M. The distance LM = 6.5 - (-2.5) = 9 units.

Now, we can divide this distance into 3 equal parts, as per the simplified ratio 2:1. Each part will be 9/3 = 3 units long.

Since LK is 2 parts of the ratio, we will multiply the length of one part (3 units) by 2. LK = 3 * 2 = 6 units.

Finally, we'll find the coordinates of point K by adding the length of LK to the coordinate of point L. So, K = -2.5 + 6 = 3.5.

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Answer:

Point K is at 3.5

Step-by-step explanation:

I just took the test

The greatest common factor is 3C and GCF form of polynomial is 3c(c² - 3).

The given polynomial is

6c³-9c

We can write it as;

3c(c² - 3)

We know that

The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor (HCF) is another name for it.

Therefore 3c is its GCD.

Divide each term of polynomial 3c,

6c³ ÷ 3c = 2c² and  -9c ÷ 3c = -3

Thus,

3c(c² - 3) is the factored version of the polynomial with the highest common factor.

Also if GCD is 1 then after dividing each term by 1 we get same result

thus the polynomial be 3c(c² - 3).

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The cost of covering 1 unit² should be $2.477 to be in the budget and the total area to be covered is 3027.22 ft².

Given is a blueprint we need to find area that be covered and then the cost of covering the area,

So, we will find the area by splitting the figure into different shapes,

So the area =

Ar(rectangle) + Ar(semicircle) + Ar(triangle) + Ar(square)

= 9×3 + 3.14×2²/2 + 1/2×3×1 + 3³

= 27 + 6.28 + 1.5 + 27

= 61.78 units²

Since 1 unit = 7 ft

So, 1 unit² = 49 ft²

therefore, 61.78 units² = 61.78 × 49 = 3027.22 ft²

Since our budget is $7500

Costing of covering the area = 3027.22 × x = 7500

x = $2.477

Hence the cost of covering 1 unit² should be $2.477 to be in the budget.

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