Write log (x^2-9) - log(x+3) as single logarithm.

ANSWER

A. 73

EXPLANATION

The given expression is

[tex](2{x})^{2} - 3{y}^{2} [/tex]

We substitute x=5 and y=3 to obtain:

[tex](2 \times 5)^{2} - 3{(3)}^{2} = {10}^{2} - 3 \times 9[/tex]

This simplifies to,

[tex] = 100 - 27[/tex]

[tex] = 73[/tex]

The correct choice is A.

m∠H = 50°

∠H is a inscribed angle, and so that the intercepted arc would be twice the amount of the angle.

Arc KI = 100°

Because ∠KGI & ∠HKI share the same arc, the measurement for ∠KGI will be the same as ∠HKI, or 50°

m∠KGI = 50°

Next, find m∠KJI. arcKJI = 2(∠H) = 2(50) = 100

m∠KJI = 100°

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In order to make 20 slices of toast, given the constants provided, it would take approximately 175 seconds total. This is calculated based on the established rate of 4 slices of toast per 35 seconds.

The subject of this question is mathematics, specifically focusing on patterns and ratios. Given that it takes 35 seconds to make 4 slices of toast, we can establish a consistent rate of toast production. Because the toaster can toast 4 slices at a time, every 35 seconds, 4 more slices are ready. If we want to make 20 slices of toast, we can calculate this as follows: 20 slices ÷ 4 slices per 35 seconds = 5 times. Therefore, 5 times multiplied by the 35 seconds it takes to toast a set of 4 slices gives us 175 seconds. So, to toast 20 slices, it would take approximately 175 seconds.

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To make 20 slices of toast, it will take 210 seconds.

To find out how long it will take to make 20 slices of toast, we can determine the time required to make 1 slice of toast and then multiply it by 20.

From the given information, we can create a pattern to determine the time required:

We can observe that doubling the number of slices doubles the time required. Therefore, 20 slices will take twice the time required for 10 slices, which is 105 seconds. So, it will take 210 seconds to make 20 slices of toast.

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Answer:  7

Step-by-step explanation:

The 1st spinner can land on 2, 3, 4, or 5

The 2nd spinner can land on 2 or 3

The 3rd spinner can land on 6, 7, or 8

1st spinner + 2nd spinner + 3rd spinner:

2 + 2 + 6 = 10,    2 + 2 + 7 = 11,     2 + 2 + 8 = 12    --> 3 different sums

2 + 3 + 6 = 11,     2 + 3 + 7 = 12,     2 + 3 + 8 = 13   --> 1 different sum

This pattern follows where the only new sums are as follows:

                                                       3 + 3 + 8 = 14

                                                       4 + 3 + 8 = 15

                                                       5 + 3 + 8 = 16

This makes a total of 7 different sums.

Answer: 188/45 or 4 8/45.

Step-by-step explanation:

1. Change the mixed numbers to improper fractions.

10 1/9 = 91/9

5 14/15 = 89/15

2. Now, we must find a common denominator by finding the LCM (Least Common Multiple). In this case, it would be 90. 9 x 10 = 90 and 15 x 6 = 90. The numerators must equal the denominators, so we would multiply 91 by 10 and 89 by 6.

Our new fractions are 910/90 and 534/90.

3. Subtract the fractions. 910/90 - 534/90 = 376/90.

4. Simplify. 376 and 90 are both divisible by 2, so our answer will be 188/45 or 4 8/45.

Answer:

[tex]A=240\ m^{2}[/tex]

Step-by-step explanation:

we know that

A rhombus is a parallelogram with four congruent sides, the diagonals are perpendicular bisectors of each other

The area of a rhombus is equal to

[tex]A=\frac{1}{2}(D1*D2)[/tex]

where

D1 and D2 are the diagonals

In this problem we have

[tex]D1=16\ m[/tex]

Applying the Pythagoras Theorem find D2

[tex]17^{2} =(D2/2)^{2}+(16/2)^{2}[/tex]

[tex](D2/2)^{2}=17^{2}-(16/2)^{2}[/tex]

[tex](D2/2)^{2}=225[/tex]

[tex](D2/2)=15[/tex]

[tex]D2=30\ m[/tex]

Find the area of the rhombus

[tex]A=\frac{1}{2}(16*30)=240\ m^{2}[/tex]

Correct option is A. The term 'kinds' likely refers to informal groupings of organisms and may align with 'species' or higher taxonomic orders. Organisms are classified into a hierarchical system, where species represent closely related organisms capable of interbreeding, but higher levels like genus and family involve organisms that share broader similarities.

The question pertains to the concept of biological classification and how created "kinds" are understood within that framework. The term "kinds" is not particularly scientific and may refer to informal groupings of organisms. However, it could be inferred that the student is asking about how closely these "kinds" align with scientifically recognized categories such as species or higher taxonomic orders (like genus, family, order, etc.).

According to the Linnaean system introduced by Carl Linnaeus, organisms are classified in a hierarchical structure based on shared physical characteristics. This system organizes living organisms into a hierarchy of taxa, with species being the most specific level and kingdoms being the most general. Species are groups of organisms that are very similar and capable of interbreeding, while higher taxonomic levels, such as genus and family, group together organisms that share fewer, but still significant, similarities.

The concept of a species can be complex, as there can be significant variation within what we consider a single species, making the categorization sometimes controversial and subject to scientific debate. Moreover, as our understanding of evolution and phylogeny has advanced, the classification system has evolved to reflect these new insights, leading to changes in how organisms are grouped.

Answer:

Step-by-step explanation:

cos(a-b)-cos(a+b)=2(sina x sinb)

using formulae of cos (a-b) & cos(a+b)

cos a cos b + sina sinb - cosa cosb + sina sinb=2 sina sinb

2 sina sinb = 2 sina sinb

proved!

Answer:

Resolved.

Step-by-step explanation:

Answer:

The Answer is B. I had this a few months ago. Good luck with Apex!

Simplify brackets

-7 + 9z + 8(3z - 4)

Expand

-7 + 9z + 24z - 32

Collect like terms

(-7 - 32) + (9z + 24z)

Simplify

-39 + 33z

Regroup terms

= 33z - 39

Answer:

10.4

Step-by-step explanation:

To get the property's gross income multiplier (GIM), you divide its appraised value by its gross annual rental income.

Rental income = 2 × $1400/1 month × (12 months/1 yr)

= $33 600/yr

GIM = $350 000/$33 600 = 10.4  

The property's GIM is 10.4.

Answer:1/2 feet

Step-by-step explanation:

6 1/12 - 5 7/12 = 6/12 = 1/2

Answer:

C. Each Sandwich has 1/4 pounds of ham

Step-by-step explanation:

Answer:

The perimeter would also be multiplied by 2.

Step-by-step explanation:

The perimeter would also be multiplied by 2. Suppose the sides of a triangle are 5, 10 and 13. The perimeter would be the sum of the side lengths or 5 + 10 + 13 = 28 ft.

Multiply each side length so 5*2 = 10, 10*2 = 20 and 13*2 = 26. Find the perimeter by finding their sum, 10 + 20 + 26 = 56.

Divide the new perimeter by the old perimeter to find a scale factor.

56/28 = 2.

The new perimeter is exactly 2 times bigger since 2*28 = 56.

Subtract the mean from Jake's score:

520 - 500 = 20

No divide that by the standard deviation:

20/60 = 0.33

This means Jake scored 0.33 standard deviations above the mean.

Now using the Z-table find 0.33:  0.33 = 0.6293 = 62.93% of students scored below Jake.

Rounded to nearest whole number = 63%

Answer:

63% of students

Step-by-step explanation:

Z = (X  -  μ) / σ

Z = 520 - 500 / 60

Z = 0.33

ON THE Z-TABLE

0.33 = 0.6293

62.93%  =  63% of students answer

Answer:

B

Step-by-step explanation:

The easiest way to do this is to look at the -1 first. That shifts the small horizontal graph downwards. So that little line is below the x axis as answer B would show you.

The next thing to notice is that the graph is at +6 which is what you might expect because the x carries a minus with it. B and C both do that. I'm not sure what D does but I think it is on the left side of the y axis and that makes it wrong. A also looks like it is on the left side of the y axis and it is not correct either.

The difference between B and C has to be that 2 in front of the cubic. I think the vertical part of the cubic in B is closer to a vertical line through 6. If that is the case B is the answer.

Graph

Red: y = (-x + 6)^3

Blue: y = 2*(-x + 6)      Notice that this is closer to a vertical line at x = 6. That's the function of the 2

Green: y = 2*(x +6)^3 - 1 Notice it is shifted down.

You end up on Point (3, 4)

Answer:

you will end up on (3,4)

Step-by-step explanation:

Answer:

should be A. Two-Solutions

Answer:

52.07

Step-by-step explanation:

We know that the sin of an angle is equal to the opposite side divided by the hypotenuse

sin  51 = opposite side/ hypotenuse

sin 51 = x/67

Multiply each side by 67

67 sin 51 = x

52.06877942=x

To the nearest hundredth

52.07 =x

Your molarity would be 0.975 M HCl because it’s moles of solute divided by liters of solvent

The answer would be 0.975

The radius of convergence of [tex]\sum\limits^{\infty}_{n=0} \frac{(-1)^n(x-6)^n}{4n+1}[/tex] is 1, and the interval notation is (5,7)

The series is given as:

[tex]\sum\limits^{\infty}_{n=0} \frac{(-1)^n(x-6)^n}{4n+1}[/tex]

The ratio test of a series states that:

[tex]L = \lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |[/tex]

By applying the ratio test considering that the series converges, we have:

[tex]\lim_{n \to \infty} | \frac{(-1)^{n+1}(x-6)^{n+1}}{4(n+1)+1} \div \frac{(-1)^n(x-6)^n}{4n+1}|[/tex]

Open the bracket

[tex]\lim_{n \to \infty} | \frac{(-1)^{n+1}(x-6)^{n+1}}{4n+4+1} \div \frac{(-1)^n(x-6)^n}{4n+1}|[/tex]

Evaluate the sum

[tex]\lim_{n \to \infty} | \frac{(-1)^{n+1}(x-6)^{n+1}}{4n+5} \div \frac{(-1)^n(x-6)^n}{4n+1}|[/tex]

Express as product

[tex]\lim_{n \to \infty} | \frac{(-1)^{n+1}(x-6)^{n+1}}{4n+5} \times \frac{4n+1}{(-1)^n(x-6)^n}|[/tex]

Expand the exponents

[tex]\lim_{n \to \infty} | \frac{(-1)^{n} \times (-1)^1 (x-6)^{n} \times (x-6)}{4n+5} \times \frac{4n+1}{(-1)^n(x-6)^n}|[/tex]

Cancel out the common factors

[tex]\lim_{n \to \infty} | \frac{(-1)(x-6)(4n+1)}{4n+5} |[/tex]

Factor out (-1)(x - 6)

[tex]|x-6|\lim_{n \to \infty} | \frac{(4n+1)}{4n+5} |[/tex]

Assume the limit to infinity is 1, the equation becomes

[tex]|x- 6| < 1[/tex] --- condition for convergence series

Split

[tex]-1 < x - 6 < 1[/tex]

Add 6 to both sides

[tex]5 < x < 7[/tex]

Rewrite as interval notation

(5,7)

Hence, the radius of convergence is 1, and the interval notation is (5,7)

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The radius of convergence, R, of the given series is 1. The interval of convergence, I, is [7,5). These are found using the Ratio Test to determine where the series converges, and then checking behavior at the endpoints.

To find the radius and interval of convergence of a series, we typically use the Ratio Test, where we consider the limit as n approaches infinity of the absolute value of the ratio of the (n+1)th term to the nth term. If this limit L is less than 1, the series converges absolutely; if it is greater than 1, the series diverges; if it equals 1, the test is inconclusive.

From the given series ∞ (−1)n (x − 6)n (4n + 1)/n, let a(n) be the nth term, so a(n+1) = (−1)^(n+1) (x − 6)^(n+1) (4*(n +1) + 1)/(n+1). Thus, we find |a(n+1)/a(n)| = |(x-6) * (4n+1) / (4n+5)|. In the limit as n approaches infinity, this becomes |x-6|. The series converges where this is less than 1, hence the radius of convergence, R, is 1.

For the interval of convergence, I, we need to check the points x = 7 and x = 5 (the endpoints of the interval centered at 6 with radius 1). Substituting these into the original series, we can use the Alternating Series Test and find the series converges for x = 7 and diverges for x = 5. Hence, the interval of convergence is I = [7,5).

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Answer:

93 1/2 in^2.

Step-by-step explanation:

The Area = 8 1/2 * 11

= 17/ 2* 11

=  187/2

=  93 1/2 in^2.

Answer:

The area of the binder paper is 93 1/2 in^2 :)

Step-by-step explanation:

Answer:

a.12.0 lb; b.0.34 g; c.120 kg

Step-by-step explanation:

To measure weight using the English system of measurements, we use ounces, pounds, tons, etc.

To measure weight using the metric system, we use grams, milligrams, kilograms, etc.

This means that pounds, grams and kilograms are all acceptable representations of weights.

Kilonewtons (kN) measure force, not weight.

Meters and centimeters (m and cm) measure length, not weight.

Answer:

a.12.0 lb

d.1600 N

Step-by-step explanation:

THe weight of objects is the force with which each object is attracted by the gravitational force where they are located, for example on earth gravitational force is equal to 9.81 m/[tex]s^{2}[/tex], so an object that is 1 kg of mass, would have a weight of 9.81 Newtons, pounds are also a measure of force.

the answer is x=(1/28)y^2

The equation of the parabola with focus at (7, 0) and directrix at x = -7 is x = (1/28)y².

The general equation of a horizontally opening parabola, using the distance between the vertex and the focus or directrix as the value of 'p'.

To find the equation of a parabola with a focus at (7, 0) and a directrix at x = -7, we first note that the vertex of the parabola is midway between the focus and the directrix. This puts the vertex at the origin (0, 0), and the parabola opens to the right since the focus is to the right of the vertex.

The general form of the equation for a parabola that opens horizontally (left or right) is

[tex](y - k)^2 = 4p(x - h)[/tex], where (h, k) is the vertex and p is the distance from the vertex to the focus.

If the parabola opens to the right (as in this case), the equation will be

[tex](y - 0)^2 = 4*(7)(x - 0)[/tex]

y² = 28x.

However, to match the format of the original options given to the student, we divide every term by 28, leading to the equation x = (1/28)y², which is the correct parabolic equation for the given focus and directrix.

Answer:

1/10c^3d^4

Step-by-step explanation:

A cube root is an operation which splits expressions and numbers within it into 3 groups of the exact same size. These groups when multiplied by themselves make the expressions and numbers under the root. For example, ∛27 = 3 since 3*3*3 = 27.

Take each part under the cube root and split it into three equal groups.

1/ 1000 = 1/10 * 1/10 * 1/10 so ∛1/1000 = 1/10

c^9 = c^3*c^3*c^3 so ∛c^9 = c^3

d^12 = d^4*d^4*d^4  so ∛d^12 = d^4

Together ∛1/1000 c^9 d^12 = 1/10 * c^3 * d^4

Answers:

See below  

Step-by-step explanation:

First transformation

Reflection about the line y = 6.

This inter-converted Points A and C and Points B and D.

The coordinate transformations were (Fig. 1):

A: (-8, 8) ⟶ (-8, 4)

B: (-2, 8) ⟶ (-2, 4)

C: (-8, 4) ⟶ (-8, 8)

D: (-2, 4) ⟶ (-2, 8)

Second transformation

Translation 10 units to the right and 14 units down.

The coordinate transformations were (Fig. 2):

A: (-8, 4)  ⟶ (2, -10)

B: (-2, 4)  ⟶ (8, -10)

C: (-8, 8)  ⟶ (2,   -6)

D: (-2, 8) ⟶ (8,    -6)

The transformations were:

Answer:

11/12

Step-by-step explanation:

Final answer:

To find the probability of rolling a sum of 444 or higher with two fair six-sided dice, calculate the sum probabilities for 444, 455, and 466, then add them together.

Explanation:

If you roll two fair six-sided dice, what is the probability that the sum is 444 or higher?

To calculate this probability, we need to first determine the total possible outcomes when rolling two dice and then find the favorable outcomes where the sum is 444 or higher.

The sum can range from 2 to 12 when rolling two dice, so we can find the probabilities for sums 444, 455, and 466, then add these probabilities up to get the final answer.

Answer:

Step-by-step explanation:

You wouldn’t put y over x Which is 15/3 you would divide which gives you five. So your tan theta would be 5

Answer:

it's definitely 3 on odyssey. tan theta= y/x =3.

Step-by-step explanation:

Answer:

28 >= 0.25x > 25

Step-by-step explanation:

25% of x

1) Greater than 25: 25%x > 25

2) Less than and equal to 28: 25%x <= 28

25%x = 25/100 * x = 0.25x

1 and 2:

28 >= 0.25x > 25

//I hope this is what you are looking for. Not sure it's right

Answer:

a)SSS b)AAS c)SAS d)SSS e)AAS dont worry i passed this lesson with a 100% if i am wrong then come and kill me :) i am sure it is right

Step-by-step explanation:

Final answer:

The rules for triangle congruence based on the given statements are SSS, ASA, SAS, SSS, and AAS, which are applied when certain combinations of angles and sides are congruent in two triangles.

Explanation:

To name the rule for each statement given for triangle congruence, we can apply the following:

a) SSS (Side-Side-Side) Congruence Postulate: Each pair of corresponding sides is congruent.

b) ASA (Angle-Side-Angle) Congruence Postulate: Two pairs of corresponding angles and one pair of corresponding sides are congruent.

c) SAS (Side-Angle-Side) Congruence Theorem: Two pairs of corresponding sides and the angles included between them are congruent.

d) SSS (Side-Side-Side) Congruence Postulate: Three sides of one triangle are congruent to three sides of a second triangle.

e) AAS (Angle-Angle-Side) Congruence Theorem: Two angles and a non-included side of each triangle are congruent.

These rules are foundational in establishing triangle congruence and are applied based on different combinations of sides and angles of triangles.