Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the
fraction bar(s).
A café owner is designing a new menu and wants to include a decorative border around the outside of her food listings. Due to the cost of
printing, the border should have an area of 48 square inches. The width of the border needs to be uniform around the entire menu. She has
already determined that her food listings will fit within a 13-inch by 9-inch rectangular area.
13 in
9 in
The area of the decorative border can be modeled by the following equation, where x represents the width of the decorative border.
x²+
X=
Is it reasonable for the border to be 2.5 inches wide?
(yes/no)

The factorization is  [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³

To answer the question, w e need to know what factorization is

Factorization is the breaking down of a larger expression into smaller expression by grouping it into its factors.

So, [{(a² - 25b²}³ + {25b² - 9c²}³ + {9c² - a²}³)/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

= [{(a² - (5b)²}³ + {(5b)² - (3c)²}³ + {(3c)² - a²)})/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

Using the fact that x² - y² = (x + y)(x - y) in the terms in the numerator, we have

[{(a - 5b)(a + 5b)}³ + {(5b - 3c)(5b + 3c)}³ + {(3c - a)(3c + a)}³/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

Factorizing out the denominator, we have

= [{(a + 5b)/(a - 5b)}³ + {(5b + 3c)/(5b - 3c)}³ + {(3c + a)/(3c - a)}³[(a - 5b)³ + (5b - 3c)³ + (3c - a)³]/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

Cancelling out the denominator, we have

= [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³

So, the factorization is  [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³

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When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other. The measure of ∠1 is 30°, while the measure of ∠2 is 60°.

When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.

for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.

Since the two angles together form a 90° angle. The angles are complementary to each other, therefore, we can write,

∠1 + ∠2 = 90°

x + x + 30 = 90°

2x = 60°

x = 30°

Thus, the measure of the angles can be written as,

∠1 = x = 30°

∠2 = x+30° = 60°

Hence, the measure of ∠1 is 30°, while the measure of ∠2 is 60°.

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Answer:

y = 108

Step-by-step explanation:

2x + 16 = 3x -12 (as you can see the F shape and are on straight lines and AB is parallel to CD) .

Now we solve for x :

Subtract 2x from both sides :

16 = x - 12

Now we add 12 to both sides :

28 = x

Angle 3x-12 and y add up to 180 as they are on a straight line :

3x-12 + y = 180

Substitute x and solve for y :

3(28) - 12 + y = 180

84 - 12 + y = 180

72 + y = 180

y = 108  

Hope this helped and have a good day

Using a calculator, it is found that the approximate slope of the line of best fit for the data is of -4.54762.

The slope is found inserting the points (x,y) in a calculator. In this problem, the points are as follows:

(1, 36), (2,34), (3,30), (4,31), (5,23), (6,16), (7,11), (8,5).

Hence, using the calculator, the slope is of -4.54762.

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Answer:

Slope: [tex]\frac{4}{1}[/tex]

Y - intercept: -1

Step-by-step explanation:

We can see from the graph that the slope is [tex]\frac{4}{1}[/tex].

We can also identify the y - intercept as -1.

Therefore, the linear equation would be y = [tex]\frac{4}{1}[/tex]x -1

Hope this helps:) Goodluck!

Answer:

The answer is B

Step-by-step explanation:

f(x) = -3x - 5

g(x) = 4x - 2

= -3x - 5 - (4x - 2)

= -7x - 3

Answer:

B. -7x - 3

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x): -3x - 5

g(x): 4x - 2

f(x) - g(x) = (-3x - 5) - (4x - 2)

              = -3x - 5 - 4x + 2

              = (-3x - 4x) + (- 5 + 2)

              = (-7x) + (-3)

Answer:

(1, 0 ) and (0, - 8 )

Step-by-step explanation:

8x - y = 8 → (1)

8x² - y = 8 → (2)

since both equations are equal to 8 then equate the left sides

8x² - y = 8x - y ( subtract 8x - y from both sides )

8x² - 8x = 0 ← factor out 8x from each term

8x(x - 1) = 0

equate each factor to zero and solve for x

8x = 0 ⇒ x = 0

x - 1 = 0 ⇒ x = 1

substitute these values into (1) and solve for y

x = 0 : 8(0) - y = 8 ⇒ y = - 8 ⇒  (0, - 8 )

x = 1 : 8(1) - y = 8 ⇒ y = 0 ⇒ (1, 0 )

Answer:

32768

Step-by-step explanation:

8^6 is 262144

then divide 262144 by 8

so 262144 / 8 = 32768

Hope This Helped

Answer:A

Step-by-step explanation:

Using the normal distribution, it is found that 2.15% of bedroom apartments in the city cost between $750 and $1,000.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 1500, \sigma = 250[/tex]

The proportion of apartments that cost between $750 and $1,000 is given by the p-value of Z when X = 1000 subtracted by the p-value of Z when X = 750, hence:

X = 1000:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1000 - 1500}{250}[/tex]

Z = -2

Z = -2 has a p-value of 0.0228.

X = 750:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{750 - 1500}{250}[/tex]

Z = -3

Z = -3 has a p-value of 0.0013.

0.0228 - 0.0013 = 0.0215.

0.02215 = 2.15% of bedroom apartments in the city cost between $750 and $1,000.

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Answer:

Ans : A. Straight angle

Step-by-step explanation:

Brainliest me pls

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Brain

Answer:

there are no indicate measure bro in circle

Step-by-step explanation:

Why was federal ruling system implemented in Nepal?Give any four reasons

Step-by-step explanation:

to find the circumference of an object take pie and the radius and multiply it by 2

equation: 2 pie r

if r is 9 the answer is 56.55

9x2=18

18xpie=56.55

Step-by-step explanation:

See above graph.......

Estimate the number of rabbits on the farm will be 417 rabbits.

Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.

Eva wants to estimate the number of rabbits on a farm.

On Monday, she catches 50 rabbits.

These rabbits are tagged and then released.

On Tuesday, she catches 100 rabbits.

12 of these rabbits have tags on them.

Then estimate the number of rabbits on the farm that will be

Let n be the number of total rabbits. Then we have

12n = 50 x 100

  n = 5000 / 12

  n = 416.67

  n ≅ 417

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Answer:

C. 9 minutes 30 seconds

Step-by-step explanation:

well you could estimate it or just add 2.5 to 6.9 and you would get pretty close to the answer

Have a good day! :)

Answer:

about $2.31 per pound

Step-by-step explanation:

35.99/15.6 = 2.30705128205

2.31

Have a good day! :)

Reason:

Choices A, C and D have repeated x values. It allows us to rule them out.

Table A has x = 6 repeating. Table C has x = 3 and x = -3 repeated. Table D has x = 4 and x = 5 show up twice each.

Whenever we have repeated x values, it indicates we do not have a function. A function is only possible when each x value goes to exactly one y value only.

Table A has the input x = 6 lead to y = 2 and y = -2 at the same time. Table C and table D are a similar story. So this is another way to rule out choices A, C and D.

Luckily table B has no repeated x values. Each x input leads to exactly one and only one y output. Therefore, table B is a function.

Side Note: the y values can repeat, but the function won't be one-to-one.

Answer:

Choice B

Step-by-step explanation:

Given radical expression:

[tex] \sqrt[4]{1296 {x}^{16} {y}^{12} } [/tex]

To Find:

The Simpler form of this expression

Soln:

[tex] = \sqrt[4]{1296 {x}^{16} {y}^{12} } [/tex]

We could re-write the given expression, according to the law of exponents:

[tex] = \tt \sqrt[4]{(6x {}^{4}y {}^{3}) {}^{4} } [/tex]

Now we need to bring terms out of the radical as:

[tex] \tt = | 6x { }^{4} y {}^{3} | [/tex]

Bring out 6x^4 from the absolute & put y^3 only in it:

[tex] \tt = 6x {}^{4} |y {}^{3} | [/tex]

Choice B is accurate.

The probability will include:

P(A and 1) = 1/24

P(C and 2) = 1/12.

P(B and 3) = 1/12.

P(A and 4) = 1/12

The probability of P(A and 1) will be:

= 1/4 × 1/6

= 1/24

The probability of P(C and 2) will be:

= 1/4 × 2/6

= 1/12

The probability of P(B and 3) will be:

= 2/4 × 1/6

= 1/12

The probability of P(A and 4) will be:

= 1/4 × 2/6

= 1/12

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The image lines constructed are called parallel lines. They are parallel because  they are all equidistant to each other at every point and at no point between any of the lines will there be an intersection of the three lines.

Equidistance is simply another word for equal in distance. That is, parallel lines maintain equal distance from each other at all points along them.

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Answer:

[tex]\bold{\green{(4x-3)(3x^{2}-1) }}[/tex]

Step-by-step explanation:

Answer:

(3x^2 - 1)(4x - 3)

Step-by-step explanation:

We can use grouping to factor this

12x^3 – 9x^2 − 4x + 3

group into: (12x^3 – 9x^2)(− 4x + 3)

Solve one side at a time:

(12x^3 – 9x^2)

3x^2(4x - 3) factor out a 3x^2

(− 4x + 3)

- 1 (4x - 3) factor out a -1

put the two equations togeth

(3x^2 - 1)(4x + 3)

The height of the skyscraper if the angle of elevation to the top of a prominent skyscraper to be 17° is 91.51 meter

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h represent the height of the skyscraper, hence:

tan(17) = h/294

h = 89.88 meter

Total height = 89.88 + 1.63 = 91.51 meter

The height of the skyscraper if the angle of elevation to the top of a prominent skyscraper to be 17° is 91.51 meter

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The solution to the inequality expression is x ≥ - 5

Inequality are expressions not separated by an equal sign. Given the inequality;

–4(x + 3) ≤ –2 – 2x

Expand

-4x - 12  ≤ -2 - 2x

Collect the like terms

-4x + 2x  ≤ -2 + 12

-2x  ≤  10

Divide both sides by -2

-2x/-2  ≤ 10/-2
x ≥ - 5

Hence the solution to the inequality expression is x ≥ - 5

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Answer:

First line

Explanation: Edge2023

The graph that best shows the line of best fit is graph (c)

A graph that shows the appropriate line of best fit has the following properties:

The graph that satisfies the above highlights is the graph (c)

Hence, the graph that best shows the line of best fit is graph (c)

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Answer:

c

Step-by-step explanation:

Answer: Lines with congruent corresponding angles are parallel.

CG is parallel to AB because Lines with congruent corresponding angles are parallel.

From the given image, we see that there is a transverse line cutting across lines AB and CG.

Now, from transverse line theorem we know that If two parallel lines are cut by a transversal, the corresponding angles are congruent. If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.

Thus, we can conclude that CG is parallel to AB because Lines with congruent corresponding angles are parallel.

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Answer:

n=5

Step-by-step explanation:

-7-2.1n=-3.5n

 +2.1n    +2.1n

-7   =  -1.4n

/-1.4   /-1.4

n=5

Hope this helps!

If not, I am sorry

Answer:

b = - 1.25

Step-by-step explanation:

-7 - 2.1n = 3.5n

-7 = 3.5n + 2.1n

-7 = (3.5+2.1)n

-7 = 5.6n

-7/5.6 = n

n = -1.25

Check:

-7 -(2.1*-1.25) = 3.5*-1.25

-7 + 2.625 = -4.375