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A square banner had 4 feet added its width and 2 feet subtracted from its height. The banner then had an area of 91 square feet. How long was a side of the original square banner?

Answer: 162

Step-by-step explanation:

3(2+4(5+2^3)]

3(2+4(5+8)

3(2+(4)(13))

3(2+52)

(3)(54)

=162

(4x)(-3x^8)(-7x^3)

4 (-3)(-7) = 84

x(-x^8)(-x^3) = x^(1 + 8 + 3) = x^12

Answer: 84x^12

Answer:

C

Step-by-step explanation:

Answer:

The length of the ladder is [tex]16\ ft[/tex]

Step-by-step explanation:

Let

L ----> the length of the ladder

we know that

Applying the Pythagoras theorem

[tex]L^{2}=15^{2} +6^{2}[/tex]

[tex]L^{2}=261[/tex]

[tex]L=\sqrt{261}\ ft[/tex]

[tex]L=16\ ft[/tex]

Answer:

Answer:

The length of the ladder is  

Step-by-step explanation:

Let

L ----> the length of the ladder

we know that

Applying the Pythagoras theorem

Step-by-step explanation:

[tex]\frac{-5}{8} * \frac{2}{3}[/tex]

Multiply the top with the top and the bottom with the bottom:

[tex]\frac{(-5)*2}{8*3}[/tex]

[tex]\frac{-10}{24}[/tex]

Then you can simplify:

[tex]\frac{-5}{12}[/tex]

Hope this helped!

Answer:

-5/12

Step-by-step explanation:

Multiply the top of both fractions and the bottom of both fractions, -5*2=-10,8*3=24

so -10/24 can be simplified to -5/12

ANSWER

A. (0.4, 1)

EXPLANATION

The given system of equations is:

y=-5x+3

y=1

We equate the two equations to obtain;

[tex] - 5x + 3 = 1[/tex]

Group the similar terms to obtain;

[tex] - 5x = 1 - 3[/tex]

[tex] - 5x = - 2[/tex]

We divide both sides by -5 to get,

[tex]x = \frac{ - 2}{ - 5} [/tex]

[tex]x = \frac{ 2}{ 5} [/tex]

[tex]x = 0.4[/tex]

Therefore the solution is (0.4,1)

Answer:

[tex]\large\boxed{A.\ (0.4,\ 1)}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=-5x+3\\y=1\end{array}\right\\\\\text{Put the value of y from the second equation to the first equation:}\\\\1=-5x+3\qquad\text{subtract 3 from both sides}\\\\-2=-5x\qquad\text{divide both sides by (-5)}\\\\\dfrac{-2}{-5}=x\to \boxed{x=0.4}[/tex]

Answer:

See below

Step-by-step explanation:

The given inequality is  

[tex]y\:>\:-5x+1[/tex]

The corresponding linear equation is y=-5x+1.

This line is of the form y=mx+b

The slope of this line is m=-5 and b=1 is the y-intercept.

Since the inequality sign is '>' the boundary line is a dashed line.

We test the origin to see if the inequality will be satisfied.

[tex]0\:>\:-5(0)+1[/tex]

[tex]0\:>\:1[/tex]

This statement is false so we shade above the dashed line.

The graph of the inequality is shown in the attachment.

Answer:

yes

Step-by-step explanation:

A rational number can be expressed in the form

[tex]\frac{a}{b}[/tex], where a, b are integers

6.610 can be expressed as

6 [tex]\frac{610}{1000}[/tex] = [tex]\frac{6610}{1000}[/tex] ← a rational number

6.610 is a rational number.

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Or in other words, any number that can be written as a ratio (or fraction) of two integers is a rational number.

Thus 6.610 is definitely a rational number as it satisfies the definition of a rational number.

We have, 6.610 = 661/100 which is expressed as the ratio of two integers.

Therefore, 6.610 is a rational number.

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Answer:

x-y-3=0

Step-by-step explanation:

The slope of the line that passes through the points (0,-3) and (3,0) is

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\ \\=\dfrac{0-(-3)}{3-0}\\ \\=\dfrac{3}{3}\\ \\=1[/tex]

The equation of the line is

[tex]y=m(x-x_1)+y_1\\ \\y=1\cdot (x-0)+(-3)\\ \\y=x-3\\ \\x-y-3=0[/tex]

the approximate height

Answer:b

Step-by-step explanation: I took the test

Answer:

B

Step-by-step explanation:

B is the only graph that starts at both intervals of 2, which would be 2, and -2

Answer:

B) x+y=120; 12x+20y=1720

Step-by-step explanation:

If variables are defined as ...

x = number of student tickets sold

y = number of adult tickets sold

then the problem statement can be modeled by ...

x + y = 120 . . . . . . the total number of tickets sold is 120

12x + 20y = 1720 . . . . . the total collected from ticket sales was $1720

___

Total revenue is the sum of the revenues from sales of each ticket type. The revenue from a given ticket type is the product of that ticket price and the number sold.

Answer:

It has no amplitud and the period is 5pi/2

Step-by-step explanation:

Given a function of the following type:

f(t) = AtanB(t + C)

The function has no amplitud, given that it doesn't have maximum or minimum value.  And the period is given by: pi/B

In this case, we have f(t)= -tan0.4t. Then:

B = 0.4

⇒ Period = pi/0.4 = 5pi/2

Therefore, the answer is: It has no amplitud and the period is 5pi/2

Answer:

4x^3 -x^2 -6x +10

Step-by-step explanation:

You can perform the division of (4x^4 +11x^3 -9x^2 -8x +30)/(x +3) by polynomial long division or by synthetic division. The latter is shown below.

The result of the division is ...

4x^3 -x^2 -6x +10

The solution to the equation X=(3x+10) is -5, which was found by isolating x on one side of the equation.

To solve the equation X = 3x + 10 for x, you begin by isolating the variable. First, subtract 3x from both sides, yielding -2x = 10. To find the value of x, divide both sides by -2. This results in x = -5. So, the solution for x in the given equation X = 3x + 10 is x = -5. This process involves balancing both sides of the equation to isolate the variable, and by subtracting 3x and then dividing by -2, we find that x equals -5, making it a clear and concise solution to the equation.

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Answer:

[tex]-\frac{3\sqrt{58} i}{{58}}-\frac{7\sqrt{58}j}{{58}}[/tex]

Step-by-step explanation:

The given vector is:

v = -3i-7j

The unit vector is found by dividing the vector by its magnitude

[tex]Unit\ vector\ of\ v=\frac{v}{||v||}[/tex]

We have to find the magnitude first

So,

[tex]||v||=\sqrt{(-3)^{2} +(-7)^{2}}\\ =\sqrt{9+49}\\ =\sqrt{58}[/tex]

The unit vector is:

[tex]\frac{-3i-7j}{\sqrt{58} } \\=>-\frac{3i}{\sqrt{58}}-\frac{7j}{\sqrt{58}}\\=>(-\frac{3i}{\sqrt{58}}*\frac{\sqrt{58}}{\sqrt{58}}) -(\frac{7j}{\sqrt{58}}*\frac{\sqrt{58}}{\sqrt{58}})\\=>-\frac{3\sqrt{58} i}{{58}}-\frac{7\sqrt{58}j}{{58}}[/tex]

Therefor the last option is the correct answer ..

The unit vector in the same direction as v = -3i-7j is found by calculating the magnitude of v and then dividing v by its magnitude. The result is (-3/sqrt(58))i + (-7/sqrt(58))j.

To find the unit vector in the same direction as v = -3i-7j, we first need to calculate the magnitude (length) of v. The magnitude of a vector can be calculated using the Pythagorean theorem as applied to vector components, so for our vector v, the magnitude |v| would be sqrt((-3)^2 + (-7)^2) = sqrt(9 + 49) = sqrt(58).

Next, we find the unit vector by dividing the vector by its magnitude. This gives us: (-3/sqrt(58))i + (-7/sqrt(58))j.

Therefore, the unit vector in the same direction as v is (-3/sqrt(58))i + (-7/sqrt(58))j.

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Hello There!

75% of 180 is 135.

Converting Percent To Decimal.

p = 75%/100 = 0.75

Y = 0.75 * 180

Y = 135

Make a proportion ([tex]\frac{part}{whole}[/tex])...

The whole is 180 but we need to find the part which would be x

75 % is also a part of 100% (the whole)

The proportion would look like this...

[tex]\frac{x}{180} =\frac{75}{100}[/tex]

Now cross multiply to solve for x. The work for this is below.

100x = 13500

To isolate x divide 100 to both sides

100x/100 = 13500/100

x = 135

So...

135 is 75% of 180

Hope this helped!

Given,

f(x)=4x^2-9

g(x)=2x+3

1.

(f+g)(x)=f(x) + g(x)

=4x^2-9+2x+3

=4x^2+2x-6

2.

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

4x^2-9-2x-3

=4x^2-2x-12

when x=3, then,

f(3)=4×(3)^2-9=27

g(3)=2×3+3=9

5.

f(g(3))=f(9)=4×(9)^2-9

=312

5.

g(f(3))=g(27)=2×27+3=57

Answer:

listen to romap they are correct

Step-by-step explanation:

After 2 months, the gym memberships at Gym A and Gym B will cost the same amount, based on the membership cost equations of each gym.

We need to determine after how many months the total costs of gym memberships at Gym A and Gym B will be the same. The cost of a gym membership at Gym A is described by the equation C = 12m + 36, where C represents the total cost and m represents the number of months. For Gym B, the cost is given by the equation C = 20m + 20.

To find the number of months where the costs are equal, we set the two equations equal to each other:

12m + 36 = 20m + 20

Subtracting 12m from both sides gives us:

36 = 8m + 20

Subtracting 20 from both sides gives us:

16 = 8m

Dividing both sides by 8 gives us:

m = 2

Therefore, after 2 months, the total costs for gym memberships at both Gym A and Gym B will be the same.

Answer:

The value is 13

Step-by-step explanation:

You can notice that 48/12 is 4 and 20/5 is 4. Therefore, divide 52 by 4

The value of x is 13.

Two triangles are said to be similar when corresponding angles of both triangles are congruent and ratio of corresponding sides are in equal proportion.

Given that, sides of one triangle are 48, 52, and 20.

Sides of other triangle are,  12, x and 5

Since, corresponding sides are in the proportion.

                   [tex]\frac{48}{12}=\frac{20}{5}=\frac{52}{x} \\\\x=\frac{52}{4}=13[/tex]

Learn more about the Similarity of triangle here:

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Answer:

3-x/x(x-1)

Step-by-step explanation:

Given

2/(x^2-x)-  1/x

To simplify, we can take x as common from the denominator of first term

=  2/(x(x-1))-  1/x

Taking LCM of denominators and then using the rules of addition and subtraction of numerators using denominator’s LCM

=  (2(1)-(x-1))/(x(x-1))

Solving the brackets

=(2-x+1)/(x(x-1))  

=  (-x+3)/(x(x-1))

The term can also be written as:

=  (3-x)/(x(x-1))

 (3-x)/(x(x-1)) is the correct answer ..  

To simplify the expression 2/x^2 - x - 1/x, we need to find a common denominator for the two fractions in the expression, which is x(x+1). The simplified form is (x + 2)/(x(x+1)).

To simplify the expression 2/x^2 - x - 1/x, we need to find a common denominator for the two fractions in the expression. The common denominator is x(x+1). Multiplying the numerator and denominator of the first fraction by x+1 and the numerator and denominator of the second fraction by x, we get:

So, the simplified form of 2/x^2 - x - 1/x is (x + 2)/(x(x+1)).

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Answer:

19°

Step-by-step explanation:

In triangle ABC, ∠A=120°, a=8, b=3.

Use the sin rule:

[tex]\dfrac{a}{\sin \angle A}=\dfrac{b}{\sin \angle B}\\ \\\dfrac{8}{\sin 120^{\circ}}=\dfrac{3}{\sin \angle B}\\ \\8\sin \angle B=3\sin 120^{\circ}\\ \\8\sin \angle B=3\cdot \dfrac{\sqrt{3}}{2}\\ \\\sin \angle B=\dfrac{3\sqrt{3}}{16}\approx 0.3248\\ \\\angle B\approx 18.95^{\circ}\approx 19^{\circ}[/tex]

Answer:

For the equation

[tex]y=\frac{x-6}{x^2+5x+6}[/tex]

There are vertical asymptotes at x=-2 and x=-3

There are no holes

Step-by-step explanation:

The equation for this graph can be factored in its denominator to get

[tex]y=\frac{x-6}{(x+2)(x+3)}[/tex]

This means that there are VA's at x=-3 and x=-2

(There are no holes as there is not a factor that cancels out.)

A function assigns the values. The asymptotes and the holes for the graph lie at x=-2 and x=-3.

A function assigns the value of each element of one set to the other specific element of another set.

The vertical asymptotes and the holes for the graph can be found by factorizing the denominator of the given function. Therefore, the factorisation of the denominator is,

x² + 5x + 6 =0

x² + 2x + 3x +6 =0

x(x+2)+3(x+2)=0

(x+2)(x+3)=0

x = -2, -3

Hence, the asymptotes and the holes for the graph lie at x=-2 and x=-3.

Learn more about Function:

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Answer:

$14,236

Step-by-step explanation:

25000 x 0.92 = 23000 = 1 Year

23000 x 0.92 = 21600 = 2 Years

19872

18282.24

16819.66

15474.09

14236 = 7 Years

The answer would be 14000

Answer: 3/2 + i/2

Step-by-step explanation: Simplify and write eht enaswer in standard form, a + bi.

Hope this helps! :) ~Zane

By setting up and solving a system of equations based on the total costs and number of animals, it is determined that there were 21 birds at the shelter on Wednesday.

To solve how many birds were at the shelter on Wednesday, we can set up a system of equations based on the costs and the total number of animals. Let the number of birds be b and the number of cats be c.

The total cost for birds and cats is $161.50, and there are 43 birds and cats together. This gives us two equations:

$3.50b + $4.00c = $161.50

b + c = 43

We can solve this system of equations by first expressing c in terms of b from the second equation:

c = 43 - b

Now we can substitute c into the first equation:

$3.50b + $4.00(43 - b) = $161.50

After simplifying:

$3.50b + $172.00 - $4.00b = $161.50

Combining like terms:

-$0.50b = -$10.50

Dividing by -0.50:

b = 21

So, there were 21 birds at the shelter on Wednesday.

Answer:

20.9, rounded answer: 21 miles

Step-by-step explanation:

x= distance between the airport and Ann's home.

since Ann is paying $2.10 per mile let 2.10 be the coefficient

our equation:

5 is our constant since that's how much Ann trips the driver

since the total is equal to 49.10, that's what our equation will be equal to

2.10x+5=49.10

sub "5"

2.10x+5-5=49.10-5

2.10x=44

divide both sides by "2.10"

2.10/2.10x=44/2.10

x=20.9

we can round 20.9 to 21

I don’t know what the answer is I wish I could help

Answer:

0.75 I think

Step-by-step explanation:

The correct trigonometry formula  [tex]tan^{-1}[/tex] (71°) . Therefore ,  [tex]tan^{-1}[/tex](71°) is correct .

The correct trigonometry formula to use to solve for the given angle is the tangent formula.

This is because you are given the side opposite to the angle (48) and the side adjacent to the angle (34), and you need to solve for the angle itself (71°).

The tangent formula is:

tan(angle) = opposite / adjacent

In this case, you would have:

[tex]tan^-1[/tex] = 48 / 34

[tex]tan^-1[/tex] = 0. 708333  degree

[tex]tan^-1[/tex] = 0.71 degree

[tex]tan^-1[/tex]  (0.71)      

= 35.3112 degree.

Therefore, the correct answer is tan(71°).

Answer:

A equals 254.46

C equals 56.54

Step-by-step explanation:

Area

pie (3.14) times the radius (9) times ^2 is equal to

254.46

Circumference

(2) times pi (3.14) times radius of (9) to get

56.54

Area of a circle formula = [tex]\pi[/tex]r² where r means radius and [tex]\pi[/tex] means 3.14

3.14(9)^2 = 254.34 = area

Circumference formula: 2[tex]\pi[/tex]r

2(3.14)(9) = 56.52 = circumference

The correct answer is C. 49.

Remember that there are 100 students divided into 7-12 and 13-18 age group. So there should be 50 for each. The table should go like this:

7-12 age group

23 adventure or biography

27 - detective 

so you just have to subtract 50 from 23, which makes it 27. The remaining belongs to the 13-18 age group.

13-18 age group

1 - detective 

49 - adventure or biography.

Answer:

49

Step-by-step explanation:

Total number of students =100

Out of the 50 students in the age group 7−12 years who participated in the survey, 23 liked adventure or biography.

So, 50-23 = 27 Out of the 50 students in the age group 7−12 years who participated in the survey liked detective

Now we are given that The total number of students of both age groups who liked detective books was 28.

No. of students of age group 13-17 who like detective books = Students of both age group like detective - No.of students of 7−12 years who liked detective = 28-27 =1

So ,The total number of students of both age groups who liked adventure or biography was 100-28 = 72

Since the age group 7−12 years who participated in the survey, 23 liked adventure or biography.

So,  the age group 13-17 years who participated in the survey liked adventure or biography = 72-23=49

Age group          Adventure or Biography       Detective     Total

 7-12                              23                                    27               50  

 13-18                            49                                     1                  50

Total                             72                                    28               100

So, Option C is true.

The total number of students in the age group 13−18 years who liked adventure or biography. is 49