What is the absolute value of
|-14|
|-16|

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:

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:

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

Step-by-step explanation:

To factorize the expression 12x^3 - 9x^2 - 4x + 3, we can start by grouping the terms:

(12x^3 - 9x^2) - (4x - 3)

Now, we can factor out common terms from each group:

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

Notice that the expression (4x - 3) is common to both terms. We can now factor it out:

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

Therefore, the factored form of 12x^3 - 9x^2 - 4x + 3 is (4x - 3)(3x^2 - 1).

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

For this case we propose a rule of three, and thus find the grams of medication.

150lb -----------> 24g

120lb -----------> x

Where the variable "x" represents the grams of medicine that a 120-pound woman should receive

[tex]x = \frac {120 * 24} {150}\\x = 19.2[/tex]

Thus, a woman of 120 pounds should receive 19.2 grams of medication.

Answer:

19.2 grams

You would have to combine terms that are the same

6x + 2x = 8x

9-1 = 8

8x + 8 =24

This is simplified enough so your answer is 8x + 8 = 24

Thanks

Answer:

[tex]Log_41024=5[/tex]

Step-by-step explanation:

The change of form formula (exponential to logarithm) is:

[tex]a^x=b\\Log_ab=x[/tex]

Looking at the problem given, we can simply write the logarithmic form as:

[tex]4^5=1024\\Log_41024=5[/tex]

This is the answer.

11 cm. Simply divide 440 by 40, and you'll get your answer.

Answer:

1 centimeter = 40 kilometers

? centimeter = 440 kilometers

The simple way to do this is to set it as a ratio as shown above. From 40 to 440, there is a increase in 11 times. (40 x 11 = 440)

So, you would do 1 x 11 = 11. This means 11 centimeters is equal to 440 kilometers.

11 centimeter = 440 kilometers

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

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:

a(n) = a(1)*(1/4)^(n - 1)

Step-by-step explanation:

The first four terms of this sequence are 64, 16, 4, 1.

Let the common ratio be r.  Then 64r = 16, and r = 1/4.

The first term is  64.

The general term is then

a(n) = a(1)*(1/4)^(n - 1)

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:

[tex](7x)^{\frac{2}{3}}[/tex]=[tex]\sqrt[3]{49x^{2} }[/tex]

Step-by-step explanation:

We have been given the expression;

7 times x to the two thirds power which can be written mathematically as;

[tex](7x)^{\frac{2}{3}}[/tex]

To express the above expression as a radical, we need to recall that;

[tex]a^{\frac{b}{n}}=\sqrt[n]{a^{b}}[/tex]

Therefore;

[tex](7x)^{\frac{2}{3}}=\sqrt[3]{(7x)^{2} }\\\\=\sqrt[3]{49x^{2} }[/tex]

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:

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:

[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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Answer:

Answer: Two students are the same age but have different heights.

Step-by-step explanation:

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 explanation

Step-by-step explanation:

These are the terms of an arithmetic sequence with n th term

[tex]a_{n}[/tex] = a + (n - 1)d

where a is the first term and d the common difference

d = 25 - 20 = 30 - 25 = 5 and a = 20, hence

[tex]a_{n}[/tex] = 20 + 5(n - 1) = 20 + 5n - 5 = 5n + 15 ← n th term formula

Answer:

1. 14/15

2. 5 7/8

3. 81.25%

Step-by-step explanation:

1. (fraction) 7/9 divided by 5/6 (fraction)

7/9 ÷ 5/6 =

= 7/9 * 6/5

= (7 * 6)/(9 * 5)

= 42/45

= 14/15

2.

1 3/8 + 4 1/2 =

= 1 + 3/8 + 4 + 1/2

= 1 + 4 + 3/8 + 4/8

= 5 + 7/8

= 5 7/8

3.

percent = part divide by whole times 100

13/16 * 100 =

= 81.25%

Answer/Step-by-step explanation:

1. 14/15

7/9 divided by 5/6

7/9 X 6/5: multiply by the reciprocal

7/3 X 2/5: reduce the numbers

7/3 X 2/5=14/15

2. 1 3/8 + 4 1/2

1+4: add all whole numbers first

3/8 +1/2 : then add the fractions

5 7/8: is your final answer in its simplest form

3. Convert fraction 13 / 16 to a Answer: 81.25%

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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m=9-5 so answer is m=4

Answer:

[tex]m=4[/tex]

Step-by-step explanation:

We have been given an equation. We are asked to find the value of m for our given equation.

[tex]\frac{6.22\times 10^9}{1.79\times 10^5}=3\times 10^m[/tex]

Let us solve left side of our given equation using exponent property for quotient [tex]\frac{a^b}{a^c}=a^{b-c}[/tex].

[tex]\frac{6.22\times 10^9}{1.79\times 10^5}=\frac{6.22}{1.79}\times 10^{9-5}[/tex]

[tex]\frac{6.22\times 10^9}{1.79\times 10^5}=3.18\times 10^{4}[/tex]

Therefore, the value of m would be 4 for our given equation.

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]

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!

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

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

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:

[tex](\frac{y^{4}}{10})^{3}[/tex]

Step-by-step explanation:

we have

[tex]0.001y^{12}[/tex]

we know that

[tex]0.001=\frac{1}{1,000}=\frac{1}{10^{3}}=(\frac{1}{10})^{3}[/tex]

[tex]y^{12}=(y^{4})^{3}[/tex]

substitute

[tex]0.001y^{12}=(\frac{1}{10})^{3}(y^{4})^{3}=(\frac{y^{4}}{10})^{3}[/tex]

The expression 0.001y12 can be written as the cube of a monomial by taking the cube root of each term. The final expression is (0.1y4)^3.

The given expression is 0.001y12. This can be written as the cube of a monomial in the form (_)^3 by finding the cube root of each term. The cube root of 0.001 is 0.1 (as 0.1^3 = 0.001) and the cube root of y12 is y4 (as (y4)^3 = y12). Hence, the monomial that can be cubed to get 0.001y12 is 0.1y4, and the final expression is (0.1y4)^3.

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Answer:

slightly more than 15

Step-by-step explanation:

5[tex]\pi[/tex] ≈ 5(3.14) ≈ 15.7 (slightly more than 15)

Hope this helped!

~Just a girl in love with Shawn Mendes

(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: