The legs of a right triangle are x + 1 and x + 4. What is the area of the triangle?

Final Answer:

x = 20

Step-by-step explanation:

we'll be using the pythagorean theorem method, in this triangle the missing letter is a.

formula: [tex]a=\sqrt{c^2-b^2}[/tex]

a = x

b = 21

c = 29

a = [tex]\sqrt{29^2-21^2}[/tex]

a = [tex]\sqrt{841-441}[/tex]     (note: 29² = 29 × 29 = 841 and 21² = 21 × 21 = 441)

a = [tex]\sqrt{400}[/tex]

a = 20

x = 20

Answer:

Last option (counting from the top)

Step-by-step explanation:

For a given function f(x), the difference quotient is:

[tex]\frac{f(x + h) - f(x)}{h} = \frac{1}{h}*(f(x + h) - f(x))[/tex]

In this case, we have:

[tex]f(x) = \frac{8}{4x + 1}[/tex]

Then the difference quotient will be:

[tex]\frac{1}{h}*( \frac{8}{4*(x + h) + 1} - \frac{8}{4x + 1})[/tex]

Now we should get a common denominator.

We can do that by multiplying and dividing each fraction by the denominator of the other fraction, so we will get:

[tex]\frac{1}{h}*( \frac{8}{4*(x + h) + 1} - \frac{8}{4x + 1}) = \frac{1}{h}*(\frac{8*(4x + 1)}{(4(x + h) +1 )*(4x + 1)} - \frac{8*(4(x + h) + 1)}{(4(x + h) +1 )*(4x + 1)})[/tex]

Now we can simplify that to get:

[tex]\frac{1}{h}*\frac{8*(4x + 1) - 8*(4(x + h) + 1)}{(4(x + h) +1 )*(4x + 1)}} = \frac{1}{h}*\frac{-32h}{(4(x + h) +1 )*(4x + 1)}} = \frac{-32}{(4(x + h) +1 )*(4x + 1)}}[/tex]

Then the correct option is the last one (counting from the top)

Answer:

C

Step-by-step explanation:

The domain is the left side of the table

Answer:

A third-degree polynomial can be written as:

f(x) = a*x^3 + b*x^2 + c*x + d

Where the leading coefficient is a, and all the coefficients are real.

If we know that the leading coefficient is 1, then the equation becomes:

f(x) = x^3 + b*x^2 + c*x + d

Now, we also know that:

(6 + i) and 5 are zeros.

This means that:

(6 + i)^3 + b*(6 + i)^2 + c*(6 + i) + d = 0

remember that:

i^2 = - 1

This is equal to:

(6 + i)*(36 + 2*6*i  + i^2) + b*(36 + 2*6*i  + i^2) + c*(6 + i) + d = 0

(6 + i)*(35 + 12i) + b*(35 + 12i) + c*(6 + i) + d  =0

(210 + 35i + 72i - 12) +  b*(35 + 12i) + c*(6 + i) + d  = 0

198 + 107i +  b*(35 + 12i) + c*(6 + i) + d  = 0

sparating in real and imaginary part, we get:

(198 + b*35 + c*6 + d) + (107 + b*12 + c)*i = 0

Then each parentheses needs to be zero, this means that:

198 + b*35 + c*6 + d = 0

107 + b*12 + c =  0

Knowing that 5 is another zero, we have:

5^3 + b*5^2 + c*5 + d = 0

125 + b*25 + c*5 + d = 0

Then we have a system of 3 equations and 3 variables:

198 + b*35 + c*6 + d = 0

107 + b*12 + c =  0

125 + b*25 + c*5 + d = 0

To solve this, we first need to isolate one of the variables in one of the equations.

Let's isolate d in the last one, so we get:

d = -125 - b*25 - c*5

now we can replace this in the first equation to get:

198 + b*35 + c*6 + d = 0

198 + b*35 + c*6 + (  -125 - b*25 - c*5) = 0

70 + b*10 + c = 0

So now we have two equations:

70 + b*10 + c = 0

107 + b*12 + c =  0

Again, now we can isolate the one variable in one of the equations, this time let's isolate c in the first one.

c = -70 - b*10

now we can replace this in the other equation:

107 + b*12 + c = 0

107 + b*12 + (-70 - b*10) = 0

38 + b*2 = 0

now we can solve this for b

b*2 = -38

b = -38/2 = -19

Now, with the equation c = -70 - b*10 we can find the value of c.

c = -70 - b*10 = c = -70 - (-19)*10 = 120

And with the equation  d = -125 - b*25 - c*5

we can find the value of d:

d = -125  - b*25 - c*5 = -125 - (-19)*25 - (120)*5 = -250

Then we have:

a = 1

b = -19

c = 120

d = -250

The eqation is:

f(x) = 1*x^3 - 19*x^2 + 120*x - 250

Answer:129

Step-by-step explanation:(621 x 0.25) + (750 x 0.10) = 230.25

750 - 621 = 129 more dimes than quarters

Answer:

x = 3

Step-by-step explanation:

using the mid segment formula since quadrilateral WZYP is similar to that of MZYT, this is expressed as;

29 = 1/2(23 +11x+2)

Cross multiply

2(29) =  23+11x+2

58 = 25 + 11x

11x = 58 - 25

11x = 33

Divide both sides by 11

11x/11 = 33/11

x = 3

Hence the value of x is 3

Answer:

18

Girl  = g

Boy = b

1g 1b  1g 2b  1g 3b

2g 1b  2g 2b  2g 3b

3g 1b  3g 2b  3g 3b

4g 1b   4g 2b  4g 3b

5g 1b   5g 2b  5g 3b

6g 1b   6g 2b  6g 3b

---------------------------------------

Another way you can do this,

6 × 3 = 18

In the end there will be 18 selections.

Answer:

The slope is 0.84

Step-by-step explanation:

View solution from above uploaded photos

Answer:

937

425

Step-by-step explanation:

9 is the square of 3

7 is 1 more than 6, the double of 3

4 is the square of 2

5 is 1 more than 4, 2x 2

Is there more?

Answer:

425

Step-by-step explanation:

1st = 2^2

3rd = 2*2 + 1

Answer:

x = 136

Step-by-step explanation:

x and 44 are same- side interior angles and sum to 180° , that is

x + 44 = 180 ( subtract 44 from both sides )

x = 136

Answer:

its A

Step-by-step explanation:

Answer:

you did not provide the numbers to answer any question...

but the formula that you want is probably this one

Combination Formula nCr=n!(n−r)!r!

Step-by-step explanation:

Answer:

9x3 - 8x2

Step-by-step explanation:

7x3+2x3 = 9x3

-4x2+(-4x2) = -8x2

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Measure of an inscribed angle intercepted by an arc is half of the measure of the arc.

From the picture attached,

m(∠A) = [tex]\frac{1}{2}m(\text{arc BD})[/tex]

           = [tex]\frac{1}{2}[m(\text{BC})+m(\text{CD}][/tex]

           = [tex]\frac{1}{2}[55^{\circ}+145^{\circ}][/tex]

           = 100°

m(∠C) = [tex]\frac{1}{2}[(360^{\circ})-m(\text{arc BCD})][/tex]

           = [tex]\frac{1}{2}(360^{\circ}-200^{\circ})[/tex]

           = 80°

m(∠B) + m(∠D) = 180° [ABCD is cyclic quadrilateral]

115° + m(∠D) = 180°

m(∠D) = 65°

m(arc AC) = 2[m(∠D)]

m(arc AB) + m(arc BC) = 2(65°) [Since, m(arc AC) = m(arc AB) + m(arc BC)]

m(arc AB) + 55° = 130°

m(arc AB) = 75°

m(arc ADC) = 2(m∠B)

m(arc AD) + m(arc DC) = 2(115°)

m(arc AD) + 145° = 230°

m(arc AD) = 85°

Answer:

-55

Step-by-step explanation:

the sqeuence seems to be subtracting by 2 everytime.

so it will be -1,-3,-5,-7,-9,-11,-13,-15,-17,-19,-21,-23,-25,-27,-29..

the answer will be 27*-2(-54) -1(because we start at -1 , not 0)

Answer:

Step-by-step explanation:

the formula for an arithmetic sequence that is explicit is

[tex]a_n=a_1+d(n-1)[/tex]  where [tex]a_1[/tex] is the first term (so -1), and d is the common difference (-2). n is the number position in the sequence. As soon as we find the formula or model for this sequence we can find any number term we want. Filling in the formula:

[tex]a_n=-1-2(n-1)[/tex] and we'll clean that up just a bit:

[tex]a_n=-1-2n+2[/tex] (I just distributed through the parenthesis) and a bit more to

[tex]a_n=-2n+1[/tex] and if we want the 21st term, fill in a 21 for n:

[tex]a_{21}=-2(21)+1[/tex] and

[tex]a_{21}=-42+1[/tex] so

[tex]a_{21}=-41[/tex]

Answer:

The GCF of the coefficients is correct.

The variable c is not common to all terms, so a power of c should not have been factored out.

In step 6, David applied the distributive property.

Step-by-step explanation:

Given the polynomial :

80b⁴ – 32b²c³ + 48b⁴c

The Greatest Common Factor (GCF) of the coefficients:

80, 32, 48

Factors of :

80 : 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80

32 : 1, 2, 4, 8, 16, and 32

48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

GCF = 16

b⁴, b², b⁴

b⁴ = b * b * b * b

b² = b * b

b⁴ = b * b * b * b

GCF = b*b = b²

GCF of c³ and c

c³ = c * c * c

c = c

GCF = c

We can see that David's GCF of the coefficients are all correct

From the polynomial ; 80b⁴ does not contain c ; so factoring out c is incorrect

In step 6 ; the distributive property was used to obtain ; 16b²c(5b² – 2c² + 3b²)

Answer:

She bought 6 first class tickets and 1 coach ticket

Step-by-step explanation:

1060(6)= 6360 and 6960-6360=300 and 300 is the price for a coach ticket.

Answer:

[tex]x-6[/tex]

Step-by-step explanation:

We can let the 'number' in the expression be equal to [tex]x[/tex]. Something 6 less than x would x minus 6, or [tex]x-6[/tex].

Answer:

x-6

Step-by-step explanation:

Let the number be x

Less than means subtract from

x-6

Answer:

20 m

[tex]p = 4a \: thus \: a = p \div 4 = 80 \div 4 = 20 \: m[/tex]

Answer:

20

Step-by-step explanation:

P=4L

80=4L

L=80/4

L=20m

Answer:

The depth to which a BASE jumper jumps in 3 seconds is 144 feet

Step-by-step explanation:

The details of the Cave of Swallows are;

The depth of the cave = 1,220 ft.

The function that represents the duration, t, in seconds it takes to fall d feet is given as follows;

[tex]t = \dfrac{1}{4} \cdot\sqrt{d}[/tex]

The distance a BASE jumper jumps in 3 seconds = Required

By substituting t = 3 in the given function, we get;

[tex]t = 3 = \dfrac{1}{4} \cdot\sqrt{d}[/tex]

Therefore;

4 × 3 = 12 = √d

d = 12² = 144

The distance a BASE jumper jumps in 3 seconds is d = 144 feet.

Answer:

For a general point (x, y), a reflection across the line x = a transforms the point into:

(a + (a - x), y) = (2a - x, y)

So if we first do a reflection across the line x = 1, the new point will be:

(2*1 - x, y) = (2 - x, y)

And if we now do a reflection across the line x = 3, the new point will be:

(2*3 - (2 - x), y) = (6 - 2 + x, y) = (4 + x, y)

Now that we have the general formula we can solve the question.

For the point (-5, 2)

The generated point after the reflections is:

(4 + (-5), 2) = (-1, 2)

For the point (-1, 5)

The generated point after the reflections is:

(4 + (-1), 5) = (3, 5)

For the point (0, 3)

The generated point after the reflections is:

(4 +0, 3) = (4, 3)

Answer:

[tex]n=35[/tex]

Step-by-step explanation:

From the question we are told that:

Standard Deviation [tex]\sigma=4min[/tex]

Let

[tex]CI=95\%[/tex]

Since

Significance level [tex]\alpha[/tex]

[tex]\alpha =1-CI[/tex]

[tex]\alpha =1-0.95[/tex]

Therefore

[tex]Z_{\alpha/2}=Z_{0.025[/tex]

[tex]Z_{\alpha/2}}=1.96[/tex]

Generally the equation for Sample size is mathematically given by

[tex]n = (Z_{\alpha/2}* \frac{\sigma}{E})^2[/tex]

[tex]n= \frac{1.96 * 3}{1}^2[/tex]

[tex]n=35[/tex]

9514 1404 393

Answer:

  ∠4 = 108°

Step-by-step explanation:

Angles 2 and 4 together form a "linear pair". That is, the sum of them is 180°, a "straight angle." They are supplementary.

  ∠4 = 180° -∠2 = 180° -72°

  ∠4 = 108°

Answer:

Step-by-step explanation:

Answer:

0.0652173

Step-by-step explanation:

Given that :

6 chocolate chip cookies

6 peanut butter cookies

6 sugar cookies

6 oatmeal cookies

Total number of cookies purchased = (6+6+6+6) = 24

Probability, P= required outcome /total possible outcomes

This is a selection without replacement probability problem :

P(peanut butter cookies) = 6/24 = 1/4

Then ;

P(chocolate chip cookie) = 6/23

Hence,

P(peanut butter cookies then chocolate chip cookie) = 1/4 * 6/23 = 0.0652173