the bae of a 13 foot ladder is 5 feet away from the wall. How far up the wall does the ladder reach

Answer:

0.42

Step-by-step explanation:

There are total 7 end points, 3 of them lead to winning $10 and the other ones lead to nothing

so, [tex]\frac{3}{7}[/tex] = 0.42

The expression 36a^2 - 49b^2 can be factored into the product of two binomials by applying the difference of squares formula. The factored form of the expression is (6a - 7b)(6a + 7b).

The expression 36a^2 - 49b^2 is a difference of squares. A difference of squares is a special type of binomial that can be factored into the product of two binomials.

In general, if you have an expression of the form x^2 - y^2, this is equal to (x - y)(x + y).

In the case of the expression 36a^2 - 49b^2, 36a^2 is the square of 6a, and 49b^2 is the square of 7b. Therefore, the expression 36a^2 - 49b^2 can be factored into (6a - 7b)(6a + 7b).

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Final answer:

The expression 36a² - 49b² is factored as (6a + 7b)(6a - 7b) using the difference of squares identity a² - b² = (a + b)(a - b).

Explanation:

The expression 36a² - 49b² is a difference of squares which can be factored using the identity a² - b² = (a + b)(a - b). In this case, the expression can be written as (6a)² - (7b)². This resembles the identity where a is 6a and b is 7b. Applying the identity, we get:

(6a + 7b)(6a - 7b)

This is the factored form of the given expression. To understand why this works, we recognize that squaring a number and then subtracting the square of another number creates two terms, one positive and one negative, whose products with themselves give us the original expression. The factored form thus represents two binomials that reflect the sum and the difference of the square roots of the original terms, respectively.

The square root of 189

the square root of 189

Answer:

9.2 ft

Step-by-step explanation:

The length of the ladder is 15 ft

The ladder makes an angle of 52° with the ground

The distance (x) from the base of the house to the foot of the ladder is given by;

[tex]\frac{x}{15}[/tex] = cos 52°

x = 15 × cos 52° = 9.23492213 ft

Which equals to 9.2 ft (rounded off to tenth of a foot)

The distance between the base of the building and the bottom of the ladder is 11.72 feet.

It is given that

Length of the ladder = 15 feet

The angle of inclination = 52°

Let us say the distance between the base of the building and the bottom of the ladder is x.

The tangent of an angle is the ratio of the opposite side(to that angle) to the base of the triangle.

Tan 52° = length of the ladder / distance between base of building and bottom of the ladder.

Tan 52 = 15/x

x= 15/Tan 52

x = 11.72 feet.

Therefore, The distance between the base of the building and the bottom of the ladder is 11.72 feet.

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Answer:

This is your answer.

Step-by-step explanation:

Hope is helps!!

Answer: (x+1) (x+2) (x+5)

Step-by-step explanation:

Answer:

[tex]\frac{13-7\sqrt{3}}{2}[/tex]

Step-by-step explanation:

We need to rationalize the denominator of [tex]= \frac{5-\sqrt{3}}{4+2\sqrt{3}}[/tex]. For rationalizing we multiply the equation by [tex]\frac{4-2\sqrt{3}}{4-2\sqrt{3}}[/tex]

So, solving

[tex]= \frac{5-\sqrt{3}}{4+2\sqrt{3}}*\frac{4-2\sqrt{3}}{4-2\sqrt{3}} \\=\frac{(5-\sqrt{3})(4-2\sqrt{3})}{4+2\sqrt{3}*4-2\sqrt{3}}\\=\frac{(5-\sqrt{3})(4-2\sqrt{3})}{(4)^2-(2\sqrt{3})^2}\\= \frac{5(4-2\sqrt{3})-\sqrt{3}(4-2\sqrt{3})}{16-(4*3)}\\=\frac{20-10\sqrt{3}-4\sqrt{3}+2*3}{16-12}\\=\frac{20+6-14\sqrt{3}}{4}\\=\frac{26-14\sqrt{3}}{4}\\= \frac{2(13-7\sqrt{3})}{4}\\=\frac{13-7\sqrt{3}}{2}[/tex]

Answer:

0.25

Step-by-step explanation:

Check the picture below.

Answer - 3.2 hours

because 4.48 miles divided by 1.4 mph equals 3.2

Answer:

3.2 hrs

Step-by-step explanation:

Recall that distance = rate times time, so:

4.48 mi = (1.4 mph)(time), and:

                                          4.48 mi

the elapsed time was ------------------- = 3.2 hours

                                       1.4 mph

Answer:

12

Step-by-step explanation:

3•4=12

Answer:

The correct answer is option "C"

"The interquartile range increases"

The value of the (RIC) will increase from 4 to 5.75, that is, 44%

Step-by-step explanation:

The range is defined as the difference between the maximum and minimum value of a series of data. Xmax - Xmin

The interleaving range (RIC) is a measure of dispersion that measures the central range of 50% of the data.

Therefore, if a low value is included, such as five, the variance of the data would be greater and, consequently, the value of the (RIC) will increase from 4 to 5.75, that is, 44%

Answer:

252 hours

Step-by-step explanation:

1 day = 24 hours

1 week = 7 days

= 24 * 7

= 168 hours

3 days = 24 * 3

= 72 hours

1/2 day = 24 / 2 = 12 hours

Add up all values/hours:

168 hours + 72 hours + 12 hours = 252 hours

Answer:

1 week- 168 hours

3 days-72 hours

1/2 day-12 hours

Step-by-step explanation:

1 week- 24x7=168

3 days- 24x3=72

1/2 day- 24x.5=12

Answer: -3

Step-by-step explanation:8-5=3 take the negative so it’s -3

Answer: OCTOBER 16th

Step-by-step explanation: The teams will meet again on October 16th

Answer:

the last one

Step-by-step explanation:

Answer:

the answer is indeed the last one

Step-by-step explanation:

7x-3x is the only one that meets the requirements for this statement

7-3x would be the difference between seven and three times a number

7x-3 would be the difference between seven times a number and three

have an absolutely fantastic day my friend!

Answer:

25%

Step-by-step explanation:

The chance of flipping heads or tails is 50%.

We have to flip heads or tails 3 times.

To make this easier, I will convert 50% to 1/2 for the time being.

Since the chance of getting heads or tails is 1/2 and there are 3 flips, multiply 1/2 to the power of 3, which is 1/8

1/8 is the probability of getting this outcome.

Step-by-step explanation:

Let's say R is the initial radius of the sphere, and r is the radius at time t.

The volume of the sphere at time t is:

V = 4/3 π r³

Taking derivative with respect to radius:

dV/dr = 4π r²

This is a maximum when r is a maximum, which is when r = R.

(dV/dr)max = 4π R²

This is 4 times the sphere's initial great circle area, but not the great circle circumference.  The problem statement contains an error.

Corresponding angles are congruent

From concept of base angle of parallel line, Option(D) Corresponding angles are congruent.

Given that ∠1 ≅ ∠2 .

In the diagram given aside, line a and b are parallel where the ∠4 and ∠2 are base angle subtended by the parallel lines.

From the traversal property of congruency, we know that the base angles of a parallel lines always subtend equal and congruent angles when it is intercepted by a common traversal.

Thus, from concept of base angle of parallel line, Option(D) Corresponding angles are congruent.

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Answer: Option G

[tex]a_6 = -2048[/tex]

Step-by-step explanation:

The geometric series have the following form:

[tex]a_n = a_1 (r) ^ {n-1}[/tex]

Where [tex]a_1[/tex] is the first term of the sequence and r is the common radius.

In this case we know that

[tex]a_1 = -2\\\\r = 4[/tex]

So:

[tex]a_n = -2(4) ^ {n-1}[/tex]

To find the sixth term [tex]a_6[/tex], substitute [tex]n = 6[/tex] in the equation.

[tex]a_6 = -2 (4) ^ {6-1}\\\\a_6 = -2 (4) ^ 5\\\\a_6 = -2048[/tex]

Answer:

[tex]\boxed{x^{2} + 2x - 8}[/tex]

Step-by-step explanation:

6. Practice

The dimensions of the current park are x long and x wide.

The new park will be 4 longer and 2 thinner.

Its new dimensions will be x + 4 long and x – 2 wide.

Its new area will be

A = width × length = (x – 2)(x + 4)

Find the product

[tex]\begin{array}{lll}\textbf{Steps} & \textbf{Problem: }(x - 2)(x + 4) & \\\textbf{1. List variables} & a = x - 2 & \\ & b = x & \\ & c = 4 &\\\textbf{2. Distribute (x - 2)} & (x -2)(x + 4)\\ & = (x - 2)(x) + (x - 2)(4)\\\textbf{3. Distribute x and 4} & x^{2} -2x + 4x - 8\\\textbf{4. Combine like terms}& x^{2} + 2x - 8\\\end{array}\\\text{The area of the updated skatepark will be }\boxed{\mathbf{ x^{2} + 2x - 8}}[/tex]

Answer: 72

Step-by-step explanation:

722 —> 720

9 —> 10

72 divided by 1 is 72

Answer:

i dont real know

Step-by-step explanation:

For this case we have that by definition of trigonometric relations of rectangular triangles, that the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle. So:

[tex]Sin (45) = \frac {leg} {h}[/tex]

Where h is the hypotenuse.

[tex]\frac {\sqrt {2}} {2} = \frac {leg} {h}[/tex]

We cleared h:

[tex]h = \frac {2leg} {\sqrt {2}}[/tex]

We rationalize:

[tex]h = \frac {2leg} {\sqrt {2}} * \frac {\sqrt {2}} {\sqrt {2}}\\h = \frac {2 \sqrt {2} * leg} {2}\\h = \sqrt {2} * leg[/tex]

ANswer:

Option A

Answer:

(x + 2)² + (y - 2)² = 64

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 2, 2), thus

(x + 2)² + (y - 2)² = r²

Given C = 2πr = 16π ( divide both sides by 2π )

r = [tex]\frac{16\pi }{2\pi }[/tex] = 8

Hence

(x + 2)² + (y - 2)² = 64 ← equation of circle

To find the equation of the circle with center at (-2,2) and a circumference of 16π, first calculate the radius r=8 from the circumference, then use the formula (x+2² + (y-2)² = 64.

The question asks for the equation of a circle with a given center and circumference. The center of the circle is located at (-2,2), and the circumference is 16π. First, we calculate the radius of the circle using the formula for circumference, C = 2πr, where C is the circumference and r is the radius. Since C = 16π, we can solve for r to find that the radius r = 8 units.

Next, we use the standard equation of a circle, which is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is its radius. Therefore, substituting h = -2, k = 2, and r = 8 into the equation, we get (x + 2)² + (y - 2)² = 64, which is the equation that represents the circle with the given center and circumference.

Answer: Angle 10 and Angle 2

Answer:

.6*.3=.18

Step-by-step explanation:

when two events must both happen, multiply their probabilities. (and=*, or=+)

I think 9 should be added to both sides.

cofficient of x = 6

half of it = 6/2 = 3

square the 3

to give 3 squared = 3*3 9

Answer:

9

Step-by-step explanation:

To make it a Perfect Square Trinomial, you can square root 9 and multiply it to get 6, therefore 9 is correct

Essentially this question is asking, If we made circle O as big as circle O1, how could we move it to the same spot. Therefore, I would expect the Answer to be D.

Answer: Option C

The equation is:

[tex](x+8)^2 +(y+3)^2=9[/tex]

Step-by-step explanation:

First we must calculate the midpoint between the two given points.

Then the midpoint will be the radius of the circumference

The midpoint between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is:

[tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

In this case the points are:

(-5 -3) and (-11 -3)

The the center is:

[tex](\frac{-5-11}{2}, \frac{-3-3}{2})[/tex]

[tex](-8,\ -3)[/tex]

Then the equation is:

[tex](x+8)^2 +(y+3)^2=r^2[/tex]

To find r we substitute one of the points in the equation and solve for r

[tex](-5+8)^2 +(-3+3)^2=r^2[/tex]

[tex](3)^2 +0=r^2[/tex]

[tex]r^2 =3^2[/tex]

[tex]r =3[/tex]

Finally the equation is:

[tex](x+8)^2 +(y+3)^2=9[/tex]

Answer:

Option C

Step-by-step explanation:

The standard form of equation of circle is:

(x-h)^2+ (y-k)^2=r^2

As we only know two points on the circle which are the ends of diameter.

As we know

Radius=Diameter/2

We have to find the length of diameter using the distance formula first to calculate radius. So,

Diameter= √((-11-(+5))^2+(-3-(-3)^2 )

= √((-11+5)^2+(-3+3)^2 )

=√((-6)^2+(0)^2 )

= √36

=6

Now,  

Radius=6/2

=3

As the diameter passes through centre, so the mid-point of diameter will be centre of the circle:

Mid-point=((x_1+x_2)/2,(y_1+y_2)/2)

=((-5-11)/2,(-3-3)/2)

=((-16)/2,(-6)/2)

=(-8,-3)

Putting the values of radius and centre in standard form

(x-h)^2+ (y-k)^2=r^2

(x-(-8))^2+ (y-(-3))^2=3^2

(x+8)^2+ (y+3)^2=9

So the correct answer is option C ..

Answer:

x ≈ 8.66

Step-by-step explanation:

Using the sine ratio in the right triangle

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex]

Multiply both sides by 10

10 × sin60° = x, thus

x ≈ 8.66 ( to 2 dec. places )

Answer:

x = -94/17, y = -6, z = -48/17

Step-by-step explanation:

If solving this system of equations is what you want, here's the answer.