Frank went to the playground at 5:20 P.M. He played on the slide for 45 minutes and the swings for 5 minutes, then went home. What time was it when Frank left the playground?

Hey there!

⇒ Use the vertex as the middle letter, and the point from each side (<ABC or <CBA)

⇒ Use the vertex only (<B)

⇒ Use a number (<1)

⇒ Acute angle: less than 90°

⇒ Right angle: exactly 90°

⇒ Obtuse angle: between 90° and 180°

⇒ Straight angle: exactly 180°

Thank you,

Eddie

See the attachment for a visual!

This exercise is about a proof in Euclidian geometry. See the explanation below.

The study of solid and flat objects using the axioms and theorems developed by the Greek mathematician Euclid is known as Euclidean geometry (c. 300 bce).

Given that S is the midpoint of [tex]\overline{QT}[/tex]:

Hence QS = TS ......................1

It is right to indicate that

PQ = TV  ........................2

And ∠RSQ is vertically opposite to ∠TSV

Hence

∠RSQ = ∠TSV.........................3

Given 1, 2, and 3,

Δ QRS ≅ ΔVTS

Therefore,

Δ QRS ≅ ΔVTS

and ∠ RSQ can be termed to be congruent to ∠TSV.

It is to be noted that the measure of an angle is the same for congruent angles. An ordinary pentagon, for instance, has five sides and five angles, each of which is 108 degrees.

The angles of a regular polygon will always be congruent, regardless of its size or scale.

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Answer:

Step-by-step explanation:

here is an solution :

Answer:

Its (-3,-5)

Step-by-step explanation:

Hope This Helps:))

Answer:

I would use equation d

Step-by-step explanation:

because need to find out X which is the second section so you would do 60 subtract 35 which gives 25 so X would be 25 .

I hope this helped . if you need any more help pls ask :)

pls give brainliest if you like my answer :)

Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

If those two functions are the factors of a quadratic, then each of them can be equated to 0 to find the roots. Sometimes the roots are called the zeros.

2x - 5 = 0                       Add 5 to both sides

2x - 5 + 5 = 0 + 5           Combine

2x = 5                             Divide both sides by 2

2x/2 = 5/2

x = 5/2

You don't really have to find the other factor's 0 point. There is only 1 option that makes x = 5/2. On a test, it is important to take short cuts and save time.  I'll find the other root anyway because this is not a test.

3x + 4 = 0                           Subtract 4 from both sides

3x + 4-4 = 0 - 4                  Combine

3x = - 4                               Divide both sides by 3

3x/3 = - 4/3

x = - 4/3

Answer: 797.4 m²

Step-by-step explanation:

The surface area is just the total of the areas of each face of of a solid. In this solid, we have 2 triangles and 3 rectangles.

We know that the two triangles of this solid are congruent, so they will have the same area. Since the area of a triangle is [tex]\frac{1}{2}bh[/tex], two triangles would have an area of [tex]bh[/tex]. Hence, the total area is

[tex]A=9 * 15\\A=135[/tex]

The area of a rectangle is lw, where l is the length and w is the width. Let's find the total area of all of them.

[tex]A=9*16+15*16+17.4*16[/tex]

All of the areas are a product of some number and 16. This makes sense as the length of this prism is 16. We can un-distribute this 16 to make the calculation easier.

[tex]A=16(9+15+17.4)\\A=16(41.4)\\A=662.4[/tex]

We can add both totals to get the total surface area of the solid.

[tex]135+662.4\\=797.4[/tex]

The surface area of this right triangular prism is 797.4 m².

Answer:

2.57

Step-by-step explanation:

The mean absolute deviation(MAD) of a data set is given by the formula

[tex]$ MAD =\frac{1}{n} \sum_{i=1}^n |x_i-\bar{x}|$[/tex]

n = number of data set values. Here n=7

[tex]\bar{x}=[/tex]mean of the data set values   = [tex](20+16+21+16+22+16+ 15)/7 = 126/7 = 18[/tex]

[tex]x_{i}[/tex] are the n individual values

Substituting in the summation we get

MAD = [tex]\frac{1}{7} |20-18| + |16-18| + |21-18| + |16-18| + |22-18| + |16-18| + |15-18|\\= (2 + 2 + 3 + 2 + 4+ 2 + 3)/7\\= 18/7 = 2.571428 \\[/tex]

Rounded to the nearest hundredth, the answer is 2.57

D. 16

Cross multiply, to cancel the denominator; so if you multiple by 6 on one side, to cancel the division of 6 - you must also multiply the other side by 6 & vice versa.

You get:

8(x-4) = 6x

Expand bracket to get:

8x - 32

Now solve for x :

8x - 32 = 6x

- 8x

- 32. = - 2x

÷ - 2

16 = x

Or

8x - 32 = 6x

+ 32

8x. = 6x + 32

- 6x

2x. = 32

÷2

x =16

Check:

16 - 4 = 12, then ÷ 6 is 2

16/8 = 2

Hope this helps!

The approximate number of text messages sent in 2011 is 2 x 10^1.

Scientific notation is used in expressing large numbers in smaller numbers. To write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

118, 000, 000, 000 in scientific notation is 1,18 x 10^11

2,357, 000, 000, 000 in scientific notation is 2.357 x 10^12

Difference in messages sent in 2011 compared to 2005 : (2.357 / 1.18) x 10^(12 - 11)

2 x 10^1

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Answer:

$6.07/hr. if I understand the question properly.  See below.

Step-by-step explanation:

I don't see the question, but will assume we want to find Larisa's base pay.  The $7/hr given is the average for the work sequence noted in the problem.  If this is incorrect, ignore the answer.

==================================

Let x be Larisa's base salary.  We are told, I think, that in one stretch of time Larisa earned an average of $7/hour.  That was composed of:

Hours  Rate($/hr)

  40           x

    3        1.5x

    6         2x

  49

Her total income over this period would be:

40x +3(1.5x) + 6(2x)  [The hours worked times the pay rate for each period]

Her average income per hour would be:

(40x +3(1.5x) + 6(2x))/49

which we are told is $7/hr.

(40x +3(1.5x) + 6(2x))/49 = 7

40x + 4.5x + 12x = 343

56.5x = 343

x = $6.07/hr

Answer: Your answers are

A. 1, 287 ways

B. 154,440 ways

Hope this helped :D

Please mark me brainliest

a.  The expressions for c and d in terms of a and b are

b.  The inverse of (2,1) is (13/15, -4/15)

The question has to do with binary operation.

A binary operation is a rule of mathematical operation on two sets of elements defined on a given set.

Since The operation * is defined over the set of ordered pairs by (a,b)*(c,d)=(ac-bd,ad+bc) for all (a,b),(c,d)€R given that the inverse of (a,b) is (c,d).

Let (e, e') be the identity element.

We know that for any binary operation * on a given set, a*e = a where e is the identity element.

So,  (a,b)*(e,e') =  (a,b)

So, (a,b)*(c,d) = (ac - bd, ad + bc)

(a,b)*(e,e') = (ae - be, ae' + be')

Since  (a,b)*(e,e') =  (a,b)

(ae - be, ae' + be') = (a, b)

So,

e = a/(a - b) and e' = b/(a + b)

So, (e, e') = (a/(a - b), b/(a + b))

Also, for any binary operation * under a given set a*a⁻¹ = e where a⁻¹ = inverse of a.

Since (c,d) is the inverse of (a,b), we have that

(a,b)*(c,d) = (e, e')

So, (a,b)*(c,d) = (ac - bd, ad + bc)

=  (a/(a - b), b/(a + b))

So,

From (3), c = bd/a + 1/(a - b)

Substituting c into (4), we have

ad + bc = b/(a + b)  

ad + b[bd/a + 1/(a - b)] = b/(a + b)  

ad + b²d/a + b/(a - b) = b/(a + b)  

ad + b²d/a = b/(a + b) -  b/(a - b)]

(a + b²/a)d = b[1/(a + b) -  1/(a - b)]

[(a² + b²)/a]d = b[a - b - (a + b)]/(a - b)(a + b)

[(a² + b²)/a]d = b[a - b - a - b)]/(a - b)(a + b)

[(a² + b²)/a]d = b(-2b)/(a² - b²)

d = -2ab²/[(a² - b²)(a² + b²)]

d = -2ab²/(a⁴ - b⁴)

Substitutind d into c, we have

c = bd/a + 1/(a - b)

c = -2ab³/(a⁴ - b⁴)a + 1/(a - b)

c = -2b³/(a⁴ - b⁴) + 1/(a - b)

So, the expressions for c and d in terms of a and b are

Since (c,d) is the inverse of (a,b) is

So, with a = 2 and b = 1, c = -2b³/(a⁴ - b⁴) + 1/(a - b)

= -2(1)³/(2⁴ - 1⁴) + 1/(2 - 1)

= -2/(16 - 1) + 1/1

= -2/15 + 1

= (-2 + 15)/15

= 13/15

So, with a = 2 and b = 1, d = -2ab²/(a⁴ - b⁴)

= -2(2)(1)²/(2⁴ - 1⁴)

= -4(1)/(16 - 1)

= -4/15

So, the inverse of (2,1) is (13/15, -4/15)

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Answer:

84

Step-by-step explanation:

substitute n = 5 into the expression

16n + 4

= 16(5) + 4

= 80 + 4

= 84

Answer:

The expression will have the value of 84

Step-by-step explanation:

[tex]16n + 4[/tex]

given expression

Thus, plug n=5

[tex]16(5) + 4 \\ 80 + 4 = 84[/tex]

Finally, we get the value 84

The measure of the angle <JKL is 56 degrees

The theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

Given the following parameters

m<IL = 112 degrees

Since the measure of the vertex is half the measure of its intercepted arc, hence;

<JKl = 1/2(m<IL)

Substitute the given parameters into the formula to have;

<JKl = 1/2(112)

<JKL = 56 degrees

Hence the measure of the angle <JKL is 56 degrees

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The degrees of freedom for the numerator and denominator for the critical value of F are _3 and 56, respectively_.

The samples, each comprised of 15 observations, were taken from the four populations.

The determine the degrees of freedom for the numerator and denominator for the critical value of F is given below:

k = 4

n = 15

Total degree of freedom;

= nk - 1

= 59

For numerator, it is

= k -1

= 4 - 1

= 3

For denominator it is

= T - (k -1 )

= 59 - 3

= 56

The degrees of freedom for the numerator and denominator for the critical value of F are _3 and 56, respectively_.

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Answer:

Step-by-step explanation:

RM 280 = 40% of 8 months

RM 700= 100% of 8 months

RM 700/8= 8 months

RM 87.5 = 1 month

Answer = 87.5

Farid's monthly salary is approximately RM 87.5. He spends 40% of his total 8-month expenditure on house rent, which amounts to RM 280 per month.

Let's assume Farid's monthly salary is RM x.

Given that he spends 40% of his total 8 monthly expenditure on house rent, and the amount he spends on house rent is RM 280, we can set up the following equation:

0.40 × 8x = 280

Now, let's solve for x:

0.40 × 8x = 280

3.2 × x = 280

x = 280 / 3.2

x ≈ 87.5

So, Farid's monthly salary is approximately RM 87.5.

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Answer:

5/10

Step-by-step explanation:

0.5 is 5/10 as a decimal. Any number that can be written as a fraction or a ratio is a rational number, so, since 0.5 can be written as 5/10, it’s a rational number.

Answer:

y= 2x + 10

Step-by-step explanation:

The variable depends on the $2 so, the green box should be 2

The surface area of the triangular prism is of 162 cm².

The surface area of a prism is given by the sum of all the areas of the prism.

This prism is composed by:

For a rectangle, the area is the multiplication of the dimensions, hence:

A1 = 10 x 15 = 150 cm².

For a right triangle, the area is half the multiplication of the sides, hence:

A2 = 0.5 x 6 x 4 = 12 cm².

Hence the surface area is:

A = A1 + A2 = 150 cm² + 12 cm² = 162 cm².

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Answer:

  Order of exponentiation can be swapped here, and the fractional power written as a root.

Step-by-step explanation:

The commutative property of multiplication and the rules of exponents apply.

The rule is ...

  (a^b)^c = a^(bc)

The given expression can be rearranged to ...

  [tex]\left(3^\frac{1}{5}\right)^2=3^{\frac{1}{5}\cdot2}=3^{2\cdot\frac{1}{5}}=\left(3^2\right)^\frac{1}{5}\\\\=9^\frac{1}{5}=\boxed{\sqrt[5]{9}}[/tex]

The slope of the line is 8.5 and the y-intercept is at the origin as shown in the graph below.

A linear function is a function that has a leading degree of 1. The standard equation for a linear function is expressed as:

y = mx + b

where

m is the slope which is equal to the rate of change of y coordinate to x-coordinates.

b is the y-intercept

Given the following equation

y=8.5x

The slope of the line is 8.5 and the y-intercept is at the origin as shown in the graph below.

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Answer:

Start with equation,

         y''(x) = f(x) = 6y/(10x-x²)               about point x₀ = 5

Then,

       y(x) = a₀ + a₁(x-5) + a₂(x-5)²+ a₃(x-5)³ + a₄(x-5)⁴...….

by inspection,

           y(5) = a₀      and       y'(5) = a₁

then,

y''(5) = 6a₀/(50-25) = 6a₀/25              

y'''(x) = 6y'/(10x-x2) - 6y(10-2x)/(10x-x2)2

then,                      

                              y'''(5) = 6a₁/25 - 0 = 6a₁/25                

y''''(x) = 6y''/(10x-x2) -12y'(10-2x)/(10x-x2)² + 12y/(10x-x2)² + 12y(10-2x)2/(10x-x2)³

then,

    y''''(5) = (6/25)(6a₀/25) + 0 + 12a₀/625 + 0

              = 48a₀/625

So,

y(x) = f(x) = f(5) + f'(5)(x-5) + f''(5)(x-5)2/2! + f'''(5)(x-5)3/3! + f''''(5)(x-5)4/4! …

                                                       or

y(x) = f(x) = a₀ + a₁(x-5) + (6ao/25)(x-5)2/2! + (6a1/25)(x-5)3/3! + (48a₀/625)(x-5)4/4!...

                                                         or

y(x) = f(x) = a₀ + a₁(x-5) + (3a₀/25)(x-5)²+ (a₁/25)(x-5)³+ (2a₀/625)(x-5)⁴.....

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Answer:

? = 4 units

Step-by-step explanation:

'2'  is to  ' 7+2 '     as  ?   is to   '14 + ? '

2/ 9 = ? / (14 + ?)      cross mutiply

28 + 2? = 9?

28 = 7?

? = 4

Answer:51 crates could have 12 oranges and one crate could hold 11 oranges.

Step-by-step explanation: 623 / 12 is 51.9... 51 x 12 is 612. 612 + 11 is 623 math checks out.

Answer:

y = -5/3 - 8

Step-by-step explanation:

We want to write this in the form y = mx + b.  We need to find the m (slope) and the b (y-intercept) ,  Whew, they already gave us the slope, so we are have way there.  I will plug in the x and y that we are given from the point (-6, 8) to solve for b.

y = mx + b

8 = -5/3(-6) + b  Multiply the fraction by -6

8 = 30/3 + b  I can make 6 a fraction by writing it 6/1 and then just multiply straight across.  A negative times a negative is a positive.

8 = 10 + b   30/3 is equal to 10.  Now subtract 10 from both sides to get b

-8 = b

I can now write the equations since I now know m and b.

y = -5/3 + (-8) which is the same as y = -5/3 - 8.  Adding a negative is the same as subtracting a positive.

Check the picture below.