In the accompanying diagram, overline BA perp overline BD and overline BC perp overline BE Which statement is true?

Answer:

a + b = 5.30

a + b = 7

No

Step-by-step explanation:

Expressing the information as system of linear equation :

Let apples = a, oranges = b

If $5.30 is charged for one apple and one orange, then we have ;

a + b = 5.30 - - - (1)

If $14 is charged for 2 apples and 2 oranges, then we have ;

2a + 2b = 14 - - - - (2)

a + b = 7

Since both equations gives varying combined cost for equal amount of the fruit, then a unique cost cannot be obtained for each fruit from the systems of equation using simultaneous equation process.

From (1)

a = 5.30 - b

Put a = 5.30 - b in (2)

2(5.30 - b) + 2b = 14

10.6 - 2b + 2b = 14

10.6 = 14 - - - - - (variables cancels out).

Answer:No the System has no solution

Step-by-step explanation:

Step-by-step explanation:

1. 22/60

2. LCM..of 3,9 is 9

So, 3+2/9 ( made the denominators equal)

5/9 Answer

Answer:

which of these fraction is not equivalent to 2/5 is 22/60

b) work out 1/2 + 2/9 = 5/9

Answer:

28.3

Step-by-step explanation:

A = [tex]\pi r^{2}[/tex]

Plug in:

A = [tex]\pi 3^{2}[/tex]

A = [tex]9 \pi[/tex]

A = 9 × 3.14 = 28.26 = 28.3

The answer is 28.3

Hope this helped.

Answer:

(k) cos(θ)·√(1 + cot²θ) = √(cosec²θ - 1)

From trigonometric identities, we have;

1 + cot²θ = cosec²θ

On the Left Hand Side of the equation, we get;

cos(θ)·√(1 + cot²θ) = cos(θ) × cosec(θ) = cot(θ)

On the Right Hand Side of the equation, we have;

√(cosec²(θ) - 1) = √(1 + cot²(θ) - 1) = √(cot²(θ)) = cot(θ)

∴ √(cosec²θ - 1) = cot(θ)

By transitive property of equality, therefore;

cos(θ)·√(1 + cot²θ) = √(cosec²θ - 1)

(l) sin⁶A + cos⁶A = 1 - 3·sin²A·cos²A

sin⁶A + cos⁶A = (sin²A)³ + (cos²A)³

(sin²A)³ + (cos²A)³ = ((sin²A) + (cos²A))³ - 3·((sin²A)·(cos²A))·((sin²A) + (cos²A))

∴ (sin²A)³ + (cos²A)³ = (1)³ - 3·((sin²A)·(cos²A))·(1) = 1 - 3·((sin²A)·(cos²A))

sin⁶A + cos⁶A = (sin²A)³ + (cos²A)³ = 1 - 3·((sin²A)·(cos²A))

sin⁶A + cos⁶A = 1 - 3·((sin²A)·(cos²A))

(m) (sinA - cosecA)² + (cosA - secA)² = cot²A + tan²A - 1

(sinA - cosecA)²  = sin²A - 2×sinA×cosecA + cosec²A = sin²A - 2 + cosec²A

(cosA - secA)² = cos²A - 2×cosA×secA + sec²A = cos²A - 2 + sec²A

∴ (sinA - cosecA)² + (cosA - secA)² = sin²A - 2 + cosec²A + cos²A - 2 + sec²A

Where;

sin²A - 2 + cosec²A + cos²A - 2 + sec²A = sin²A + cos²A  - 2  - 2 + cosec²A + sec²A

sin²A + cos²A  - 2  - 2 + cosec²A + sec²A = 1 - 4 + cosec²A + sec²A

1 - 4 + cosec²A + sec²A = cosec²A + sec²A - 3

Where;

cosec²A = cot²A + 1

sec²A = tan²A + 1

∴ cosec²A + sec²A - 3 = cot²A + 1 + tan²A + 1 - 3 = cot²A + tan²A - 1 = The Right Hand Side of the equation

∴ (sinA - cosecA)² + (cosA - secA)² = cot²A + tan²A - 1

(n) [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex] = sinA - cosA

Squaring the Right Hand Side of the equation, we get;

(sinA - cosA)² = sin²A -2·sinA·cosA + cos²A = sin²A + cos²A -2·sinA·cosA

sin²A + cos²A -2·sinA·cosA = 1 - 2·sinA·cosA

∴ (sinA - cosA)² =  1 - 2·sinA·cosA

Taking the square root of both sides gives;

√((sinA - cosA)²) = [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex]

∴ sinA - cosA = [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex]

By symmetric property of equality, we have;

[tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex] = sinA - cosA

Step-by-step explanation:

cosec(2t)=1/sin(2t) ==> 1/(2×cos(t)×sin(t))

cos(2t)= 1-2sin²t

or 2cos²t-1

or cos²t - sin²t

after we knew this informations we have to write it in the question

1/2×sint×cost-1/1/2×sint×cost=cos2t

-2×sint×cost+1/2sint×cost/1/2sint×cost=cos2t

the 2sint×cost will gone

-2×sint×cost+1=cos2t

lets take cos2t =1-2sin²t

-2×sint×cost+1=1-2sin²t

-2sint×cost=-2sin²t

cost=sint

that means the t is equal to 45 because sin45 and cos45 equal to √2/2

hopefully i didn't waste your time by reading and not understanding my English is not that good sorry

Answer:

see explanation

Step-by-step explanation:

Using the identities

cosec x = [tex]\frac{1}{sinx}[/tex]  , 1 - sin²θ = 1

Consider the left side

[tex]\frac{cosec^20-1}{cosec^20}[/tex]

= [tex]\frac{\frac{1}{sin^20}-\frac{sin^20}{sin^20} }{\frac{1}{sin^20} }[/tex]

= ( [tex]\frac{1}{sin^20}-\frac{sin^20}{sin^20}[/tex] ) × [tex]\frac{sin^20}{1}[/tex] ← distribute parenthesis by sin²θ

= 1 - sin²θ

= cos²θ

= right side, thus proven

Answer:

0

Step-by-step explanation:

Replace q with 7 .

[tex]7 + ( - 7) = 0[/tex]

[tex] \sf \: q + ( - 7) \\ \sf \: q = 7 \\ \\ \sf \: q + ( - 7) \\ \sf= 7 + ( - 7) \\ \sf= 7 - 7 \\ \sf= \boxed{\bf \: 0}[/tex]

Hope it helps.

RainbowSalt2222

(5,-8) after a 180 degree counterclockwise rotation about the origin is (-5,8)

Answer:

125 sweets

Step-by-step explanation:

Let the total # of sweets the teacher bought be the variable, x.

We can set up this equation to find the # of sweets she bought:

40 · 3 + 5 = x

Because she gave 3 sweets each to her 40 students, we have to multiply these two numbers to get the # of sweets the teacher gave out.

120 + 5 = x

Then, since there's 5 extra sweets left, we can add it to the # of sweets the teacher gave out to get the total amount of sweets she bought.

125 = x

x = 125

125 sweets

Answer:

Total sweets = 125

Step-by-step explanation:

Number of sweets given to each student = 3

Number of sweets given to 40 students = 40*3 = 120

Number of sweets left with the teacher = 5

Total sweets = 120 + 5 = 125

Answer:

Đổi 60% = 3/5

a) Số học sinh trung bình là:  40 * 1/4 = 10 (hsinh)

Tổng số hsk và hsg là:  40 - 10 = 30 (hsinh)

Số học sinh khá bằng 60% số học sinh còn lại nên số hsk là:

             30 * 60% = 18 (hsinh)

Số học sinh giỏi là:  30 - 18 = 12 (hsinh)

b) Tổng số hs khá và giỏi chiếm số phần trăm trong lớp là:

             30 : 40 * 100 = 75%

Answer:

Step-by-step explanation:

The dimensions as a pair, appear twice for each combination.

SA = 2* 16 * 8 + 2 * 16 * 6 + 2*8* 6

That's because when you look at the figure, there are 2 places each face is positioned.

SA = 256 + 192 + 96

SA = 544

Answer:

-3x(3x+5)(3x-4)

= -(9x²+15x)(3x-4)

= -27x³-9x²+60x

Answered by GAUTHMATH

Answer:

10 or -2 (Both work)

Step-by-step explanation:

Solve the equation |x - 4| = 6:

|x - 4| = 6

Now do the inverse operation of negative 4 to get positive 4.

|x - 4| = 6

  + 4  + 4

|x| = |10|

x = 10

Answer: 5

Step-by-step explanation:

⇒ (x - 4) = 1

⇒ x = 1 + 4

⇒ x = 5

Therefore value of x = 5

Answered by Gauthmath must click thanks and mark brainliest

Answer:

1.2x10^-1 seconds

Step-by-step explanation:

Answer:

0.12 seconds

Step-by-step explanation:

just think - how long does it take you to travel for example 30 km, if you are going 60 km/h ?

you have to divide 30 by 60 and get 0.5 or 1/2. meaning it takes you (logically) 30 minutes or half an hour to do so.

it is the same principle for all these kinds of questions.

we only need to keep an eye on the dimension of what we are talking about. is it hours or seconds ? meters or kilometers ? and do in

we need here to focus on seconds and to calculate

3.6×10⁷ / 3×10⁸ = 3.6 / 3×10¹ = 1.2 / 10 = 0.12 seconds

or

[tex]1.2 \times {10}^{ - 1} [/tex]

seconds

Answer:

1 term

Step-by-step explanation:

Writing an expression of 5 terms such that all 5 terms are like terms ;

Using the analogy :

x, 2x, 4x, 3x, 5x

Writing as an expression :

x + 2x + 4x - 3x + 5x

7x - x + 5x

6x + 5x

11x

The least number of terms in its equivalent expression is 1 ;

As the expression x + 2x + 4x - 3x + 5x is equivalent to 11x

Answer:

0.5

Step-by-step explanation:

k = y/x

k = 0.5/1

k = 0.5

Answer:

Step-by-step explanation:

a1=-8

a2=3

D=11

n=-8+11(n-1)

Answer:

2.21

Step-by-step explanation:

Answer:

$5.00

Step-by-step explanation:

$3.50+$1.50=$5.00

Answer:

2x-4(x+7)=2

Step-by-step explanation:

Peter's age:x.... twice age:2x

Phil's age:x+7...4times age:4(x+7)

Difference if ages is 2

Hence; 2x-4(x+7)=2

Answer:

Answer

4.9/5

38

loitzl9006

Ambitious

54 answers

6.5K people helped

Answer:

x=25

Step-by-step explanation:

we know that "x" is Peter's age

assume that "y" is Phil's age

In the sentence "Phil's age is 7 years more than 1/5 times than Peter's age" are two things: "Phil's age": y and "1/5 times Peter's age": 1/5 x

create equation with these two things

y = 1/5 x

including "7 years more"

many people make a lot of errors with it, they dont know: y+7 = 1/5 x or y=1/5 x + 7 ?

in order to avoid mistakes

read the sentence and point, which: y or 1/5 x is greater and smaller

"Phil's age is 7 years more than ..."

so y is greater, and 1/5 x smaller

y = 1/5 x

greater = smaller

we must add 7 to smaller number to make an equality

greater = smaller + 7

y = 1/5 x + 7

Second sentence:

"4 times Phil's age is 2 years less than twice Peter's age."

Two things: "4 times Phil's age": 4y and "twice Peter's age": 2x

4y = 2x

read the sentence once again

"4 times Phil's age is 2 years less than (...)" , so 4y - smaller, 2x - greater

4y = 2x

smaller = greater

including "2 years less" we add 2 to a smaller number

smaller + 2 = greater

4y + 2 = 2x

Substitute y=1/5 x + 7 to the equation 4y+2 = 2x

Step-by-step explanation:

Answer:

pandn

Step-by-step explanation:

jsubeuodoqok1kwnebhxhhw

emdndiiwjwkd

d

ddnjd

Answer:

1

Step-by-step explanation:

In this situation, the slope is 1.

This is because the ski rental service charges $1 per hour.

The $12.50 initial flat rate represents the y intercept, while the hourly charge is the slope.

So, the value of the slope is 1.

Let

ATQ

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 40x+50x=45000[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 90x=45000[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow x=\dfrac{45000}{90}[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow x=500[/tex]

Now

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Rita=50x=50(500)=25000[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Mina=40x=40(500)=20000[/tex]

Answer:

D. Five pounds of oats are divided equally among eight horses.

Step-by-step explanation:

A scenario representing 5/8 has to involve a quantity of 5 being divided by 8.

The situation with the oats and horses represents 5/8, because the 5 pounds of oats are being equally divided among the 8 horses.

The other answer choices are incorrect because they are dividing 8 by 5 instead, which is 8/5 instead of 5/8.

So, the correct answer is D. Five pounds of oats are divided equally among eight horses.

Transformations are operators that can act on functions, modifying them in different ways. In this particular problem, we see the translations.

The correct option is B:

g(x) can be graphed by translating the basic rational function ƒ(x)=  1∕x left by 3 units and downward by 5 units.

Let's describe the transformations:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N)

If N is positive, the shift is to the left.

If N is negative, the shift is to the right

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N

If N is positive, the shift is upwards.

If N is negative, the shift is downwards.

Now that we know this, let's see the problem.

We have:

[tex]g(x) = \frac{1}{x + 3} - 5[/tex]

So, the original function is:

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

Now from f(x) we can apply translations to create g(x).

If first, we apply a translation of 3 units to the left, we get:

[tex]g(x) = f(x + 3) = \frac{1}{x + 3}[/tex]

If now we apply a translation of 5 units downwards, we get:

[tex]g(x) = f(x + 3) - 5 = \frac{1}{x + 3} - 5[/tex]

So we can conclude that the correct option is B:

g(x) can be graphed by translating the basic rational function ƒ(x) 1∕x left by 3 units and downward by 5 units.

If you want to learn more about translations, you can read:

https://brainly.com/question/12463306

Answer:

A(9,3)

B(9,0)

C(5,1)

Step-by-step explanation:

Answer:

x=9 ⇒AC=24

Step-by-step explanation:

vì DE//B C⇒ΔABC  Tương ung ti tỉ lệ vớiv  ΔADE

⇒DB/AB=EC/AC

⇒AC=(EC.AB)/DB

⇒AC=24

Answer:

0.1667 = 16.67% probability that they are both black.

Step-by-step explanation:

The balls are drawn without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

5 + 4 = 9 balls, which means that [tex]N = 9[/tex]

4 are black, which means that [tex]k = 4[/tex]

2 are chosen, which means that [tex]n = 2[/tex]

What is the probability that they are both black?

This is P(X = 2). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,9,2,4) = \frac{C_{4,2}*C_{5,0}}{C_{9,2}} = 0.1667[/tex]

0.1667 = 16.67% probability that they are both black.